TSTP Solution File: SWV674-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV674-1 : 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 : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 06:34:54 EDT 2024
% Result : Unsatisfiable 56.57s 8.47s
% Output : Refutation 56.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1526
% Syntax : Number of formulae : 3903 ( 398 unt; 0 def)
% Number of atoms : 16558 (1190 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 23690 (11035 ~;11459 |; 0 &)
% (1196 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 1236 (1234 usr;1197 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 7823 (7823 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f93452,plain,
$false,
inference(avatar_sat_refutation,[],[f694,f699,f704,f709,f714,f719,f724,f729,f734,f739,f744,f749,f754,f759,f764,f769,f774,f779,f784,f789,f794,f799,f804,f809,f814,f819,f824,f829,f834,f839,f844,f849,f854,f859,f864,f869,f874,f879,f884,f889,f894,f899,f904,f909,f914,f919,f924,f929,f934,f939,f944,f949,f954,f959,f964,f969,f974,f978,f982,f986,f990,f994,f998,f1002,f1006,f1010,f1014,f1018,f1022,f1026,f1030,f1034,f1038,f1042,f1046,f1061,f1071,f1075,f1080,f1085,f1091,f1096,f1100,f1104,f1108,f1112,f1116,f1121,f1126,f1130,f1134,f1138,f1143,f1147,f1153,f1157,f1161,f1165,f1169,f1174,f1178,f1182,f1186,f1201,f1206,f1210,f1214,f1218,f1222,f1226,f1230,f1234,f1238,f1243,f1247,f1251,f1255,f1259,f1263,f1278,f1303,f1308,f1312,f1316,f1320,f1324,f1328,f1332,f1336,f1340,f1344,f1348,f1353,f1357,f1361,f1365,f1369,f1373,f1377,f1381,f1385,f1389,f1393,f1397,f1414,f1471,f1491,f1495,f1499,f1503,f1507,f1511,f1515,f1520,f1524,f1528,f1532,f1536,f1602,f1638,f1642,f1646,f1650,f1654,f1659,f1663,f1667,f1671,f1719,f1727,f1731,f1735,f1739,f1743,f1747,f1751,f1755,f1759,f1765,f1769,f1773,f1913,f1917,f1921,f1925,f1929,f1940,f1944,f1948,f1952,f1956,f1960,f1964,f1968,f1972,f1976,f1980,f1984,f1988,f1992,f1996,f2247,f2251,f2255,f2259,f2263,f2267,f2271,f2275,f2279,f2283,f2287,f2291,f2295,f2299,f2474,f2478,f2482,f2486,f2490,f2524,f2528,f2532,f2536,f2540,f2544,f2548,f2556,f2560,f2564,f2568,f2626,f2630,f2634,f2638,f2642,f2646,f2650,f2654,f2658,f2795,f2799,f2803,f2807,f2811,f2815,f2819,f2871,f2875,f2879,f2883,f2887,f2891,f2895,f2899,f2903,f2907,f2911,f2915,f2919,f2923,f2928,f2932,f2936,f2940,f2944,f2948,f2952,f2956,f2960,f2964,f2968,f2972,f2976,f2980,f2984,f2988,f2992,f2996,f3000,f3004,f3008,f3012,f3016,f3090,f3211,f3373,f3397,f3401,f3405,f3409,f3413,f3417,f3421,f3425,f3429,f3433,f3437,f3441,f3445,f3449,f3453,f3457,f3461,f3493,f3497,f3501,f3505,f3509,f3513,f3517,f3521,f3525,f3529,f3570,f3574,f3578,f3582,f3586,f3590,f3594,f3598,f3602,f3606,f4419,f4423,f4427,f4431,f4435,f4439,f4443,f4588,f4592,f4678,f4682,f4686,f4741,f4745,f4749,f4765,f4769,f4773,f4837,f4841,f4845,f4849,f4853,f4857,f4951,f4961,f4965,f4969,f4973,f4977,f4981,f4985,f5124,f5182,f5187,f5192,f5203,f5207,f5481,f5499,f5536,f5551,f5559,f5564,f5572,f5609,f5613,f5617,f5621,f5625,f5772,f5776,f5780,f5784,f6564,f6568,f6572,f6576,f6580,f6584,f6588,f6662,f6671,f7311,f7433,f7476,f7480,f7484,f7488,f7981,f7985,f7989,f7993,f8167,f8171,f8175,f8179,f8183,f8356,f8360,f8364,f8368,f8372,f8376,f8380,f8571,f8597,f8601,f8605,f8609,f8613,f8617,f8626,f8630,f8634,f8638,f8642,f8668,f8697,f8701,f8705,f9037,f9087,f9091,f9141,f9145,f9149,f9154,f9158,f9162,f9166,f9238,f9310,f9442,f9446,f9450,f9454,f9458,f9462,f9466,f9470,f9474,f9478,f9482,f9486,f11230,f11234,f11238,f11242,f11246,f11250,f11254,f11258,f11262,f11266,f11270,f11274,f11278,f11282,f11286,f11294,f11298,f11302,f11306,f11310,f11314,f11318,f11322,f11326,f11360,f11392,f11400,f12232,f12485,f12489,f12543,f12720,f12724,f12778,f12838,f12842,f12846,f12850,f12854,f12858,f12862,f12866,f12870,f12874,f12878,f12882,f12886,f12890,f12894,f12899,f12903,f12907,f12911,f12918,f13191,f13690,f13694,f13698,f13702,f13731,f13735,f13739,f13743,f13747,f13787,f13791,f13795,f13799,f13803,f13807,f13822,f14014,f14452,f14456,f14460,f14464,f14604,f14608,f14612,f14616,f14620,f14624,f14628,f14632,f14636,f14640,f14792,f14821,f14853,f14888,f14889,f14935,f14939,f15781,f15785,f15789,f15793,f15805,f15809,f15813,f15817,f15821,f15825,f15829,f15833,f15866,f15871,f15903,f15940,f15973,f16004,f16040,f16044,f16048,f16052,f16056,f16060,f16064,f16068,f16072,f16076,f16080,f16114,f16149,f16153,f16157,f16161,f16165,f16169,f16173,f16177,f16204,f16208,f16212,f16216,f16257,f16298,f16332,f16336,f16340,f16344,f16348,f16352,f17168,f18085,f18089,f18093,f18097,f18101,f18105,f18109,f18113,f18117,f18121,f18125,f18140,f18144,f18148,f18152,f18156,f18160,f18164,f18168,f18172,f18176,f18180,f18184,f18188,f18192,f18196,f18200,f18204,f18208,f18212,f18216,f18220,f18225,f18283,f18347,f18410,f18468,f18508,f18512,f18552,f18556,f18560,f18564,f19424,f20124,f21281,f21285,f21289,f21303,f21337,f21341,f21345,f21349,f21364,f21368,f21372,f21376,f21380,f21384,f21388,f21392,f21396,f21400,f21404,f21408,f21412,f21416,f21420,f21424,f21428,f21432,f21436,f21440,f21444,f21448,f21452,f21456,f21460,f21464,f21468,f21472,f21476,f21480,f21484,f21488,f21492,f21496,f21500,f21504,f21508,f21512,f21516,f21520,f21524,f21528,f21532,f21715,f21719,f21723,f21727,f21731,f21735,f21739,f21743,f21747,f21751,f21755,f21759,f21763,f21767,f21771,f21775,f21779,f21783,f21787,f21791,f21795,f21945,f21949,f21953,f21957,f21961,f21965,f21969,f21973,f21977,f21981,f22181,f22185,f22786,f24349,f24907,f26976,f27382,f27386,f27390,f27394,f27398,f27402,f27406,f27410,f27414,f27418,f27422,f27426,f27430,f27434,f27438,f27442,f27446,f27450,f27454,f27458,f27462,f27466,f27470,f27474,f27478,f27482,f27486,f27490,f27494,f27498,f27502,f27506,f27511,f27515,f27519,f27523,f27527,f27531,f27535,f27539,f27543,f27547,f27552,f27556,f27560,f27564,f27568,f27572,f27576,f27580,f27584,f27588,f28090,f28094,f28098,f28102,f28106,f28110,f28114,f28118,f28122,f28126,f28130,f28134,f28138,f28142,f28146,f28150,f28154,f28158,f28162,f28166,f28170,f28174,f28178,f28182,f28186,f28190,f28194,f28198,f28202,f28206,f28210,f28214,f28218,f28222,f28226,f28230,f28234,f28238,f28242,f28246,f28250,f28254,f28258,f28262,f28836,f30054,f31334,f32649,f33877,f39441,f39445,f39449,f39453,f39457,f39461,f39501,f39505,f39509,f39513,f39894,f39898,f39902,f39906,f39910,f39914,f39918,f39922,f39926,f39930,f39934,f39975,f40026,f40067,f40118,f40122,f40126,f40499,f40503,f40507,f40511,f40515,f40519,f40523,f40527,f40531,f40582,f40586,f40641,f40645,f40678,f40718,f41166,f41170,f41174,f41178,f41182,f41186,f45979,f45983,f45987,f45991,f45995,f45999,f46003,f46007,f46011,f46015,f46019,f46023,f46027,f46031,f46035,f46140,f46242,f46300,f46430,f46480,f46526,f46586,f46637,f47954,f48283,f48287,f48291,f48295,f48299,f48303,f48307,f48311,f48315,f48319,f48323,f48327,f48331,f48335,f48339,f48343,f48347,f48351,f48355,f48359,f48363,f48367,f48371,f48375,f48379,f48383,f48387,f48391,f48395,f48399,f48403,f48407,f48411,f48415,f48419,f48423,f48427,f48431,f48435,f48439,f48443,f48447,f48451,f48455,f48459,f48463,f48467,f48471,f48475,f48479,f48483,f48487,f48491,f48495,f48499,f48503,f48507,f48511,f48515,f48519,f48523,f48527,f48531,f48535,f48539,f48543,f48547,f48551,f48555,f48559,f48563,f48567,f48571,f48575,f48579,f48583,f48587,f48591,f48595,f48599,f48603,f48607,f48712,f48768,f48772,f48832,f64849,f65145,f65149,f65153,f65157,f65161,f65165,f65169,f65173,f65177,f65181,f65185,f65189,f65193,f65197,f65201,f65205,f65209,f65213,f65217,f65221,f65225,f65229,f65233,f65237,f65241,f65245,f65249,f65253,f65257,f65261,f66467,f66471,f66475,f66479,f66483,f66487,f66491,f66495,f66499,f66503,f66563,f66567,f66571,f66575,f66579,f66583,f66587,f66591,f66595,f66599,f66781,f66785,f66789,f66793,f66797,f66801,f66805,f66809,f66813,f66817,f66821,f66825,f66829,f66833,f66837,f66841,f66845,f66849,f66853,f66857,f66861,f66867,f66871,f66875,f66879,f66883,f66887,f66891,f66895,f66899,f66903,f66907,f66911,f66915,f66919,f66923,f66927,f66931,f69123,f72556,f74397,f78607,f79597,f79601,f79605,f79609,f79613,f79617,f79621,f79625,f79629,f79633,f79637,f79641,f79645,f79649,f79653,f79657,f79661,f79665,f79669,f79673,f79677,f81025,f81726,f81730,f81734,f81738,f81742,f81746,f81750,f81754,f81758,f81762,f81766,f81770,f81774,f81778,f81782,f81786,f81790,f81794,f81798,f81802,f81806,f81810,f81815,f81819,f81823,f81827,f81831,f81835,f81839,f81843,f81847,f85249,f86367,f86371,f86375,f86379,f86383,f86387,f86391,f86395,f86399,f86403,f86606,f86851,f86976,f87199,f87310,f87513,f87591,f87704,f87812,f87862,f87970,f88081,f88085,f88139,f88247,f88251,f88255,f88259,f88263,f88267,f88271,f88275,f88279,f88283,f88287,f88291,f88295,f88299,f88365,f88369,f88373,f88468,f88564,f88662,f89135,f93446,f93450,f93451]) ).
fof(f93451,plain,
( spl0_88
| spl0_568
| ~ spl0_1171 ),
inference(avatar_split_clause,[],[f91696,f88079,f15868,f1118]) ).
fof(f1118,plain,
( spl0_88
<=> v_a = c_HOL_Ozero__class_Ozero(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f15868,plain,
( spl0_568
<=> c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_x,t_a) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f88079,plain,
( spl0_1171
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(t_a) = X0
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X0,X1,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,t_a),X1,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f91696,plain,
( v_a = c_HOL_Ozero__class_Ozero(t_a)
| spl0_568
| ~ spl0_1171 ),
inference(trivial_inequality_removal,[],[f91427]) ).
fof(f91427,plain,
( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) != c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a)
| v_a = c_HOL_Ozero__class_Ozero(t_a)
| spl0_568
| ~ spl0_1171 ),
inference(superposition,[],[f15870,f88080]) ).
fof(f88080,plain,
( ! [X0,X1] :
( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X0,X1,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,t_a),X1,t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_1171 ),
inference(avatar_component_clause,[],[f88079]) ).
fof(f15870,plain,
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_x,t_a) != c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a)
| spl0_568 ),
inference(avatar_component_clause,[],[f15868]) ).
fof(f93450,plain,
( spl0_1196
| ~ spl0_177
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3023,f2877,f1753,f93448]) ).
fof(f93448,plain,
( spl0_1196
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| c_HOL_Oord__class_Oless(X1,X0,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| c_HOL_Otimes__class_Otimes(X3,X1,X2) = c_HOL_Otimes__class_Otimes(X3,X0,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f1753,plain,
( spl0_177
<=> ! [X4,X0,X2] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X2 = X4
| c_HOL_Oord__class_Oless(X2,X4,X0)
| c_HOL_Oord__class_Oless(X4,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f2877,plain,
( spl0_250
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f3023,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| c_HOL_Oord__class_Oless(X1,X0,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| c_HOL_Otimes__class_Otimes(X3,X1,X2) = c_HOL_Otimes__class_Otimes(X3,X0,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) )
| ~ spl0_177
| ~ spl0_250 ),
inference(resolution,[],[f2878,f1754]) ).
fof(f1754,plain,
( ! [X2,X0,X4] :
( c_HOL_Oord__class_Oless(X4,X2,X0)
| c_HOL_Oord__class_Oless(X2,X4,X0)
| X2 = X4
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_177 ),
inference(avatar_component_clause,[],[f1753]) ).
fof(f2878,plain,
( ! [X3,X0,X1,X13] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_250 ),
inference(avatar_component_clause,[],[f2877]) ).
fof(f93446,plain,
( spl0_1195
| ~ spl0_186
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f2826,f2793,f1927,f93444]) ).
fof(f93444,plain,
( spl0_1195
<=> ! [X0,X3,X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Orderings_Opreorder(X3)
| c_lessequals(c_Power_Opower__class_Opower(X2,X0,X3),c_Power_Opower__class_Opower(X1,X0,X3),X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X0,X3),c_Power_Opower__class_Opower(X2,X0,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f1927,plain,
( spl0_186
<=> ! [X4,X0,X2] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X2,X4,X0)
| c_lessequals(X4,X2,X0)
| c_HOL_Oord__class_Oless(X2,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f2793,plain,
( spl0_241
<=> ! [X4,X0,X9,X2] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_lessequals(X2,X4,X0)
| c_lessequals(c_Power_Opower__class_Opower(X2,X9,X0),c_Power_Opower__class_Opower(X4,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f2826,plain,
( ! [X2,X3,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Orderings_Opreorder(X3)
| c_lessequals(c_Power_Opower__class_Opower(X2,X0,X3),c_Power_Opower__class_Opower(X1,X0,X3),X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X0,X3),c_Power_Opower__class_Opower(X2,X0,X3),X3) )
| ~ spl0_186
| ~ spl0_241 ),
inference(resolution,[],[f2794,f1928]) ).
fof(f1928,plain,
( ! [X2,X0,X4] :
( ~ c_lessequals(X2,X4,X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(X4,X2,X0)
| c_HOL_Oord__class_Oless(X2,X4,X0) )
| ~ spl0_186 ),
inference(avatar_component_clause,[],[f1927]) ).
fof(f2794,plain,
( ! [X2,X0,X9,X4] :
( c_lessequals(c_Power_Opower__class_Opower(X2,X9,X0),c_Power_Opower__class_Opower(X4,X9,X0),X0)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_lessequals(X2,X4,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_241 ),
inference(avatar_component_clause,[],[f2793]) ).
fof(f89135,plain,
( spl0_1194
| ~ spl0_1
| ~ spl0_350
| ~ spl0_733 ),
inference(avatar_split_clause,[],[f27358,f22179,f4959,f691,f89133]) ).
fof(f89133,plain,
( spl0_1194
<=> ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X1,t_a),c_Power_Opower__class_Opower(X0,X1,t_a),t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f691,plain,
( spl0_1
<=> class_Ring__and__Field_Ofield(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f4959,plain,
( spl0_350
<=> ! [X0] : c_HOL_Oone__class_Oone(t_a) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f22179,plain,
( spl0_733
<=> ! [X2,X0,X1] :
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,X2,X0),X0)
| ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f27358,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X1,t_a),c_Power_Opower__class_Opower(X0,X1,t_a),t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_1
| ~ spl0_350
| ~ spl0_733 ),
inference(forward_demodulation,[],[f27357,f4960]) ).
fof(f4960,plain,
( ! [X0] : c_HOL_Oone__class_Oone(t_a) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),t_a)
| ~ spl0_350 ),
inference(avatar_component_clause,[],[f4959]) ).
fof(f27357,plain,
( ! [X0,X1] :
( c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X1,t_a),c_Power_Opower__class_Opower(X0,X1,t_a),t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_1
| ~ spl0_733 ),
inference(resolution,[],[f22180,f693]) ).
fof(f693,plain,
( class_Ring__and__Field_Ofield(t_a)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f691]) ).
fof(f22180,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,X2,X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = X1 )
| ~ spl0_733 ),
inference(avatar_component_clause,[],[f22179]) ).
fof(f88662,plain,
( ~ spl0_4
| spl0_1193
| ~ spl0_97
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f5102,f4975,f1159,f88660,f706]) ).
fof(f706,plain,
( spl0_4
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f88660,plain,
( spl0_1193
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f1159,plain,
( spl0_97
<=> ! [X4,X2] :
( ~ c_HOL_Oord__class_Oless(X2,X4,tc_nat)
| c_lessequals(X2,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f4975,plain,
( spl0_354
<=> ! [X0,X14,X13,X3,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f5102,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) )
| ~ spl0_97
| ~ spl0_354 ),
inference(resolution,[],[f4976,f1160]) ).
fof(f1160,plain,
( ! [X2,X4] :
( ~ c_HOL_Oord__class_Oless(X2,X4,tc_nat)
| c_lessequals(X2,X4,tc_nat) )
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f1159]) ).
fof(f4976,plain,
( ! [X3,X0,X1,X14,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X14,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0) )
| ~ spl0_354 ),
inference(avatar_component_clause,[],[f4975]) ).
fof(f88564,plain,
( ~ spl0_4
| spl0_1192
| ~ spl0_97
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f5068,f4971,f1159,f88562,f706]) ).
fof(f88562,plain,
( spl0_1192
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).
fof(f4971,plain,
( spl0_353
<=> ! [X0,X14,X13,X3,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f5068,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) )
| ~ spl0_97
| ~ spl0_353 ),
inference(resolution,[],[f4972,f1160]) ).
fof(f4972,plain,
( ! [X3,X0,X1,X14,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X14,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0) )
| ~ spl0_353 ),
inference(avatar_component_clause,[],[f4971]) ).
fof(f88468,plain,
( ~ spl0_4
| spl0_1191
| ~ spl0_97
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f5034,f4967,f1159,f88466,f706]) ).
fof(f88466,plain,
( spl0_1191
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f4967,plain,
( spl0_352
<=> ! [X0,X14,X13,X3,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f5034,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) )
| ~ spl0_97
| ~ spl0_352 ),
inference(resolution,[],[f4968,f1160]) ).
fof(f4968,plain,
( ! [X3,X0,X1,X14,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X14,X0),X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0) )
| ~ spl0_352 ),
inference(avatar_component_clause,[],[f4967]) ).
fof(f88373,plain,
( spl0_1190
| ~ spl0_329
| ~ spl0_364 ),
inference(avatar_split_clause,[],[f5502,f5497,f4433,f88371]) ).
fof(f88371,plain,
( spl0_1190
<=> ! [X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(t_a),X1,t_a),X0,t_a) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(t_a),c_HOL_Oinverse__class_Odivide(X1,X0,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f4433,plain,
( spl0_329
<=> ! [X0] : c_HOL_Ozero__class_Ozero(t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(t_a),X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f5497,plain,
( spl0_364
<=> ! [X2,X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X0,X1,t_a),X2,t_a) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X0,X2,t_a),c_HOL_Oinverse__class_Odivide(X1,X2,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f5502,plain,
( ! [X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(t_a),X1,t_a),X0,t_a) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(t_a),c_HOL_Oinverse__class_Odivide(X1,X0,t_a),t_a)
| ~ spl0_329
| ~ spl0_364 ),
inference(superposition,[],[f5498,f4434]) ).
fof(f4434,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(t_a),X0,t_a)
| ~ spl0_329 ),
inference(avatar_component_clause,[],[f4433]) ).
fof(f5498,plain,
( ! [X2,X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X0,X1,t_a),X2,t_a) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X0,X2,t_a),c_HOL_Oinverse__class_Odivide(X1,X2,t_a),t_a)
| ~ spl0_364 ),
inference(avatar_component_clause,[],[f5497]) ).
fof(f88369,plain,
( ~ spl0_4
| spl0_1189
| ~ spl0_97
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f5001,f4963,f1159,f88367,f706]) ).
fof(f88367,plain,
( spl0_1189
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X0,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).
fof(f4963,plain,
( spl0_351
<=> ! [X13,X0,X14,X3,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(X13,X14,X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f5001,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X0,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat) )
| ~ spl0_97
| ~ spl0_351 ),
inference(resolution,[],[f4964,f1160]) ).
fof(f4964,plain,
( ! [X3,X0,X1,X14,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X14,X0),X0)
| ~ c_lessequals(X13,X14,X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0) )
| ~ spl0_351 ),
inference(avatar_component_clause,[],[f4963]) ).
fof(f88365,plain,
( spl0_1188
| ~ spl0_94
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f4884,f4855,f1145,f88363]) ).
fof(f88363,plain,
( spl0_1188
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat),X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
fof(f1145,plain,
( spl0_94
<=> ! [X9,X19] : c_lessequals(c_HOL_Ominus__class_Ominus(X19,X9,tc_nat),X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f4855,plain,
( spl0_348
<=> ! [X19,X0,X9,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ c_lessequals(X9,X19,tc_nat)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(X19,X9,tc_nat),X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X19,X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f4884,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat),X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X0),X0) )
| ~ spl0_94
| ~ spl0_348 ),
inference(resolution,[],[f4856,f1146]) ).
fof(f1146,plain,
( ! [X19,X9] : c_lessequals(c_HOL_Ominus__class_Ominus(X19,X9,tc_nat),X19,tc_nat)
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f1145]) ).
fof(f4856,plain,
( ! [X0,X1,X19,X9] :
( ~ c_lessequals(X9,X19,tc_nat)
| ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(X19,X9,tc_nat),X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X19,X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) )
| ~ spl0_348 ),
inference(avatar_component_clause,[],[f4855]) ).
fof(f88299,plain,
( ~ spl0_8
| spl0_1187
| ~ spl0_164
| ~ spl0_342 ),
inference(avatar_split_clause,[],[f4827,f4771,f1652,f88297,f726]) ).
fof(f726,plain,
( spl0_8
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f88297,plain,
( spl0_1187
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X2,X1,tc_nat),X3,tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X0,tc_nat),X3,tc_nat)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).
fof(f1652,plain,
( spl0_164
<=> ! [X22,X27,X23] :
( ~ c_lessequals(X27,X22,tc_nat)
| ~ c_lessequals(X22,X23,tc_nat)
| c_lessequals(X27,X23,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f4771,plain,
( spl0_342
<=> ! [X24,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X9,X24,tc_nat)
| ~ c_lessequals(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X24,X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f4827,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X0,tc_nat),X3,tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X2,X1,tc_nat),X3,tc_nat) )
| ~ spl0_164
| ~ spl0_342 ),
inference(resolution,[],[f4772,f1653]) ).
fof(f1653,plain,
( ! [X27,X22,X23] :
( ~ c_lessequals(X27,X22,tc_nat)
| ~ c_lessequals(X22,X23,tc_nat)
| c_lessequals(X27,X23,tc_nat) )
| ~ spl0_164 ),
inference(avatar_component_clause,[],[f1652]) ).
fof(f4772,plain,
( ! [X0,X1,X9,X24] :
( c_lessequals(c_Power_Opower__class_Opower(X1,X24,X0),c_Power_Opower__class_Opower(X1,X9,X0),X0)
| ~ c_lessequals(X9,X24,tc_nat)
| ~ c_lessequals(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_342 ),
inference(avatar_component_clause,[],[f4771]) ).
fof(f88295,plain,
( spl0_1186
| ~ spl0_195
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f4722,f4680,f1970,f88293]) ).
fof(f88293,plain,
( spl0_1186
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).
fof(f1970,plain,
( spl0_195
<=> ! [X4,X11,X0,X2] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X2,X4,X0)
| ~ c_lessequals(X4,X11,X0)
| c_lessequals(X2,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f4680,plain,
( spl0_335
<=> ! [X4,X0,X2] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f4722,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X3,X2,X1) )
| ~ spl0_195
| ~ spl0_335 ),
inference(resolution,[],[f4681,f1971]) ).
fof(f1971,plain,
( ! [X2,X0,X11,X4] :
( ~ c_lessequals(X4,X11,X0)
| ~ c_lessequals(X2,X4,X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(X2,X11,X0) )
| ~ spl0_195 ),
inference(avatar_component_clause,[],[f1970]) ).
fof(f4681,plain,
( ! [X2,X0,X4] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X0),X2,X0)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_335 ),
inference(avatar_component_clause,[],[f4680]) ).
fof(f88291,plain,
( spl0_1185
| ~ spl0_194
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f4721,f4680,f1966,f88289]) ).
fof(f88289,plain,
( spl0_1185
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f1966,plain,
( spl0_194
<=> ! [X4,X11,X0,X2] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X4,X2,X0)
| ~ c_lessequals(X11,X4,X0)
| c_lessequals(X11,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f4721,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1) )
| ~ spl0_194
| ~ spl0_335 ),
inference(resolution,[],[f4681,f1967]) ).
fof(f1967,plain,
( ! [X2,X0,X11,X4] :
( ~ c_lessequals(X11,X4,X0)
| ~ c_lessequals(X4,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X11,X2,X0) )
| ~ spl0_194 ),
inference(avatar_component_clause,[],[f1966]) ).
fof(f88287,plain,
( spl0_1184
| ~ spl0_190
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f4720,f4680,f1950,f88285]) ).
fof(f88285,plain,
( spl0_1184
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f1950,plain,
( spl0_190
<=> ! [X4,X11,X0,X2] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X11,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X2,X0)
| c_HOL_Oord__class_Oless(X11,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f4720,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1) )
| ~ spl0_190
| ~ spl0_335 ),
inference(resolution,[],[f4681,f1951]) ).
fof(f1951,plain,
( ! [X2,X0,X11,X4] :
( ~ c_lessequals(X11,X4,X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X2,X0)
| c_HOL_Oord__class_Oless(X11,X2,X0) )
| ~ spl0_190 ),
inference(avatar_component_clause,[],[f1950]) ).
fof(f88283,plain,
( spl0_1183
| ~ spl0_189
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f4719,f4680,f1946,f88281]) ).
fof(f88281,plain,
( spl0_1183
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| c_HOL_Oord__class_Oless(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).
fof(f1946,plain,
( spl0_189
<=> ! [X4,X11,X0,X2] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X4,X2,X0)
| ~ c_HOL_Oord__class_Oless(X11,X4,X0)
| c_HOL_Oord__class_Oless(X11,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f4719,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| c_HOL_Oord__class_Oless(X3,X2,X1) )
| ~ spl0_189
| ~ spl0_335 ),
inference(resolution,[],[f4681,f1947]) ).
fof(f1947,plain,
( ! [X2,X0,X11,X4] :
( ~ c_lessequals(X4,X2,X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X11,X4,X0)
| c_HOL_Oord__class_Oless(X11,X2,X0) )
| ~ spl0_189 ),
inference(avatar_component_clause,[],[f1946]) ).
fof(f88279,plain,
( spl0_1182
| ~ spl0_188
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f4718,f4680,f1942,f88277]) ).
fof(f88277,plain,
( spl0_1182
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| c_HOL_Oord__class_Oless(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f1942,plain,
( spl0_188
<=> ! [X4,X11,X0,X2] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X4,X11,X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0)
| c_HOL_Oord__class_Oless(X2,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f4718,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| c_HOL_Oord__class_Oless(X3,X2,X1) )
| ~ spl0_188
| ~ spl0_335 ),
inference(resolution,[],[f4681,f1943]) ).
fof(f1943,plain,
( ! [X2,X0,X11,X4] :
( ~ c_lessequals(X4,X11,X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0)
| c_HOL_Oord__class_Oless(X2,X11,X0) )
| ~ spl0_188 ),
inference(avatar_component_clause,[],[f1942]) ).
fof(f88275,plain,
( spl0_1181
| ~ spl0_187
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f4717,f4680,f1938,f88273]) ).
fof(f88273,plain,
( spl0_1181
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f1938,plain,
( spl0_187
<=> ! [X4,X11,X0,X2] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X2,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X11,X0)
| c_HOL_Oord__class_Oless(X2,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f4717,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1) )
| ~ spl0_187
| ~ spl0_335 ),
inference(resolution,[],[f4681,f1939]) ).
fof(f1939,plain,
( ! [X2,X0,X11,X4] :
( ~ c_lessequals(X2,X4,X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X11,X0)
| c_HOL_Oord__class_Oless(X2,X11,X0) )
| ~ spl0_187 ),
inference(avatar_component_clause,[],[f1938]) ).
fof(f88271,plain,
( spl0_1180
| ~ spl0_361
| ~ spl0_363 ),
inference(avatar_split_clause,[],[f5485,f5479,f5201,f88269]) ).
fof(f88269,plain,
( spl0_1180
<=> ! [X0,X1] :
( c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Odivide(X0,X1,t_a),c_HOL_Oinverse__class_Oinverse(X1,t_a),t_a) = X0
| c_HOL_Ozero__class_Ozero(t_a) = c_HOL_Oinverse__class_Oinverse(X1,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).
fof(f5201,plain,
( spl0_361
<=> ! [X0,X1] : c_HOL_Oinverse__class_Odivide(X0,X1,t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X1,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f5479,plain,
( spl0_363
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(t_a) = X0
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X0,t_a),X0,t_a) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f5485,plain,
( ! [X0,X1] :
( c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Odivide(X0,X1,t_a),c_HOL_Oinverse__class_Oinverse(X1,t_a),t_a) = X0
| c_HOL_Ozero__class_Ozero(t_a) = c_HOL_Oinverse__class_Oinverse(X1,t_a) )
| ~ spl0_361
| ~ spl0_363 ),
inference(superposition,[],[f5480,f5202]) ).
fof(f5202,plain,
( ! [X0,X1] : c_HOL_Oinverse__class_Odivide(X0,X1,t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X1,t_a),t_a)
| ~ spl0_361 ),
inference(avatar_component_clause,[],[f5201]) ).
fof(f5480,plain,
( ! [X0,X1] :
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X0,t_a),X0,t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_363 ),
inference(avatar_component_clause,[],[f5479]) ).
fof(f88267,plain,
( spl0_1179
| ~ spl0_195
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4698,f4676,f1970,f88265]) ).
fof(f88265,plain,
( spl0_1179
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f4676,plain,
( spl0_334
<=> ! [X4,X0,X2] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f4698,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X3,X2,X1) )
| ~ spl0_195
| ~ spl0_334 ),
inference(resolution,[],[f4677,f1971]) ).
fof(f4677,plain,
( ! [X2,X0,X4] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X0),X2,X0)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_334 ),
inference(avatar_component_clause,[],[f4676]) ).
fof(f88263,plain,
( spl0_1178
| ~ spl0_194
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4697,f4676,f1966,f88261]) ).
fof(f88261,plain,
( spl0_1178
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X0,X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).
fof(f4697,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X0,X1),X3,X1) )
| ~ spl0_194
| ~ spl0_334 ),
inference(resolution,[],[f4677,f1967]) ).
fof(f88259,plain,
( spl0_1177
| ~ spl0_190
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4696,f4676,f1950,f88257]) ).
fof(f88257,plain,
( spl0_1177
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f4696,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,X1),X3,X1) )
| ~ spl0_190
| ~ spl0_334 ),
inference(resolution,[],[f4677,f1951]) ).
fof(f88255,plain,
( spl0_1176
| ~ spl0_189
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4695,f4676,f1946,f88253]) ).
fof(f88253,plain,
( spl0_1176
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| c_HOL_Oord__class_Oless(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).
fof(f4695,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| c_HOL_Oord__class_Oless(X3,X2,X1) )
| ~ spl0_189
| ~ spl0_334 ),
inference(resolution,[],[f4677,f1947]) ).
fof(f88251,plain,
( spl0_1175
| ~ spl0_188
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4694,f4676,f1942,f88249]) ).
fof(f88249,plain,
( spl0_1175
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| c_HOL_Oord__class_Oless(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
fof(f4694,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| c_HOL_Oord__class_Oless(X3,X2,X1) )
| ~ spl0_188
| ~ spl0_334 ),
inference(resolution,[],[f4677,f1943]) ).
fof(f88247,plain,
( spl0_1174
| ~ spl0_187
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4693,f4676,f1938,f88245]) ).
fof(f88245,plain,
( spl0_1174
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f4693,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,X1),X3,X1) )
| ~ spl0_187
| ~ spl0_334 ),
inference(resolution,[],[f4677,f1939]) ).
fof(f88139,plain,
( ~ spl0_8
| spl0_1173
| ~ spl0_149
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4410,f3604,f1497,f88137,f726]) ).
fof(f88137,plain,
( spl0_1173
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X0,X2,tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat)
| c_Power_Opower__class_Opower(X0,X2,tc_nat) = c_Power_Opower__class_Opower(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f1497,plain,
( spl0_149
<=> ! [X9,X19] :
( X9 = X19
| ~ c_lessequals(X19,X9,tc_nat)
| c_HOL_Oord__class_Oless(X19,X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f3604,plain,
( spl0_324
<=> ! [X3,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X3,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f4410,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_Power_Opower__class_Opower(X0,X2,tc_nat) = c_Power_Opower__class_Opower(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X0,X2,tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat) )
| ~ spl0_149
| ~ spl0_324 ),
inference(resolution,[],[f3605,f1498]) ).
fof(f1498,plain,
( ! [X19,X9] :
( ~ c_lessequals(X19,X9,tc_nat)
| X9 = X19
| c_HOL_Oord__class_Oless(X19,X9,tc_nat) )
| ~ spl0_149 ),
inference(avatar_component_clause,[],[f1497]) ).
fof(f3605,plain,
( ! [X3,X0,X1,X9] :
( c_lessequals(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X3,X9,X0),X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_324 ),
inference(avatar_component_clause,[],[f3604]) ).
fof(f88085,plain,
( ~ spl0_8
| spl0_1172
| ~ spl0_157
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4408,f3604,f1530,f88083,f726]) ).
fof(f88083,plain,
( spl0_1172
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X2,tc_nat),c_Power_Opower__class_Opower(X0,X2,tc_nat),tc_nat)
| c_Power_Opower__class_Opower(X0,X2,tc_nat) = c_Power_Opower__class_Opower(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f1530,plain,
( spl0_157
<=> ! [X9,X19] :
( X9 = X19
| ~ c_lessequals(X19,X9,tc_nat)
| ~ c_lessequals(X9,X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f4408,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_Power_Opower__class_Opower(X0,X2,tc_nat) = c_Power_Opower__class_Opower(X1,X2,tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X2,tc_nat),c_Power_Opower__class_Opower(X0,X2,tc_nat),tc_nat) )
| ~ spl0_157
| ~ spl0_324 ),
inference(resolution,[],[f3605,f1531]) ).
fof(f1531,plain,
( ! [X19,X9] :
( ~ c_lessequals(X19,X9,tc_nat)
| X9 = X19
| ~ c_lessequals(X9,X19,tc_nat) )
| ~ spl0_157 ),
inference(avatar_component_clause,[],[f1530]) ).
fof(f88081,plain,
( spl0_1171
| ~ spl0_114
| ~ spl0_244 ),
inference(avatar_split_clause,[],[f2850,f2805,f1240,f88079]) ).
fof(f1240,plain,
( spl0_114
<=> class_Ring__and__Field_Odivision__ring(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f2805,plain,
( spl0_244
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X9,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f2850,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(t_a) = X0
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X0,X1,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,t_a),X1,t_a) )
| ~ spl0_114
| ~ spl0_244 ),
inference(resolution,[],[f2806,f1242]) ).
fof(f1242,plain,
( class_Ring__and__Field_Odivision__ring(t_a)
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f1240]) ).
fof(f2806,plain,
( ! [X0,X1,X9] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X9,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),X9,X0) )
| ~ spl0_244 ),
inference(avatar_component_clause,[],[f2805]) ).
fof(f87970,plain,
( ~ spl0_8
| spl0_1170
| ~ spl0_152
| ~ spl0_323 ),
inference(avatar_split_clause,[],[f4388,f3600,f1509,f87968,f726]) ).
fof(f87968,plain,
( spl0_1170
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_Power_Opower__class_Opower(X2,X0,tc_nat) = c_Power_Opower__class_Opower(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X1,tc_nat),c_Power_Opower__class_Opower(X2,X0,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f1509,plain,
( spl0_152
<=> ! [X4,X2] :
( X2 = X4
| c_HOL_Oord__class_Oless(X2,X4,tc_nat)
| c_HOL_Oord__class_Oless(X4,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f3600,plain,
( spl0_323
<=> ! [X4,X0,X3,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X2,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X2,X0),c_Power_Opower__class_Opower(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f4388,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X1,tc_nat),c_Power_Opower__class_Opower(X2,X0,tc_nat),tc_nat)
| c_Power_Opower__class_Opower(X2,X0,tc_nat) = c_Power_Opower__class_Opower(X2,X1,tc_nat) )
| ~ spl0_152
| ~ spl0_323 ),
inference(resolution,[],[f3601,f1510]) ).
fof(f1510,plain,
( ! [X2,X4] :
( c_HOL_Oord__class_Oless(X4,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X4,tc_nat)
| X2 = X4 )
| ~ spl0_152 ),
inference(avatar_component_clause,[],[f1509]) ).
fof(f3601,plain,
( ! [X2,X3,X0,X4] :
( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X2,X0),c_Power_Opower__class_Opower(X3,X4,X0),X0)
| c_HOL_Oord__class_Oless(X2,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_323 ),
inference(avatar_component_clause,[],[f3600]) ).
fof(f87862,plain,
( ~ spl0_8
| spl0_1169
| ~ spl0_149
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4362,f3592,f1497,f87860,f726]) ).
fof(f87860,plain,
( spl0_1169
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,tc_nat),c_Power_Opower__class_Opower(X2,X1,tc_nat),tc_nat)
| c_Power_Opower__class_Opower(X2,X0,tc_nat) = c_Power_Opower__class_Opower(X2,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f3592,plain,
( spl0_321
<=> ! [X24,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X9,X24,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X1,X24,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f4362,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_Power_Opower__class_Opower(X2,X0,tc_nat) = c_Power_Opower__class_Opower(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,tc_nat),c_Power_Opower__class_Opower(X2,X1,tc_nat),tc_nat) )
| ~ spl0_149
| ~ spl0_321 ),
inference(resolution,[],[f3593,f1498]) ).
fof(f3593,plain,
( ! [X0,X1,X9,X24] :
( c_lessequals(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X1,X24,X0),X0)
| ~ c_lessequals(X9,X24,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_321 ),
inference(avatar_component_clause,[],[f3592]) ).
fof(f87812,plain,
( ~ spl0_8
| spl0_1168
| ~ spl0_157
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4360,f3592,f1530,f87810,f726]) ).
fof(f87810,plain,
( spl0_1168
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X1,tc_nat),c_Power_Opower__class_Opower(X2,X0,tc_nat),tc_nat)
| c_Power_Opower__class_Opower(X2,X0,tc_nat) = c_Power_Opower__class_Opower(X2,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f4360,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_Power_Opower__class_Opower(X2,X0,tc_nat) = c_Power_Opower__class_Opower(X2,X1,tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X1,tc_nat),c_Power_Opower__class_Opower(X2,X0,tc_nat),tc_nat) )
| ~ spl0_157
| ~ spl0_321 ),
inference(resolution,[],[f3593,f1531]) ).
fof(f87704,plain,
( ~ spl0_8
| spl0_1167
| ~ spl0_152
| ~ spl0_319 ),
inference(avatar_split_clause,[],[f4322,f3584,f1509,f87702,f726]) ).
fof(f87702,plain,
( spl0_1167
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_Power_Opower__class_Opower(X0,X2,tc_nat) = c_Power_Opower__class_Opower(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,tc_nat),c_Power_Opower__class_Opower(X0,X2,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f3584,plain,
( spl0_319
<=> ! [X3,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X3,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f4322,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,tc_nat),c_Power_Opower__class_Opower(X0,X2,tc_nat),tc_nat)
| c_Power_Opower__class_Opower(X0,X2,tc_nat) = c_Power_Opower__class_Opower(X1,X2,tc_nat) )
| ~ spl0_152
| ~ spl0_319 ),
inference(resolution,[],[f3585,f1510]) ).
fof(f3585,plain,
( ! [X3,X0,X1,X9] :
( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X3,X9,X0),X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_319 ),
inference(avatar_component_clause,[],[f3584]) ).
fof(f87591,plain,
( ~ spl0_8
| spl0_1166
| ~ spl0_149
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f4299,f3580,f1497,f87589,f726]) ).
fof(f87589,plain,
( spl0_1166
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,tc_nat),c_Power_Opower__class_Opower(X2,X1,tc_nat),tc_nat)
| c_Power_Opower__class_Opower(X2,X0,tc_nat) = c_Power_Opower__class_Opower(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f3580,plain,
( spl0_318
<=> ! [X4,X0,X3,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X2,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0)
| c_lessequals(c_Power_Opower__class_Opower(X3,X2,X0),c_Power_Opower__class_Opower(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f4299,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_Power_Opower__class_Opower(X2,X0,tc_nat) = c_Power_Opower__class_Opower(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,tc_nat),c_Power_Opower__class_Opower(X2,X1,tc_nat),tc_nat) )
| ~ spl0_149
| ~ spl0_318 ),
inference(resolution,[],[f3581,f1498]) ).
fof(f3581,plain,
( ! [X2,X3,X0,X4] :
( c_lessequals(c_Power_Opower__class_Opower(X3,X2,X0),c_Power_Opower__class_Opower(X3,X4,X0),X0)
| ~ c_lessequals(X2,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_318 ),
inference(avatar_component_clause,[],[f3580]) ).
fof(f87513,plain,
( ~ spl0_8
| spl0_1165
| ~ spl0_157
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f4297,f3580,f1530,f87511,f726]) ).
fof(f87511,plain,
( spl0_1165
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X1,tc_nat),c_Power_Opower__class_Opower(X2,X0,tc_nat),tc_nat)
| c_Power_Opower__class_Opower(X2,X0,tc_nat) = c_Power_Opower__class_Opower(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f4297,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_Power_Opower__class_Opower(X2,X0,tc_nat) = c_Power_Opower__class_Opower(X2,X1,tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X1,tc_nat),c_Power_Opower__class_Opower(X2,X0,tc_nat),tc_nat) )
| ~ spl0_157
| ~ spl0_318 ),
inference(resolution,[],[f3581,f1531]) ).
fof(f87310,plain,
( ~ spl0_16
| spl0_1164
| ~ spl0_149
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f4193,f3523,f1497,f87308,f766]) ).
fof(f766,plain,
( spl0_16
<=> class_Ring__and__Field_Omult__mono(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f87308,plain,
( spl0_1164
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X0,X2,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f3523,plain,
( spl0_313
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f4193,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Omult__mono(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X0,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) )
| ~ spl0_149
| ~ spl0_313 ),
inference(resolution,[],[f3524,f1498]) ).
fof(f3524,plain,
( ! [X3,X0,X1,X13] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ class_Ring__and__Field_Omult__mono(X0) )
| ~ spl0_313 ),
inference(avatar_component_clause,[],[f3523]) ).
fof(f87199,plain,
( ~ spl0_16
| spl0_1163
| ~ spl0_157
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f4191,f3523,f1530,f87197,f766]) ).
fof(f87197,plain,
( spl0_1163
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X0,X2,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).
fof(f4191,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Omult__mono(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X0,X2,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat) )
| ~ spl0_157
| ~ spl0_313 ),
inference(resolution,[],[f3524,f1531]) ).
fof(f86976,plain,
( ~ spl0_14
| spl0_1162
| ~ spl0_149
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f4141,f3515,f1497,f86974,f756]) ).
fof(f756,plain,
( spl0_14
<=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f86974,plain,
( spl0_1162
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X0,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).
fof(f3515,plain,
( spl0_311
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Omult__mono1(X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f4141,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Omult__mono1(tc_nat)
| c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) )
| ~ spl0_149
| ~ spl0_311 ),
inference(resolution,[],[f3516,f1498]) ).
fof(f3516,plain,
( ! [X3,X0,X1,X13] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ class_Ring__and__Field_Omult__mono1(X0) )
| ~ spl0_311 ),
inference(avatar_component_clause,[],[f3515]) ).
fof(f86851,plain,
( ~ spl0_14
| spl0_1161
| ~ spl0_157
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f4139,f3515,f1530,f86849,f756]) ).
fof(f86849,plain,
( spl0_1161
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X2,X0,tc_nat),tc_nat)
| c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X0,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f4139,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Omult__mono1(tc_nat)
| c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X0,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X2,X0,tc_nat),tc_nat) )
| ~ spl0_157
| ~ spl0_311 ),
inference(resolution,[],[f3516,f1531]) ).
fof(f86606,plain,
( ~ spl0_4
| spl0_1160
| ~ spl0_152
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3657,f3399,f1509,f86604,f706]) ).
fof(f86604,plain,
( spl0_1160
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X2,X0,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f3399,plain,
( spl0_289
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f3657,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X2,X0,tc_nat),tc_nat)
| c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X0,tc_nat) )
| ~ spl0_152
| ~ spl0_289 ),
inference(resolution,[],[f3400,f1510]) ).
fof(f3400,plain,
( ! [X3,X0,X1,X13] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0) )
| ~ spl0_289 ),
inference(avatar_component_clause,[],[f3399]) ).
fof(f86403,plain,
( ~ spl0_4
| spl0_1159
| ~ spl0_152
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3644,f3395,f1509,f86401,f706]) ).
fof(f86401,plain,
( spl0_1159
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X0,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f3395,plain,
( spl0_288
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f3644,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X0,X2,tc_nat) )
| ~ spl0_152
| ~ spl0_288 ),
inference(resolution,[],[f3396,f1510]) ).
fof(f3396,plain,
( ! [X3,X0,X1,X13] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0) )
| ~ spl0_288 ),
inference(avatar_component_clause,[],[f3395]) ).
fof(f86399,plain,
( spl0_1158
| ~ spl0_186
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f3332,f2982,f1927,f86397]) ).
fof(f86397,plain,
( spl0_1158
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).
fof(f2982,plain,
( spl0_276
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f3332,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_186
| ~ spl0_276 ),
inference(resolution,[],[f2983,f1928]) ).
fof(f2983,plain,
( ! [X3,X0,X1] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0) )
| ~ spl0_276 ),
inference(avatar_component_clause,[],[f2982]) ).
fof(f86395,plain,
( spl0_1157
| ~ spl0_186
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f3310,f2978,f1927,f86393]) ).
fof(f86393,plain,
( spl0_1157
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f2978,plain,
( spl0_275
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f3310,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,X1),c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_186
| ~ spl0_275 ),
inference(resolution,[],[f2979,f1928]) ).
fof(f2979,plain,
( ! [X3,X0,X1] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0) )
| ~ spl0_275 ),
inference(avatar_component_clause,[],[f2978]) ).
fof(f86391,plain,
( spl0_1156
| ~ spl0_186
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f3194,f2946,f1927,f86389]) ).
fof(f86389,plain,
( spl0_1156
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).
fof(f2946,plain,
( spl0_267
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f3194,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) )
| ~ spl0_186
| ~ spl0_267 ),
inference(resolution,[],[f2947,f1928]) ).
fof(f2947,plain,
( ! [X3,X0,X1] :
( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0) )
| ~ spl0_267 ),
inference(avatar_component_clause,[],[f2946]) ).
fof(f86387,plain,
( spl0_1155
| ~ spl0_186
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f3140,f2934,f1927,f86385]) ).
fof(f86385,plain,
( spl0_1155
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f2934,plain,
( spl0_264
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f3140,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) )
| ~ spl0_186
| ~ spl0_264 ),
inference(resolution,[],[f2935,f1928]) ).
fof(f2935,plain,
( ! [X3,X0,X1] :
( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Opordered__ring(X0) )
| ~ spl0_264 ),
inference(avatar_component_clause,[],[f2934]) ).
fof(f86383,plain,
( spl0_1154
| ~ spl0_186
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f3122,f2930,f1927,f86381]) ).
fof(f86381,plain,
( spl0_1154
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f2930,plain,
( spl0_263
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f3122,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) )
| ~ spl0_186
| ~ spl0_263 ),
inference(resolution,[],[f2931,f1928]) ).
fof(f2931,plain,
( ! [X3,X0,X1] :
( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0) )
| ~ spl0_263 ),
inference(avatar_component_clause,[],[f2930]) ).
fof(f86379,plain,
( spl0_1153
| ~ spl0_181
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f2825,f2793,f1771,f86377]) ).
fof(f86377,plain,
( spl0_1153
<=> ! [X0,X3,X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Power_Opower__class_Opower(X2,X0,X3) = c_Power_Opower__class_Opower(X1,X0,X3)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X0,X3),c_Power_Opower__class_Opower(X1,X0,X3),X3)
| ~ class_Orderings_Oorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f1771,plain,
( spl0_181
<=> ! [X4,X0,X2] :
( ~ class_Orderings_Oorder(X0)
| X2 = X4
| ~ c_lessequals(X2,X4,X0)
| ~ c_lessequals(X4,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f2825,plain,
( ! [X2,X3,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Power_Opower__class_Opower(X2,X0,X3) = c_Power_Opower__class_Opower(X1,X0,X3)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X0,X3),c_Power_Opower__class_Opower(X1,X0,X3),X3)
| ~ class_Orderings_Oorder(X3) )
| ~ spl0_181
| ~ spl0_241 ),
inference(resolution,[],[f2794,f1772]) ).
fof(f1772,plain,
( ! [X2,X0,X4] :
( ~ c_lessequals(X4,X2,X0)
| X2 = X4
| ~ c_lessequals(X2,X4,X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_181 ),
inference(avatar_component_clause,[],[f1771]) ).
fof(f86375,plain,
( spl0_1152
| ~ spl0_484
| ~ spl0_738 ),
inference(avatar_split_clause,[],[f27375,f26974,f12230,f86373]) ).
fof(f86373,plain,
( spl0_1152
<=> ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != c_HOL_Oinverse__class_Odivide(X1,X0,t_a)
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X0,t_a),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).
fof(f12230,plain,
( spl0_484
<=> ! [X0,X1] : c_HOL_Oinverse__class_Odivide(X0,X1,t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,t_a),X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f26974,plain,
( spl0_738
<=> ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Otimes__class_Otimes(X0,X1,t_a)
| c_HOL_Oone__class_Oone(t_a) != c_HOL_Otimes__class_Otimes(X1,X0,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f27375,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != c_HOL_Oinverse__class_Odivide(X1,X0,t_a)
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X0,t_a),t_a) )
| ~ spl0_484
| ~ spl0_738 ),
inference(superposition,[],[f26975,f12231]) ).
fof(f12231,plain,
( ! [X0,X1] : c_HOL_Oinverse__class_Odivide(X0,X1,t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,t_a),X0,t_a)
| ~ spl0_484 ),
inference(avatar_component_clause,[],[f12230]) ).
fof(f26975,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != c_HOL_Otimes__class_Otimes(X1,X0,t_a)
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Otimes__class_Otimes(X0,X1,t_a) )
| ~ spl0_738 ),
inference(avatar_component_clause,[],[f26974]) ).
fof(f86371,plain,
( spl0_1151
| ~ spl0_175
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f2824,f2793,f1745,f86369]) ).
fof(f86369,plain,
( spl0_1151
<=> ! [X0,X3,X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Power_Opower__class_Opower(X2,X0,X3) = c_Power_Opower__class_Opower(X1,X0,X3)
| ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X0,X3),c_Power_Opower__class_Opower(X2,X0,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f1745,plain,
( spl0_175
<=> ! [X4,X0,X2] :
( ~ class_Orderings_Olinorder(X0)
| X2 = X4
| ~ c_lessequals(X2,X4,X0)
| c_HOL_Oord__class_Oless(X2,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f2824,plain,
( ! [X2,X3,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Power_Opower__class_Opower(X2,X0,X3) = c_Power_Opower__class_Opower(X1,X0,X3)
| ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X0,X3),c_Power_Opower__class_Opower(X2,X0,X3),X3) )
| ~ spl0_175
| ~ spl0_241 ),
inference(resolution,[],[f2794,f1746]) ).
fof(f1746,plain,
( ! [X2,X0,X4] :
( ~ c_lessequals(X2,X4,X0)
| X2 = X4
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X2,X4,X0) )
| ~ spl0_175 ),
inference(avatar_component_clause,[],[f1745]) ).
fof(f86367,plain,
( spl0_1150
| ~ spl0_174
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f2823,f2793,f1741,f86365]) ).
fof(f86365,plain,
( spl0_1150
<=> ! [X0,X3,X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Power_Opower__class_Opower(X2,X0,X3) = c_Power_Opower__class_Opower(X1,X0,X3)
| ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X0,X3),c_Power_Opower__class_Opower(X2,X0,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f1741,plain,
( spl0_174
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Oorder(X0)
| X1 = X3
| ~ c_lessequals(X1,X3,X0)
| c_HOL_Oord__class_Oless(X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f2823,plain,
( ! [X2,X3,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Power_Opower__class_Opower(X2,X0,X3) = c_Power_Opower__class_Opower(X1,X0,X3)
| ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X0,X3),c_Power_Opower__class_Opower(X2,X0,X3),X3) )
| ~ spl0_174
| ~ spl0_241 ),
inference(resolution,[],[f2794,f1742]) ).
fof(f1742,plain,
( ! [X3,X0,X1] :
( ~ c_lessequals(X1,X3,X0)
| X1 = X3
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0) )
| ~ spl0_174 ),
inference(avatar_component_clause,[],[f1741]) ).
fof(f85249,plain,
( spl0_1149
| ~ spl0_361
| ~ spl0_738 ),
inference(avatar_split_clause,[],[f27366,f26974,f5201,f85247]) ).
fof(f85247,plain,
( spl0_1149
<=> ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != c_HOL_Oinverse__class_Odivide(X0,X1,t_a)
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,t_a),X0,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f27366,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != c_HOL_Oinverse__class_Odivide(X0,X1,t_a)
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,t_a),X0,t_a) )
| ~ spl0_361
| ~ spl0_738 ),
inference(superposition,[],[f26975,f5202]) ).
fof(f81847,plain,
( ~ spl0_8
| spl0_1148
| ~ spl0_156
| ~ spl0_342 ),
inference(avatar_split_clause,[],[f4829,f4771,f1526,f81845,f726]) ).
fof(f81845,plain,
( spl0_1148
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(X2,X1,tc_nat),c_Power_Opower__class_Opower(X2,X0,tc_nat),tc_nat)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f1526,plain,
( spl0_156
<=> ! [X9,X19] :
( ~ c_lessequals(X19,X9,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X19,X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f4829,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(X2,X1,tc_nat),c_Power_Opower__class_Opower(X2,X0,tc_nat),tc_nat) )
| ~ spl0_156
| ~ spl0_342 ),
inference(resolution,[],[f4772,f1527]) ).
fof(f1527,plain,
( ! [X19,X9] :
( ~ c_lessequals(X19,X9,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X19,X9,tc_nat) )
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f1526]) ).
fof(f81843,plain,
( spl0_1147
| ~ spl0_215
| ~ spl0_284 ),
inference(avatar_split_clause,[],[f3383,f3014,f2297,f81841]) ).
fof(f81841,plain,
( spl0_1147
<=> ! [X0,X3,X2,X1] :
( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat) != c_HOL_Ominus__class_Ominus(X3,X2,tc_nat)
| ~ c_lessequals(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ c_lessequals(X2,X3,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
fof(f2297,plain,
( spl0_215
<=> ! [X22,X27,X23] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X27,X22,tc_nat),X23,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X27,X23,tc_nat),X22,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f3014,plain,
( spl0_284
<=> ! [X9,X23,X19] :
( X9 = X19
| ~ c_lessequals(X23,X19,tc_nat)
| ~ c_lessequals(X23,X9,tc_nat)
| c_HOL_Ominus__class_Ominus(X19,X23,tc_nat) != c_HOL_Ominus__class_Ominus(X9,X23,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f3383,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat) != c_HOL_Ominus__class_Ominus(X3,X2,tc_nat)
| ~ c_lessequals(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ c_lessequals(X2,X3,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = X3 )
| ~ spl0_215
| ~ spl0_284 ),
inference(superposition,[],[f3015,f2298]) ).
fof(f2298,plain,
( ! [X27,X22,X23] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X27,X22,tc_nat),X23,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X27,X23,tc_nat),X22,tc_nat)
| ~ spl0_215 ),
inference(avatar_component_clause,[],[f2297]) ).
fof(f3015,plain,
( ! [X19,X9,X23] :
( c_HOL_Ominus__class_Ominus(X19,X23,tc_nat) != c_HOL_Ominus__class_Ominus(X9,X23,tc_nat)
| ~ c_lessequals(X23,X19,tc_nat)
| ~ c_lessequals(X23,X9,tc_nat)
| X9 = X19 )
| ~ spl0_284 ),
inference(avatar_component_clause,[],[f3014]) ).
fof(f81839,plain,
( spl0_1146
| ~ spl0_181
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f3331,f2982,f1771,f81837]) ).
fof(f81837,plain,
( spl0_1146
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f3331,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_181
| ~ spl0_276 ),
inference(resolution,[],[f2983,f1772]) ).
fof(f81835,plain,
( spl0_1145
| ~ spl0_175
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f3330,f2982,f1745,f81833]) ).
fof(f81833,plain,
( spl0_1145
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X2,X1)
| ~ class_Orderings_Olinorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f3330,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X2,X1)
| ~ class_Orderings_Olinorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_175
| ~ spl0_276 ),
inference(resolution,[],[f2983,f1746]) ).
fof(f81831,plain,
( spl0_1144
| ~ spl0_174
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f3329,f2982,f1741,f81829]) ).
fof(f81829,plain,
( spl0_1144
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X2,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f3329,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X2,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_174
| ~ spl0_276 ),
inference(resolution,[],[f2983,f1742]) ).
fof(f81827,plain,
( spl0_1143
| ~ spl0_181
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f3309,f2978,f1771,f81825]) ).
fof(f81825,plain,
( spl0_1143
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X2,X0,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).
fof(f3309,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X2,X0,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_181
| ~ spl0_275 ),
inference(resolution,[],[f2979,f1772]) ).
fof(f81823,plain,
( spl0_1142
| ~ spl0_175
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f3308,f2978,f1745,f81821]) ).
fof(f81821,plain,
( spl0_1142
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X2,X0,X1)
| ~ class_Orderings_Olinorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).
fof(f3308,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X2,X0,X1)
| ~ class_Orderings_Olinorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,X1),c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_175
| ~ spl0_275 ),
inference(resolution,[],[f2979,f1746]) ).
fof(f81819,plain,
( spl0_1141
| ~ spl0_174
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f3307,f2978,f1741,f81817]) ).
fof(f81817,plain,
( spl0_1141
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X2,X0,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f3307,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X2,X0,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,X1),c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_174
| ~ spl0_275 ),
inference(resolution,[],[f2979,f1742]) ).
fof(f81815,plain,
( spl0_1140
| ~ spl0_181
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3285,f2974,f1771,f81813]) ).
fof(f81813,plain,
( spl0_1140
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f2974,plain,
( spl0_274
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f3285,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_181
| ~ spl0_274 ),
inference(resolution,[],[f2975,f1772]) ).
fof(f2975,plain,
( ! [X3,X0,X1] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_274 ),
inference(avatar_component_clause,[],[f2974]) ).
fof(f81810,plain,
( spl0_1139
| ~ spl0_175
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3284,f2974,f1745,f81808]) ).
fof(f81808,plain,
( spl0_1139
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X2,X1)
| ~ class_Orderings_Olinorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
fof(f3284,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X2,X1)
| ~ class_Orderings_Olinorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_175
| ~ spl0_274 ),
inference(resolution,[],[f2975,f1746]) ).
fof(f81806,plain,
( spl0_1138
| ~ spl0_174
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3283,f2974,f1741,f81804]) ).
fof(f81804,plain,
( spl0_1138
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X2,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f3283,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X2,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_174
| ~ spl0_274 ),
inference(resolution,[],[f2975,f1742]) ).
fof(f81802,plain,
( spl0_1137
| ~ spl0_181
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f3261,f2970,f1771,f81800]) ).
fof(f81800,plain,
( spl0_1137
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X2,X0,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f2970,plain,
( spl0_273
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f3261,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X2,X0,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_181
| ~ spl0_273 ),
inference(resolution,[],[f2971,f1772]) ).
fof(f2971,plain,
( ! [X3,X0,X1] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_273 ),
inference(avatar_component_clause,[],[f2970]) ).
fof(f81798,plain,
( spl0_1136
| ~ spl0_175
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f3260,f2970,f1745,f81796]) ).
fof(f81796,plain,
( spl0_1136
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X2,X0,X1)
| ~ class_Orderings_Olinorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f3260,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X2,X0,X1)
| ~ class_Orderings_Olinorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,X1),c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_175
| ~ spl0_273 ),
inference(resolution,[],[f2971,f1746]) ).
fof(f81794,plain,
( spl0_1135
| ~ spl0_174
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f3259,f2970,f1741,f81792]) ).
fof(f81792,plain,
( spl0_1135
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X2,X0,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f3259,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X2,X0,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,X1),c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_174
| ~ spl0_273 ),
inference(resolution,[],[f2971,f1742]) ).
fof(f81790,plain,
( spl0_1134
| ~ spl0_181
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f3193,f2946,f1771,f81788]) ).
fof(f81788,plain,
( spl0_1134
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,X2,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f3193,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,X2,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_181
| ~ spl0_267 ),
inference(resolution,[],[f2947,f1772]) ).
fof(f81786,plain,
( spl0_1133
| ~ spl0_175
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f3192,f2946,f1745,f81784]) ).
fof(f81784,plain,
( spl0_1133
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f3192,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) )
| ~ spl0_175
| ~ spl0_267 ),
inference(resolution,[],[f2947,f1746]) ).
fof(f81782,plain,
( spl0_1132
| ~ spl0_174
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f3191,f2946,f1741,f81780]) ).
fof(f81780,plain,
( spl0_1132
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f3191,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) )
| ~ spl0_174
| ~ spl0_267 ),
inference(resolution,[],[f2947,f1742]) ).
fof(f81778,plain,
( spl0_1131
| ~ spl0_181
| ~ spl0_266 ),
inference(avatar_split_clause,[],[f3175,f2942,f1771,f81776]) ).
fof(f81776,plain,
( spl0_1131
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X2,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f2942,plain,
( spl0_266
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f3175,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X2,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_181
| ~ spl0_266 ),
inference(resolution,[],[f2943,f1772]) ).
fof(f2943,plain,
( ! [X3,X0,X1] :
( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_266 ),
inference(avatar_component_clause,[],[f2942]) ).
fof(f81774,plain,
( spl0_1130
| ~ spl0_175
| ~ spl0_266 ),
inference(avatar_split_clause,[],[f3174,f2942,f1745,f81772]) ).
fof(f81772,plain,
( spl0_1130
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X2,X1)
| ~ class_Orderings_Olinorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f3174,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X2,X1)
| ~ class_Orderings_Olinorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) )
| ~ spl0_175
| ~ spl0_266 ),
inference(resolution,[],[f2943,f1746]) ).
fof(f81770,plain,
( spl0_1129
| ~ spl0_643
| ~ spl0_860 ),
inference(avatar_split_clause,[],[f40162,f39932,f18506,f81768]) ).
fof(f81768,plain,
( spl0_1129
<=> ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != X0
| c_HOL_Oinverse__class_Oinverse(X0,t_a) = c_HOL_Oinverse__class_Odivide(X1,X1,t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f18506,plain,
( spl0_643
<=> ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != c_HOL_Otimes__class_Otimes(X1,X0,t_a)
| c_HOL_Oinverse__class_Oinverse(X1,t_a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f39932,plain,
( spl0_860
<=> ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(X0,X0,t_a),t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f40162,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != X0
| c_HOL_Oinverse__class_Oinverse(X0,t_a) = c_HOL_Oinverse__class_Odivide(X1,X1,t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X1 )
| ~ spl0_643
| ~ spl0_860 ),
inference(superposition,[],[f18507,f39933]) ).
fof(f39933,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(X0,X0,t_a),t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_860 ),
inference(avatar_component_clause,[],[f39932]) ).
fof(f18507,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != c_HOL_Otimes__class_Otimes(X1,X0,t_a)
| c_HOL_Oinverse__class_Oinverse(X1,t_a) = X0 )
| ~ spl0_643 ),
inference(avatar_component_clause,[],[f18506]) ).
fof(f81766,plain,
( spl0_1128
| ~ spl0_174
| ~ spl0_266 ),
inference(avatar_split_clause,[],[f3173,f2942,f1741,f81764]) ).
fof(f81764,plain,
( spl0_1128
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X2,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f3173,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X2,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) )
| ~ spl0_174
| ~ spl0_266 ),
inference(resolution,[],[f2943,f1742]) ).
fof(f81762,plain,
( spl0_1127
| ~ spl0_181
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f3157,f2938,f1771,f81760]) ).
fof(f81760,plain,
( spl0_1127
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,X2,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f2938,plain,
( spl0_265
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f3157,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,X2,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_181
| ~ spl0_265 ),
inference(resolution,[],[f2939,f1772]) ).
fof(f2939,plain,
( ! [X3,X0,X1] :
( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_265 ),
inference(avatar_component_clause,[],[f2938]) ).
fof(f81758,plain,
( spl0_1126
| ~ spl0_175
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f3156,f2938,f1745,f81756]) ).
fof(f81756,plain,
( spl0_1126
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).
fof(f3156,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) )
| ~ spl0_175
| ~ spl0_265 ),
inference(resolution,[],[f2939,f1746]) ).
fof(f81754,plain,
( spl0_1125
| ~ spl0_174
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f3155,f2938,f1741,f81752]) ).
fof(f81752,plain,
( spl0_1125
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f3155,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) )
| ~ spl0_174
| ~ spl0_265 ),
inference(resolution,[],[f2939,f1742]) ).
fof(f81750,plain,
( spl0_1124
| ~ spl0_181
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f3139,f2934,f1771,f81748]) ).
fof(f81748,plain,
( spl0_1124
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X2,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f3139,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X2,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_181
| ~ spl0_264 ),
inference(resolution,[],[f2935,f1772]) ).
fof(f81746,plain,
( spl0_1123
| ~ spl0_175
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f3138,f2934,f1745,f81744]) ).
fof(f81744,plain,
( spl0_1123
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X2,X1)
| ~ class_Orderings_Olinorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f3138,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X2,X1)
| ~ class_Orderings_Olinorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) )
| ~ spl0_175
| ~ spl0_264 ),
inference(resolution,[],[f2935,f1746]) ).
fof(f81742,plain,
( spl0_1122
| ~ spl0_174
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f3137,f2934,f1741,f81740]) ).
fof(f81740,plain,
( spl0_1122
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X2,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f3137,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X2,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) )
| ~ spl0_174
| ~ spl0_264 ),
inference(resolution,[],[f2935,f1742]) ).
fof(f81738,plain,
( spl0_1121
| ~ spl0_181
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f3121,f2930,f1771,f81736]) ).
fof(f81736,plain,
( spl0_1121
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,X2,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f3121,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,X2,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_181
| ~ spl0_263 ),
inference(resolution,[],[f2931,f1772]) ).
fof(f81734,plain,
( spl0_1120
| ~ spl0_175
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f3120,f2930,f1745,f81732]) ).
fof(f81732,plain,
( spl0_1120
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f3120,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) )
| ~ spl0_175
| ~ spl0_263 ),
inference(resolution,[],[f2931,f1746]) ).
fof(f81730,plain,
( spl0_1119
| ~ spl0_174
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f3119,f2930,f1741,f81728]) ).
fof(f81728,plain,
( spl0_1119
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f3119,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) )
| ~ spl0_174
| ~ spl0_263 ),
inference(resolution,[],[f2931,f1742]) ).
fof(f81726,plain,
( spl0_1118
| ~ spl0_606
| ~ spl0_860 ),
inference(avatar_split_clause,[],[f40161,f39932,f18083,f81724]) ).
fof(f81724,plain,
( spl0_1118
<=> ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != X0
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X1,X1,t_a),t_a) = X0
| c_HOL_Ozero__class_Ozero(t_a) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f18083,plain,
( spl0_606
<=> ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != c_HOL_Otimes__class_Otimes(X1,X0,t_a)
| c_HOL_Oinverse__class_Oinverse(X0,t_a) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f40161,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != X0
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X1,X1,t_a),t_a) = X0
| c_HOL_Ozero__class_Ozero(t_a) = X1 )
| ~ spl0_606
| ~ spl0_860 ),
inference(superposition,[],[f18084,f39933]) ).
fof(f18084,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != c_HOL_Otimes__class_Otimes(X1,X0,t_a)
| c_HOL_Oinverse__class_Oinverse(X0,t_a) = X1 )
| ~ spl0_606 ),
inference(avatar_component_clause,[],[f18083]) ).
fof(f81025,plain,
( spl0_1117
| ~ spl0_643
| ~ spl0_712 ),
inference(avatar_split_clause,[],[f21814,f21753,f18506,f81023]) ).
fof(f81023,plain,
( spl0_1117
<=> ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != X1
| c_HOL_Oinverse__class_Oinverse(X0,t_a) = c_HOL_Oinverse__class_Odivide(X1,X0,t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f21753,plain,
( spl0_712
<=> ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Odivide(X1,X0,t_a),t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f21814,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != X1
| c_HOL_Oinverse__class_Oinverse(X0,t_a) = c_HOL_Oinverse__class_Odivide(X1,X0,t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_643
| ~ spl0_712 ),
inference(superposition,[],[f18507,f21754]) ).
fof(f21754,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Odivide(X1,X0,t_a),t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_712 ),
inference(avatar_component_clause,[],[f21753]) ).
fof(f79677,plain,
( spl0_1116
| ~ spl0_102
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f4888,f4855,f1180,f79675]) ).
fof(f79675,plain,
( spl0_1116
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,X3,X0),X0)
| c_lessequals(X2,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f1180,plain,
( spl0_102
<=> ! [X9,X19] :
( c_lessequals(X19,X9,tc_nat)
| c_lessequals(X9,X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f4888,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,X3,X0),X0)
| c_lessequals(X2,X3,tc_nat) )
| ~ spl0_102
| ~ spl0_348 ),
inference(resolution,[],[f4856,f1181]) ).
fof(f1181,plain,
( ! [X19,X9] :
( c_lessequals(X19,X9,tc_nat)
| c_lessequals(X9,X19,tc_nat) )
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f1180]) ).
fof(f79673,plain,
( spl0_1115
| ~ spl0_136
| ~ spl0_342 ),
inference(avatar_split_clause,[],[f4814,f4771,f1363,f79671]) ).
fof(f79671,plain,
( spl0_1115
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X3),c_Power_Opower__class_Opower(X2,X1,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f1363,plain,
( spl0_136
<=> ! [X2,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X4,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f4814,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X3),c_Power_Opower__class_Opower(X2,X1,X3),X3) )
| ~ spl0_136
| ~ spl0_342 ),
inference(resolution,[],[f4772,f1364]) ).
fof(f1364,plain,
( ! [X2,X0,X4] :
( ~ c_lessequals(X4,X2,X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0) )
| ~ spl0_136 ),
inference(avatar_component_clause,[],[f1363]) ).
fof(f79669,plain,
( spl0_1114
| ~ spl0_134
| ~ spl0_342 ),
inference(avatar_split_clause,[],[f4813,f4771,f1355,f79667]) ).
fof(f79667,plain,
( spl0_1114
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X3),c_Power_Opower__class_Opower(X2,X1,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).
fof(f1355,plain,
( spl0_134
<=> ! [X2,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X4,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f4813,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X3),c_Power_Opower__class_Opower(X2,X1,X3),X3) )
| ~ spl0_134
| ~ spl0_342 ),
inference(resolution,[],[f4772,f1356]) ).
fof(f1356,plain,
( ! [X2,X0,X4] :
( ~ c_lessequals(X4,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0) )
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f1355]) ).
fof(f79665,plain,
( spl0_1113
| ~ spl0_142
| ~ spl0_341 ),
inference(avatar_split_clause,[],[f4805,f4767,f1387,f79663]) ).
fof(f79663,plain,
( spl0_1113
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X3),c_Power_Opower__class_Opower(X2,X1,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f1387,plain,
( spl0_142
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f4767,plain,
( spl0_341
<=> ! [X24,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X9,X24,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X24,X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f4805,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X3),c_Power_Opower__class_Opower(X2,X1,X3),X3) )
| ~ spl0_142
| ~ spl0_341 ),
inference(resolution,[],[f4768,f1388]) ).
fof(f1388,plain,
( ! [X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0) )
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1387]) ).
fof(f4768,plain,
( ! [X0,X1,X9,X24] :
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X24,X0),c_Power_Opower__class_Opower(X1,X9,X0),X0)
| ~ c_HOL_Oord__class_Oless(X9,X24,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_341 ),
inference(avatar_component_clause,[],[f4767]) ).
fof(f79661,plain,
( spl0_1112
| ~ spl0_141
| ~ spl0_341 ),
inference(avatar_split_clause,[],[f4804,f4767,f1383,f79659]) ).
fof(f79659,plain,
( spl0_1112
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X3),c_Power_Opower__class_Opower(X2,X1,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f1383,plain,
( spl0_141
<=> ! [X2,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f4804,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X3),c_Power_Opower__class_Opower(X2,X1,X3),X3) )
| ~ spl0_141
| ~ spl0_341 ),
inference(resolution,[],[f4768,f1384]) ).
fof(f1384,plain,
( ! [X2,X0,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0) )
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f1383]) ).
fof(f79657,plain,
( spl0_1111
| ~ spl0_140
| ~ spl0_341 ),
inference(avatar_split_clause,[],[f4803,f4767,f1379,f79655]) ).
fof(f79655,plain,
( spl0_1111
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X3),c_Power_Opower__class_Opower(X2,X1,X3),X3)
| ~ class_Orderings_Opreorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).
fof(f1379,plain,
( spl0_140
<=> ! [X4,X0,X2] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f4803,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X3),c_Power_Opower__class_Opower(X2,X1,X3),X3)
| ~ class_Orderings_Opreorder(X3) )
| ~ spl0_140
| ~ spl0_341 ),
inference(resolution,[],[f4768,f1380]) ).
fof(f1380,plain,
( ! [X2,X0,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f1379]) ).
fof(f79653,plain,
( spl0_1110
| ~ spl0_138
| ~ spl0_341 ),
inference(avatar_split_clause,[],[f4802,f4767,f1371,f79651]) ).
fof(f79651,plain,
( spl0_1110
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ class_Orderings_Opreorder(X3)
| c_lessequals(c_Power_Opower__class_Opower(X2,X1,X3),c_Power_Opower__class_Opower(X2,X0,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).
fof(f1371,plain,
( spl0_138
<=> ! [X4,X0,X2] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0)
| c_lessequals(X2,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f4802,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ class_Orderings_Opreorder(X3)
| c_lessequals(c_Power_Opower__class_Opower(X2,X1,X3),c_Power_Opower__class_Opower(X2,X0,X3),X3) )
| ~ spl0_138
| ~ spl0_341 ),
inference(resolution,[],[f4768,f1372]) ).
fof(f1372,plain,
( ! [X2,X0,X4] :
( ~ c_HOL_Oord__class_Oless(X2,X4,X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(X2,X4,X0) )
| ~ spl0_138 ),
inference(avatar_component_clause,[],[f1371]) ).
fof(f79649,plain,
( spl0_1109
| ~ spl0_137
| ~ spl0_341 ),
inference(avatar_split_clause,[],[f4801,f4767,f1367,f79647]) ).
fof(f79647,plain,
( spl0_1109
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ class_Orderings_Oorder(X3)
| c_lessequals(c_Power_Opower__class_Opower(X2,X1,X3),c_Power_Opower__class_Opower(X2,X0,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).
fof(f1367,plain,
( spl0_137
<=> ! [X4,X0,X2] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0)
| c_lessequals(X2,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f4801,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ class_Orderings_Oorder(X3)
| c_lessequals(c_Power_Opower__class_Opower(X2,X1,X3),c_Power_Opower__class_Opower(X2,X0,X3),X3) )
| ~ spl0_137
| ~ spl0_341 ),
inference(resolution,[],[f4768,f1368]) ).
fof(f1368,plain,
( ! [X2,X0,X4] :
( ~ c_HOL_Oord__class_Oless(X2,X4,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X2,X4,X0) )
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f1367]) ).
fof(f79645,plain,
( spl0_1108
| ~ spl0_142
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f4785,f4763,f1387,f79643]) ).
fof(f79643,plain,
( spl0_1108
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X2),c_Power_Opower__class_Opower(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f4763,plain,
( spl0_340
<=> ! [X3,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X3,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f4785,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X2),c_Power_Opower__class_Opower(X0,X3,X2),X2) )
| ~ spl0_142
| ~ spl0_340 ),
inference(resolution,[],[f4764,f1388]) ).
fof(f4764,plain,
( ! [X3,X0,X1,X9] :
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X3,X9,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_340 ),
inference(avatar_component_clause,[],[f4763]) ).
fof(f79641,plain,
( spl0_1107
| ~ spl0_141
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f4784,f4763,f1383,f79639]) ).
fof(f79639,plain,
( spl0_1107
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X2),c_Power_Opower__class_Opower(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f4784,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X2),c_Power_Opower__class_Opower(X0,X3,X2),X2) )
| ~ spl0_141
| ~ spl0_340 ),
inference(resolution,[],[f4764,f1384]) ).
fof(f79637,plain,
( spl0_1106
| ~ spl0_285
| ~ spl0_361
| ~ spl0_1095 ),
inference(avatar_split_clause,[],[f79583,f78605,f5201,f3088,f79635]) ).
fof(f79635,plain,
( spl0_1106
<=> ! [X0,X1] :
( c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oinverse__class_Odivide(X0,X0,t_a),t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).
fof(f3088,plain,
( spl0_285
<=> ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(t_a),t_a) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f78605,plain,
( spl0_1095
<=> ! [X0] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X0,X0,t_a),t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).
fof(f79583,plain,
( ! [X0,X1] :
( c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oinverse__class_Odivide(X0,X0,t_a),t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_285
| ~ spl0_361
| ~ spl0_1095 ),
inference(forward_demodulation,[],[f79562,f3089]) ).
fof(f3089,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(t_a),t_a) = X0
| ~ spl0_285 ),
inference(avatar_component_clause,[],[f3088]) ).
fof(f79562,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(t_a),t_a) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oinverse__class_Odivide(X0,X0,t_a),t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_361
| ~ spl0_1095 ),
inference(superposition,[],[f5202,f78606]) ).
fof(f78606,plain,
( ! [X0] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X0,X0,t_a),t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_1095 ),
inference(avatar_component_clause,[],[f78605]) ).
fof(f79633,plain,
( spl0_1105
| ~ spl0_140
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f4783,f4763,f1379,f79631]) ).
fof(f79631,plain,
( spl0_1105
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X2),c_Power_Opower__class_Opower(X0,X3,X2),X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).
fof(f4783,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X2),c_Power_Opower__class_Opower(X0,X3,X2),X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_140
| ~ spl0_340 ),
inference(resolution,[],[f4764,f1380]) ).
fof(f79629,plain,
( spl0_1104
| ~ spl0_138
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f4782,f4763,f1371,f79627]) ).
fof(f79627,plain,
( spl0_1104
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(c_Power_Opower__class_Opower(X0,X3,X2),c_Power_Opower__class_Opower(X1,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).
fof(f4782,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(c_Power_Opower__class_Opower(X0,X3,X2),c_Power_Opower__class_Opower(X1,X3,X2),X2) )
| ~ spl0_138
| ~ spl0_340 ),
inference(resolution,[],[f4764,f1372]) ).
fof(f79625,plain,
( spl0_1103
| ~ spl0_137
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f4781,f4763,f1367,f79623]) ).
fof(f79623,plain,
( spl0_1103
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_Power_Opower__class_Opower(X0,X3,X2),c_Power_Opower__class_Opower(X1,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).
fof(f4781,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_Power_Opower__class_Opower(X0,X3,X2),c_Power_Opower__class_Opower(X1,X3,X2),X2) )
| ~ spl0_137
| ~ spl0_340 ),
inference(resolution,[],[f4764,f1368]) ).
fof(f79621,plain,
( spl0_1102
| ~ spl0_94
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4604,f4590,f1145,f79619]) ).
fof(f79619,plain,
( spl0_1102
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f4590,plain,
( spl0_333
<=> ! [X9,X23,X19] :
( ~ c_lessequals(X23,X19,tc_nat)
| ~ c_lessequals(X23,X9,tc_nat)
| c_HOL_Ominus__class_Ominus(X19,X9,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X19,X23,tc_nat),c_HOL_Ominus__class_Ominus(X9,X23,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f4604,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),tc_nat) )
| ~ spl0_94
| ~ spl0_333 ),
inference(resolution,[],[f4591,f1146]) ).
fof(f4591,plain,
( ! [X19,X9,X23] :
( ~ c_lessequals(X23,X19,tc_nat)
| ~ c_lessequals(X23,X9,tc_nat)
| c_HOL_Ominus__class_Ominus(X19,X9,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X19,X23,tc_nat),c_HOL_Ominus__class_Ominus(X9,X23,tc_nat),tc_nat) )
| ~ spl0_333 ),
inference(avatar_component_clause,[],[f4590]) ).
fof(f79617,plain,
( spl0_1101
| ~ spl0_195
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f4546,f4437,f1970,f79615]) ).
fof(f79615,plain,
( spl0_1101
<=> ! [X0,X3,X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_lessequals(X3,c_Power_Opower__class_Opower(X1,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f4437,plain,
( spl0_330
<=> ! [X9,X0,X2] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X9
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_Power_Opower__class_Opower(X2,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f4546,plain,
( ! [X2,X3,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_lessequals(X3,c_Power_Opower__class_Opower(X1,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2) )
| ~ spl0_195
| ~ spl0_330 ),
inference(resolution,[],[f4438,f1971]) ).
fof(f4438,plain,
( ! [X2,X0,X9] :
( c_lessequals(c_Power_Opower__class_Opower(X2,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X9
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_330 ),
inference(avatar_component_clause,[],[f4437]) ).
fof(f79613,plain,
( spl0_1100
| ~ spl0_194
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f4545,f4437,f1966,f79611]) ).
fof(f79611,plain,
( spl0_1100
<=> ! [X0,X3,X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_Power_Opower__class_Opower(X1,X0,X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f4545,plain,
( ! [X2,X3,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_Power_Opower__class_Opower(X1,X0,X2),X3,X2) )
| ~ spl0_194
| ~ spl0_330 ),
inference(resolution,[],[f4438,f1967]) ).
fof(f79609,plain,
( spl0_1099
| ~ spl0_190
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f4544,f4437,f1950,f79607]) ).
fof(f79607,plain,
( spl0_1099
<=> ! [X0,X3,X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X0,X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).
fof(f4544,plain,
( ! [X2,X3,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X0,X2),X3,X2) )
| ~ spl0_190
| ~ spl0_330 ),
inference(resolution,[],[f4438,f1951]) ).
fof(f79605,plain,
( spl0_1098
| ~ spl0_189
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f4543,f4437,f1946,f79603]) ).
fof(f79603,plain,
( spl0_1098
<=> ! [X0,X3,X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X1,X0,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).
fof(f4543,plain,
( ! [X2,X3,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X1,X0,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2) )
| ~ spl0_189
| ~ spl0_330 ),
inference(resolution,[],[f4438,f1947]) ).
fof(f79601,plain,
( spl0_1097
| ~ spl0_188
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f4542,f4437,f1942,f79599]) ).
fof(f79599,plain,
( spl0_1097
<=> ! [X0,X3,X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X1,X0,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f4542,plain,
( ! [X2,X3,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X1,X0,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2) )
| ~ spl0_188
| ~ spl0_330 ),
inference(resolution,[],[f4438,f1943]) ).
fof(f79597,plain,
( spl0_1096
| ~ spl0_187
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f4541,f4437,f1938,f79595]) ).
fof(f79595,plain,
( spl0_1096
<=> ! [X0,X3,X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X0,X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).
fof(f4541,plain,
( ! [X2,X3,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X0,X2),X3,X2) )
| ~ spl0_187
| ~ spl0_330 ),
inference(resolution,[],[f4438,f1939]) ).
fof(f78607,plain,
( spl0_1095
| ~ spl0_484
| ~ spl0_527
| ~ spl0_1094 ),
inference(avatar_split_clause,[],[f77605,f74395,f13797,f12230,f78605]) ).
fof(f13797,plain,
( spl0_527
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(t_a) = X0
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X0,t_a),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f74395,plain,
( spl0_1094
<=> ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != c_HOL_Otimes__class_Otimes(X1,X0,t_a)
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X0,X1,t_a),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
fof(f77605,plain,
( ! [X0] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X0,X0,t_a),t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_484
| ~ spl0_527
| ~ spl0_1094 ),
inference(forward_demodulation,[],[f77588,f12231]) ).
fof(f77588,plain,
( ! [X0] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,t_a),X0,t_a),t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_527
| ~ spl0_1094 ),
inference(trivial_inequality_removal,[],[f77567]) ).
fof(f77567,plain,
( ! [X0] :
( c_HOL_Oone__class_Oone(t_a) != c_HOL_Oone__class_Oone(t_a)
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,t_a),X0,t_a),t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_527
| ~ spl0_1094 ),
inference(superposition,[],[f74396,f13798]) ).
fof(f13798,plain,
( ! [X0] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X0,t_a),t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_527 ),
inference(avatar_component_clause,[],[f13797]) ).
fof(f74396,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != c_HOL_Otimes__class_Otimes(X1,X0,t_a)
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X0,X1,t_a),t_a) )
| ~ spl0_1094 ),
inference(avatar_component_clause,[],[f74395]) ).
fof(f74397,plain,
( spl0_1094
| ~ spl0_606
| ~ spl0_735 ),
inference(avatar_split_clause,[],[f23514,f22784,f18083,f74395]) ).
fof(f22784,plain,
( spl0_735
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_HOL_Otimes__class_Otimes(X1,X0,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f23514,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != c_HOL_Otimes__class_Otimes(X1,X0,t_a)
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X0,X1,t_a),t_a) )
| ~ spl0_606
| ~ spl0_735 ),
inference(superposition,[],[f18084,f22785]) ).
fof(f22785,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_HOL_Otimes__class_Otimes(X1,X0,t_a),t_a)
| ~ spl0_735 ),
inference(avatar_component_clause,[],[f22784]) ).
fof(f72556,plain,
( spl0_1093
| ~ spl0_606
| ~ spl0_712 ),
inference(avatar_split_clause,[],[f21813,f21753,f18083,f72554]) ).
fof(f72554,plain,
( spl0_1093
<=> ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != X1
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X1,X0,t_a),t_a) = X0
| c_HOL_Ozero__class_Ozero(t_a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).
fof(f21813,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != X1
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X1,X0,t_a),t_a) = X0
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_606
| ~ spl0_712 ),
inference(superposition,[],[f18084,f21754]) ).
fof(f69123,plain,
( ~ spl0_1
| spl0_1092
| ~ spl0_216
| ~ spl0_574 ),
inference(avatar_split_clause,[],[f16195,f16042,f2472,f69121,f691]) ).
fof(f69121,plain,
( spl0_1092
<=> ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != X1
| c_HOL_Ozero__class_Ozero(t_a) = X0
| c_HOL_Otimes__class_Otimes(X0,X1,t_a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f2472,plain,
( spl0_216
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| X1 = X3
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oone__class_Oone(X0) != c_HOL_Oinverse__class_Odivide(X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f16042,plain,
( spl0_574
<=> ! [X0,X1] :
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X0,t_a),X1,t_a) = X0
| c_HOL_Ozero__class_Ozero(t_a) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f16195,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != X1
| c_HOL_Otimes__class_Otimes(X0,X1,t_a) = X0
| c_HOL_Ozero__class_Ozero(t_a) = X0
| ~ class_Ring__and__Field_Ofield(t_a) )
| ~ spl0_216
| ~ spl0_574 ),
inference(duplicate_literal_removal,[],[f16193]) ).
fof(f16193,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != X1
| c_HOL_Otimes__class_Otimes(X0,X1,t_a) = X0
| c_HOL_Ozero__class_Ozero(t_a) = X0
| ~ class_Ring__and__Field_Ofield(t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_216
| ~ spl0_574 ),
inference(superposition,[],[f2473,f16043]) ).
fof(f16043,plain,
( ! [X0,X1] :
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X0,t_a),X1,t_a) = X0
| c_HOL_Ozero__class_Ozero(t_a) = X1 )
| ~ spl0_574 ),
inference(avatar_component_clause,[],[f16042]) ).
fof(f2473,plain,
( ! [X3,X0,X1] :
( c_HOL_Oone__class_Oone(X0) != c_HOL_Oinverse__class_Odivide(X1,X3,X0)
| X1 = X3
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ class_Ring__and__Field_Ofield(X0) )
| ~ spl0_216 ),
inference(avatar_component_clause,[],[f2472]) ).
fof(f66931,plain,
( spl0_1091
| ~ spl0_142
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f4756,f4743,f1387,f66929]) ).
fof(f66929,plain,
( spl0_1091
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X0,X2,X1),c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X2,X1),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f4743,plain,
( spl0_338
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X9,X0),X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f4756,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X0,X2,X1),c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X2,X1),X1),X1) )
| ~ spl0_142
| ~ spl0_338 ),
inference(resolution,[],[f4744,f1388]) ).
fof(f4744,plain,
( ! [X0,X1,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X9,X0),X0),c_Power_Opower__class_Opower(X1,X9,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_338 ),
inference(avatar_component_clause,[],[f4743]) ).
fof(f66927,plain,
( spl0_1090
| ~ spl0_141
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f4755,f4743,f1383,f66925]) ).
fof(f66925,plain,
( spl0_1090
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X0,X2,X1),c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X2,X1),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f4755,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X0,X2,X1),c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X2,X1),X1),X1) )
| ~ spl0_141
| ~ spl0_338 ),
inference(resolution,[],[f4744,f1384]) ).
fof(f66923,plain,
( spl0_1089
| ~ spl0_140
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f4754,f4743,f1379,f66921]) ).
fof(f66921,plain,
( spl0_1089
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X0,X2,X1),c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X2,X1),X1),X1)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f4754,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X0,X2,X1),c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X2,X1),X1),X1)
| ~ class_Orderings_Opreorder(X1) )
| ~ spl0_140
| ~ spl0_338 ),
inference(resolution,[],[f4744,f1380]) ).
fof(f66919,plain,
( spl0_1088
| ~ spl0_138
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f4753,f4743,f1371,f66917]) ).
fof(f66917,plain,
( spl0_1088
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X2,X1),X1),c_Power_Opower__class_Opower(X0,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f4753,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X2,X1),X1),c_Power_Opower__class_Opower(X0,X2,X1),X1) )
| ~ spl0_138
| ~ spl0_338 ),
inference(resolution,[],[f4744,f1372]) ).
fof(f66915,plain,
( spl0_1087
| ~ spl0_137
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f4752,f4743,f1367,f66913]) ).
fof(f66913,plain,
( spl0_1087
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X2,X1),X1),c_Power_Opower__class_Opower(X0,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f4752,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X2,X1),X1),c_Power_Opower__class_Opower(X0,X2,X1),X1) )
| ~ spl0_137
| ~ spl0_338 ),
inference(resolution,[],[f4744,f1368]) ).
fof(f66911,plain,
( spl0_1086
| ~ spl0_195
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4405,f3604,f1970,f66909]) ).
fof(f66909,plain,
( spl0_1086
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(X3,c_Power_Opower__class_Opower(X0,X4,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X3,c_Power_Opower__class_Opower(X1,X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f4405,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(X3,c_Power_Opower__class_Opower(X0,X4,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X3,c_Power_Opower__class_Opower(X1,X4,X2),X2) )
| ~ spl0_195
| ~ spl0_324 ),
inference(resolution,[],[f3605,f1971]) ).
fof(f66907,plain,
( ~ spl0_1
| spl0_1085
| ~ spl0_216
| ~ spl0_363 ),
inference(avatar_split_clause,[],[f5491,f5479,f2472,f66905,f691]) ).
fof(f66905,plain,
( spl0_1085
<=> ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != X0
| c_HOL_Ozero__class_Ozero(t_a) = X1
| c_HOL_Otimes__class_Otimes(X0,X1,t_a) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).
fof(f5491,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != X0
| c_HOL_Otimes__class_Otimes(X0,X1,t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X1
| ~ class_Ring__and__Field_Ofield(t_a) )
| ~ spl0_216
| ~ spl0_363 ),
inference(duplicate_literal_removal,[],[f5489]) ).
fof(f5489,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != X0
| c_HOL_Otimes__class_Otimes(X0,X1,t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X1
| ~ class_Ring__and__Field_Ofield(t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X1 )
| ~ spl0_216
| ~ spl0_363 ),
inference(superposition,[],[f2473,f5480]) ).
fof(f66903,plain,
( spl0_1084
| ~ spl0_194
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4404,f3604,f1966,f66901]) ).
fof(f66901,plain,
( spl0_1084
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X3,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_Power_Opower__class_Opower(X0,X3,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f4404,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X3,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_Power_Opower__class_Opower(X0,X3,X2),X4,X2) )
| ~ spl0_194
| ~ spl0_324 ),
inference(resolution,[],[f3605,f1967]) ).
fof(f66899,plain,
( spl0_1083
| ~ spl0_190
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4403,f3604,f1950,f66897]) ).
fof(f66897,plain,
( spl0_1083
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X0,X3,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).
fof(f4403,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X0,X3,X2),X4,X2) )
| ~ spl0_190
| ~ spl0_324 ),
inference(resolution,[],[f3605,f1951]) ).
fof(f66895,plain,
( spl0_1082
| ~ spl0_189
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4402,f3604,f1946,f66893]) ).
fof(f66893,plain,
( spl0_1082
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X0,X4,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X1,X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).
fof(f4402,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X0,X4,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X1,X4,X2),X2) )
| ~ spl0_189
| ~ spl0_324 ),
inference(resolution,[],[f3605,f1947]) ).
fof(f66891,plain,
( spl0_1081
| ~ spl0_188
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4401,f3604,f1942,f66889]) ).
fof(f66889,plain,
( spl0_1081
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X0,X4,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X1,X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).
fof(f4401,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X0,X4,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X1,X4,X2),X2) )
| ~ spl0_188
| ~ spl0_324 ),
inference(resolution,[],[f3605,f1943]) ).
fof(f66887,plain,
( spl0_1080
| ~ spl0_187
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4400,f3604,f1938,f66885]) ).
fof(f66885,plain,
( spl0_1080
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X0,X3,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f4400,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X0,X3,X2),X4,X2) )
| ~ spl0_187
| ~ spl0_324 ),
inference(resolution,[],[f3605,f1939]) ).
fof(f66883,plain,
( spl0_1079
| ~ spl0_193
| ~ spl0_322 ),
inference(avatar_split_clause,[],[f4378,f3596,f1962,f66881]) ).
fof(f66881,plain,
( spl0_1079
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X0,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f1962,plain,
( spl0_193
<=> ! [X4,X11,X0,X2] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X2,X0)
| ~ c_HOL_Oord__class_Oless(X11,X4,X0)
| c_HOL_Oord__class_Oless(X11,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f3596,plain,
( spl0_322
<=> ! [X24,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X9,X24,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X1,X24,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f4378,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X0,X2),X4,X2) )
| ~ spl0_193
| ~ spl0_322 ),
inference(resolution,[],[f3597,f1963]) ).
fof(f1963,plain,
( ! [X2,X0,X11,X4] :
( ~ c_HOL_Oord__class_Oless(X11,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(X11,X2,X0) )
| ~ spl0_193 ),
inference(avatar_component_clause,[],[f1962]) ).
fof(f3597,plain,
( ! [X0,X1,X9,X24] :
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X1,X24,X0),X0)
| ~ c_HOL_Oord__class_Oless(X9,X24,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_322 ),
inference(avatar_component_clause,[],[f3596]) ).
fof(f66879,plain,
( spl0_1078
| ~ spl0_192
| ~ spl0_322 ),
inference(avatar_split_clause,[],[f4377,f3596,f1958,f66877]) ).
fof(f66877,plain,
( spl0_1078
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).
fof(f1958,plain,
( spl0_192
<=> ! [X4,X11,X0,X2] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X11,X0)
| c_HOL_Oord__class_Oless(X2,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f4377,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X3,X1,X2),X2) )
| ~ spl0_192
| ~ spl0_322 ),
inference(resolution,[],[f3597,f1959]) ).
fof(f1959,plain,
( ! [X2,X0,X11,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X11,X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0)
| ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X2,X11,X0) )
| ~ spl0_192 ),
inference(avatar_component_clause,[],[f1958]) ).
fof(f66875,plain,
( spl0_1077
| ~ spl0_195
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4357,f3592,f1970,f66873]) ).
fof(f66873,plain,
( spl0_1077
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(X4,c_Power_Opower__class_Opower(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X4,c_Power_Opower__class_Opower(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).
fof(f4357,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(X4,c_Power_Opower__class_Opower(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X4,c_Power_Opower__class_Opower(X3,X1,X2),X2) )
| ~ spl0_195
| ~ spl0_321 ),
inference(resolution,[],[f3593,f1971]) ).
fof(f66871,plain,
( spl0_1076
| ~ spl0_194
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4356,f3592,f1966,f66869]) ).
fof(f66869,plain,
( spl0_1076
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_Power_Opower__class_Opower(X3,X1,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_Power_Opower__class_Opower(X3,X0,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
fof(f4356,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_Power_Opower__class_Opower(X3,X1,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_Power_Opower__class_Opower(X3,X0,X2),X4,X2) )
| ~ spl0_194
| ~ spl0_321 ),
inference(resolution,[],[f3593,f1967]) ).
fof(f66867,plain,
( spl0_1075
| ~ spl0_190
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4355,f3592,f1950,f66865]) ).
fof(f66865,plain,
( spl0_1075
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X0,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f4355,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X0,X2),X4,X2) )
| ~ spl0_190
| ~ spl0_321 ),
inference(resolution,[],[f3593,f1951]) ).
fof(f66861,plain,
( spl0_1074
| ~ spl0_189
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4354,f3592,f1946,f66859]) ).
fof(f66859,plain,
( spl0_1074
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X3,X0,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f4354,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X3,X0,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X3,X1,X2),X2) )
| ~ spl0_189
| ~ spl0_321 ),
inference(resolution,[],[f3593,f1947]) ).
fof(f66857,plain,
( spl0_1073
| ~ spl0_188
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4353,f3592,f1942,f66855]) ).
fof(f66855,plain,
( spl0_1073
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X3,X0,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f4353,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X3,X0,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X3,X1,X2),X2) )
| ~ spl0_188
| ~ spl0_321 ),
inference(resolution,[],[f3593,f1943]) ).
fof(f66853,plain,
( spl0_1072
| ~ spl0_187
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4352,f3592,f1938,f66851]) ).
fof(f66851,plain,
( spl0_1072
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X0,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f4352,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X0,X2),X4,X2) )
| ~ spl0_187
| ~ spl0_321 ),
inference(resolution,[],[f3593,f1939]) ).
fof(f66849,plain,
( spl0_1071
| ~ spl0_195
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f4294,f3580,f1970,f66847]) ).
fof(f66847,plain,
( spl0_1071
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(X4,c_Power_Opower__class_Opower(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X4,c_Power_Opower__class_Opower(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f4294,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(X4,c_Power_Opower__class_Opower(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X4,c_Power_Opower__class_Opower(X3,X1,X2),X2) )
| ~ spl0_195
| ~ spl0_318 ),
inference(resolution,[],[f3581,f1971]) ).
fof(f66845,plain,
( spl0_1070
| ~ spl0_194
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f4293,f3580,f1966,f66843]) ).
fof(f66843,plain,
( spl0_1070
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_Power_Opower__class_Opower(X3,X1,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_Power_Opower__class_Opower(X3,X0,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f4293,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_Power_Opower__class_Opower(X3,X1,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_Power_Opower__class_Opower(X3,X0,X2),X4,X2) )
| ~ spl0_194
| ~ spl0_318 ),
inference(resolution,[],[f3581,f1967]) ).
fof(f66841,plain,
( spl0_1069
| ~ spl0_190
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f4292,f3580,f1950,f66839]) ).
fof(f66839,plain,
( spl0_1069
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X0,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f4292,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X0,X2),X4,X2) )
| ~ spl0_190
| ~ spl0_318 ),
inference(resolution,[],[f3581,f1951]) ).
fof(f66837,plain,
( spl0_1068
| ~ spl0_189
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f4291,f3580,f1946,f66835]) ).
fof(f66835,plain,
( spl0_1068
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X3,X0,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f4291,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X3,X0,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X3,X1,X2),X2) )
| ~ spl0_189
| ~ spl0_318 ),
inference(resolution,[],[f3581,f1947]) ).
fof(f66833,plain,
( spl0_1067
| ~ spl0_188
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f4290,f3580,f1942,f66831]) ).
fof(f66831,plain,
( spl0_1067
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X3,X0,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f4290,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X3,X0,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X3,X1,X2),X2) )
| ~ spl0_188
| ~ spl0_318 ),
inference(resolution,[],[f3581,f1943]) ).
fof(f66829,plain,
( spl0_1066
| ~ spl0_187
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f4289,f3580,f1938,f66827]) ).
fof(f66827,plain,
( spl0_1066
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X0,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f4289,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X0,X2),X4,X2) )
| ~ spl0_187
| ~ spl0_318 ),
inference(resolution,[],[f3581,f1939]) ).
fof(f66825,plain,
( spl0_1065
| ~ spl0_195
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f4240,f3568,f1970,f66823]) ).
fof(f66823,plain,
( spl0_1065
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X4,c_HOL_Otimes__class_Otimes(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f3568,plain,
( spl0_315
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_lessequals(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f4240,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X4,c_HOL_Otimes__class_Otimes(X0,X3,X2),X2) )
| ~ spl0_195
| ~ spl0_315 ),
inference(resolution,[],[f3569,f1971]) ).
fof(f3569,plain,
( ! [X3,X0,X1,X13] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_lessequals(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Opordered__ring(X0) )
| ~ spl0_315 ),
inference(avatar_component_clause,[],[f3568]) ).
fof(f66821,plain,
( ~ spl0_1
| spl0_1064
| ~ spl0_216
| ~ spl0_360 ),
inference(avatar_split_clause,[],[f5196,f5190,f2472,f66819,f691]) ).
fof(f66819,plain,
( spl0_1064
<=> ! [X0] :
( c_HOL_Oone__class_Oone(t_a) != c_HOL_Oinverse__class_Oinverse(X0,t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0
| c_HOL_Oone__class_Oone(t_a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f5190,plain,
( spl0_360
<=> ! [X0] : c_HOL_Oinverse__class_Oinverse(X0,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f5196,plain,
( ! [X0] :
( c_HOL_Oone__class_Oone(t_a) != c_HOL_Oinverse__class_Oinverse(X0,t_a)
| c_HOL_Oone__class_Oone(t_a) = X0
| c_HOL_Ozero__class_Ozero(t_a) = X0
| ~ class_Ring__and__Field_Ofield(t_a) )
| ~ spl0_216
| ~ spl0_360 ),
inference(superposition,[],[f2473,f5191]) ).
fof(f5191,plain,
( ! [X0] : c_HOL_Oinverse__class_Oinverse(X0,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),X0,t_a)
| ~ spl0_360 ),
inference(avatar_component_clause,[],[f5190]) ).
fof(f66817,plain,
( spl0_1063
| ~ spl0_194
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f4239,f3568,f1966,f66815]) ).
fof(f66815,plain,
( spl0_1063
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,X3,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f4239,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,X3,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),X4,X2) )
| ~ spl0_194
| ~ spl0_315 ),
inference(resolution,[],[f3569,f1967]) ).
fof(f66813,plain,
( spl0_1062
| ~ spl0_190
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f4238,f3568,f1950,f66811]) ).
fof(f66811,plain,
( spl0_1062
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).
fof(f4238,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),X4,X2) )
| ~ spl0_190
| ~ spl0_315 ),
inference(resolution,[],[f3569,f1951]) ).
fof(f66809,plain,
( spl0_1061
| ~ spl0_189
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f4237,f3568,f1946,f66807]) ).
fof(f66807,plain,
( spl0_1061
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f4237,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X0,X3,X2),X2) )
| ~ spl0_189
| ~ spl0_315 ),
inference(resolution,[],[f3569,f1947]) ).
fof(f66805,plain,
( spl0_1060
| ~ spl0_188
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f4236,f3568,f1942,f66803]) ).
fof(f66803,plain,
( spl0_1060
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f4236,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X0,X3,X2),X2) )
| ~ spl0_188
| ~ spl0_315 ),
inference(resolution,[],[f3569,f1943]) ).
fof(f66801,plain,
( spl0_1059
| ~ spl0_187
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f4235,f3568,f1938,f66799]) ).
fof(f66799,plain,
( spl0_1059
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f4235,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),X4,X2) )
| ~ spl0_187
| ~ spl0_315 ),
inference(resolution,[],[f3569,f1939]) ).
fof(f66797,plain,
( spl0_1058
| ~ spl0_195
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f4214,f3527,f1970,f66795]) ).
fof(f66795,plain,
( spl0_1058
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).
fof(f3527,plain,
( spl0_314
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_lessequals(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f4214,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) )
| ~ spl0_195
| ~ spl0_314 ),
inference(resolution,[],[f3528,f1971]) ).
fof(f3528,plain,
( ! [X3,X0,X1,X13] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_lessequals(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Opordered__ring(X0) )
| ~ spl0_314 ),
inference(avatar_component_clause,[],[f3527]) ).
fof(f66793,plain,
( spl0_1057
| ~ spl0_194
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f4213,f3527,f1966,f66791]) ).
fof(f66791,plain,
( spl0_1057
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f4213,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2) )
| ~ spl0_194
| ~ spl0_314 ),
inference(resolution,[],[f3528,f1967]) ).
fof(f66789,plain,
( spl0_1056
| ~ spl0_190
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f4212,f3527,f1950,f66787]) ).
fof(f66787,plain,
( spl0_1056
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f4212,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2) )
| ~ spl0_190
| ~ spl0_314 ),
inference(resolution,[],[f3528,f1951]) ).
fof(f66785,plain,
( spl0_1055
| ~ spl0_189
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f4211,f3527,f1946,f66783]) ).
fof(f66783,plain,
( spl0_1055
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f4211,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) )
| ~ spl0_189
| ~ spl0_314 ),
inference(resolution,[],[f3528,f1947]) ).
fof(f66781,plain,
( spl0_1054
| ~ spl0_188
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f4210,f3527,f1942,f66779]) ).
fof(f66779,plain,
( spl0_1054
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f4210,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) )
| ~ spl0_188
| ~ spl0_314 ),
inference(resolution,[],[f3528,f1943]) ).
fof(f66599,plain,
( spl0_1053
| ~ spl0_187
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f4209,f3527,f1938,f66597]) ).
fof(f66597,plain,
( spl0_1053
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f4209,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2) )
| ~ spl0_187
| ~ spl0_314 ),
inference(resolution,[],[f3528,f1939]) ).
fof(f66595,plain,
( spl0_1052
| ~ spl0_195
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f4188,f3523,f1970,f66593]) ).
fof(f66593,plain,
( spl0_1052
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X0,X3,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
fof(f4188,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X0,X3,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) )
| ~ spl0_195
| ~ spl0_313 ),
inference(resolution,[],[f3524,f1971]) ).
fof(f66591,plain,
( spl0_1051
| ~ spl0_194
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f4187,f3523,f1966,f66589]) ).
fof(f66589,plain,
( spl0_1051
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X3,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
fof(f4187,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X3,X2),X4,X2) )
| ~ spl0_194
| ~ spl0_313 ),
inference(resolution,[],[f3524,f1967]) ).
fof(f66587,plain,
( spl0_1050
| ~ spl0_190
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f4186,f3523,f1950,f66585]) ).
fof(f66585,plain,
( spl0_1050
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X3,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f4186,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X3,X2),X4,X2) )
| ~ spl0_190
| ~ spl0_313 ),
inference(resolution,[],[f3524,f1951]) ).
fof(f66583,plain,
( spl0_1049
| ~ spl0_189
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f4185,f3523,f1946,f66581]) ).
fof(f66581,plain,
( spl0_1049
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X0,X3,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f4185,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X0,X3,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) )
| ~ spl0_189
| ~ spl0_313 ),
inference(resolution,[],[f3524,f1947]) ).
fof(f66579,plain,
( spl0_1048
| ~ spl0_188
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f4184,f3523,f1942,f66577]) ).
fof(f66577,plain,
( spl0_1048
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X0,X3,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f4184,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X0,X3,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) )
| ~ spl0_188
| ~ spl0_313 ),
inference(resolution,[],[f3524,f1943]) ).
fof(f66575,plain,
( spl0_1047
| ~ spl0_187
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f4183,f3523,f1938,f66573]) ).
fof(f66573,plain,
( spl0_1047
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X3,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f4183,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X3,X2),X4,X2) )
| ~ spl0_187
| ~ spl0_313 ),
inference(resolution,[],[f3524,f1939]) ).
fof(f66571,plain,
( spl0_1046
| ~ spl0_195
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f4162,f3519,f1970,f66569]) ).
fof(f66569,plain,
( spl0_1046
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f3519,plain,
( spl0_312
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f4162,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) )
| ~ spl0_195
| ~ spl0_312 ),
inference(resolution,[],[f3520,f1971]) ).
fof(f3520,plain,
( ! [X3,X0,X1,X13] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ class_Ring__and__Field_Omult__mono(X0) )
| ~ spl0_312 ),
inference(avatar_component_clause,[],[f3519]) ).
fof(f66567,plain,
( spl0_1045
| ~ spl0_194
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f4161,f3519,f1966,f66565]) ).
fof(f66565,plain,
( spl0_1045
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f4161,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2) )
| ~ spl0_194
| ~ spl0_312 ),
inference(resolution,[],[f3520,f1967]) ).
fof(f66563,plain,
( spl0_1044
| ~ spl0_190
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f4160,f3519,f1950,f66561]) ).
fof(f66561,plain,
( spl0_1044
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f4160,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2) )
| ~ spl0_190
| ~ spl0_312 ),
inference(resolution,[],[f3520,f1951]) ).
fof(f66503,plain,
( spl0_1043
| ~ spl0_189
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f4159,f3519,f1946,f66501]) ).
fof(f66501,plain,
( spl0_1043
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).
fof(f4159,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) )
| ~ spl0_189
| ~ spl0_312 ),
inference(resolution,[],[f3520,f1947]) ).
fof(f66499,plain,
( spl0_1042
| ~ spl0_188
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f4158,f3519,f1942,f66497]) ).
fof(f66497,plain,
( spl0_1042
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).
fof(f4158,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) )
| ~ spl0_188
| ~ spl0_312 ),
inference(resolution,[],[f3520,f1943]) ).
fof(f66495,plain,
( spl0_1041
| ~ spl0_187
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f4157,f3519,f1938,f66493]) ).
fof(f66493,plain,
( spl0_1041
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).
fof(f4157,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2) )
| ~ spl0_187
| ~ spl0_312 ),
inference(resolution,[],[f3520,f1939]) ).
fof(f66491,plain,
( spl0_1040
| ~ spl0_195
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f4136,f3515,f1970,f66489]) ).
fof(f66489,plain,
( spl0_1040
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono1(X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f4136,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono1(X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) )
| ~ spl0_195
| ~ spl0_311 ),
inference(resolution,[],[f3516,f1971]) ).
fof(f66487,plain,
( spl0_1039
| ~ spl0_194
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f4135,f3515,f1966,f66485]) ).
fof(f66485,plain,
( spl0_1039
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono1(X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f4135,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono1(X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2) )
| ~ spl0_194
| ~ spl0_311 ),
inference(resolution,[],[f3516,f1967]) ).
fof(f66483,plain,
( spl0_1038
| ~ spl0_190
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f4134,f3515,f1950,f66481]) ).
fof(f66481,plain,
( spl0_1038
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono1(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f4134,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono1(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2) )
| ~ spl0_190
| ~ spl0_311 ),
inference(resolution,[],[f3516,f1951]) ).
fof(f66479,plain,
( spl0_1037
| ~ spl0_189
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f4133,f3515,f1946,f66477]) ).
fof(f66477,plain,
( spl0_1037
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono1(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f4133,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono1(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) )
| ~ spl0_189
| ~ spl0_311 ),
inference(resolution,[],[f3516,f1947]) ).
fof(f66475,plain,
( spl0_1036
| ~ spl0_188
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f4132,f3515,f1942,f66473]) ).
fof(f66473,plain,
( spl0_1036
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono1(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f4132,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono1(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) )
| ~ spl0_188
| ~ spl0_311 ),
inference(resolution,[],[f3516,f1943]) ).
fof(f66471,plain,
( spl0_1035
| ~ spl0_187
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f4131,f3515,f1938,f66469]) ).
fof(f66469,plain,
( spl0_1035
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono1(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
fof(f4131,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono1(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2) )
| ~ spl0_187
| ~ spl0_311 ),
inference(resolution,[],[f3516,f1939]) ).
fof(f66467,plain,
( spl0_1034
| ~ spl0_193
| ~ spl0_306 ),
inference(avatar_split_clause,[],[f4004,f3495,f1962,f66465]) ).
fof(f66465,plain,
( spl0_1034
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f3495,plain,
( spl0_306
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f4004,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2) )
| ~ spl0_193
| ~ spl0_306 ),
inference(resolution,[],[f3496,f1963]) ).
fof(f3496,plain,
( ! [X3,X0,X1,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0) )
| ~ spl0_306 ),
inference(avatar_component_clause,[],[f3495]) ).
fof(f65261,plain,
( spl0_1033
| ~ spl0_192
| ~ spl0_306 ),
inference(avatar_split_clause,[],[f4003,f3495,f1958,f65259]) ).
fof(f65259,plain,
( spl0_1033
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f4003,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) )
| ~ spl0_192
| ~ spl0_306 ),
inference(resolution,[],[f3496,f1959]) ).
fof(f65257,plain,
( spl0_1032
| ~ spl0_193
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3974,f3491,f1962,f65255]) ).
fof(f65255,plain,
( spl0_1032
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X3,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f3491,plain,
( spl0_305
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f3974,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X3,X2),X4,X2) )
| ~ spl0_193
| ~ spl0_305 ),
inference(resolution,[],[f3492,f1963]) ).
fof(f3492,plain,
( ! [X3,X0,X1,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_305 ),
inference(avatar_component_clause,[],[f3491]) ).
fof(f65253,plain,
( spl0_1031
| ~ spl0_192
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3973,f3491,f1958,f65251]) ).
fof(f65251,plain,
( spl0_1031
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X0,X3,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f3973,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X0,X3,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) )
| ~ spl0_192
| ~ spl0_305 ),
inference(resolution,[],[f3492,f1959]) ).
fof(f65249,plain,
( spl0_1030
| ~ spl0_193
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3945,f3459,f1962,f65247]) ).
fof(f65247,plain,
( spl0_1030
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X3,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).
fof(f3459,plain,
( spl0_304
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f3945,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X3,X2),X4,X2) )
| ~ spl0_193
| ~ spl0_304 ),
inference(resolution,[],[f3460,f1963]) ).
fof(f3460,plain,
( ! [X3,X0,X1,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0) )
| ~ spl0_304 ),
inference(avatar_component_clause,[],[f3459]) ).
fof(f65245,plain,
( spl0_1029
| ~ spl0_192
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3944,f3459,f1958,f65243]) ).
fof(f65243,plain,
( spl0_1029
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X0,X3,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f3944,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X0,X3,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) )
| ~ spl0_192
| ~ spl0_304 ),
inference(resolution,[],[f3460,f1959]) ).
fof(f65241,plain,
( spl0_1028
| ~ spl0_193
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f3917,f3455,f1962,f65239]) ).
fof(f65239,plain,
( spl0_1028
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X3,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f3455,plain,
( spl0_303
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f3917,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X3,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),X4,X2) )
| ~ spl0_193
| ~ spl0_303 ),
inference(resolution,[],[f3456,f1963]) ).
fof(f3456,plain,
( ! [X3,X0,X1,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_303 ),
inference(avatar_component_clause,[],[f3455]) ).
fof(f65237,plain,
( spl0_1027
| ~ spl0_192
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f3916,f3455,f1958,f65235]) ).
fof(f65235,plain,
( spl0_1027
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f3916,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X0,X3,X2),X2) )
| ~ spl0_192
| ~ spl0_303 ),
inference(resolution,[],[f3456,f1959]) ).
fof(f65233,plain,
( spl0_1026
| ~ spl0_193
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3887,f3451,f1962,f65231]) ).
fof(f65231,plain,
( spl0_1026
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f3451,plain,
( spl0_302
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f3887,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2) )
| ~ spl0_193
| ~ spl0_302 ),
inference(resolution,[],[f3452,f1963]) ).
fof(f3452,plain,
( ! [X3,X0,X1,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_302 ),
inference(avatar_component_clause,[],[f3451]) ).
fof(f65229,plain,
( spl0_1025
| ~ spl0_192
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3886,f3451,f1958,f65227]) ).
fof(f65227,plain,
( spl0_1025
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f3886,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) )
| ~ spl0_192
| ~ spl0_302 ),
inference(resolution,[],[f3452,f1959]) ).
fof(f65225,plain,
( spl0_1024
| ~ spl0_193
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3857,f3447,f1962,f65223]) ).
fof(f65223,plain,
( spl0_1024
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f3447,plain,
( spl0_301
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f3857,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2) )
| ~ spl0_193
| ~ spl0_301 ),
inference(resolution,[],[f3448,f1963]) ).
fof(f3448,plain,
( ! [X3,X0,X1,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0) )
| ~ spl0_301 ),
inference(avatar_component_clause,[],[f3447]) ).
fof(f65221,plain,
( spl0_1023
| ~ spl0_839
| ~ spl0_933 ),
inference(avatar_split_clause,[],[f50850,f48349,f33875,f65219]) ).
fof(f65219,plain,
( spl0_1023
<=> ! [X2,X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X0,X1,t_a),X2,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X0,t_a),X2,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f33875,plain,
( spl0_839
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Odivide(X0,X1,t_a),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X0,X2,t_a),X1,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f48349,plain,
( spl0_933
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(X2,X0,t_a),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X2,t_a),X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f50850,plain,
( ! [X2,X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X0,X1,t_a),X2,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X0,t_a),X2,t_a)
| ~ spl0_839
| ~ spl0_933 ),
inference(superposition,[],[f48350,f33876]) ).
fof(f33876,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Odivide(X0,X1,t_a),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X0,X2,t_a),X1,t_a)
| ~ spl0_839 ),
inference(avatar_component_clause,[],[f33875]) ).
fof(f48350,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(X2,X0,t_a),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X2,t_a),X0,t_a)
| ~ spl0_933 ),
inference(avatar_component_clause,[],[f48349]) ).
fof(f65217,plain,
( spl0_1022
| ~ spl0_192
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3856,f3447,f1958,f65215]) ).
fof(f65215,plain,
( spl0_1022
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f3856,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) )
| ~ spl0_192
| ~ spl0_301 ),
inference(resolution,[],[f3448,f1959]) ).
fof(f65213,plain,
( spl0_1021
| ~ spl0_193
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3829,f3443,f1962,f65211]) ).
fof(f65211,plain,
( spl0_1021
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f3443,plain,
( spl0_300
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f3829,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2) )
| ~ spl0_193
| ~ spl0_300 ),
inference(resolution,[],[f3444,f1963]) ).
fof(f3444,plain,
( ! [X3,X0,X1,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_300 ),
inference(avatar_component_clause,[],[f3443]) ).
fof(f65209,plain,
( spl0_1020
| ~ spl0_192
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3828,f3443,f1958,f65207]) ).
fof(f65207,plain,
( spl0_1020
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f3828,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) )
| ~ spl0_192
| ~ spl0_300 ),
inference(resolution,[],[f3444,f1959]) ).
fof(f65205,plain,
( spl0_1019
| ~ spl0_195
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f3772,f3431,f1970,f65203]) ).
fof(f65203,plain,
( spl0_1019
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f3431,plain,
( spl0_297
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f3772,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) )
| ~ spl0_195
| ~ spl0_297 ),
inference(resolution,[],[f3432,f1971]) ).
fof(f3432,plain,
( ! [X3,X0,X1,X13] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_297 ),
inference(avatar_component_clause,[],[f3431]) ).
fof(f65201,plain,
( spl0_1018
| ~ spl0_194
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f3771,f3431,f1966,f65199]) ).
fof(f65199,plain,
( spl0_1018
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f3771,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2) )
| ~ spl0_194
| ~ spl0_297 ),
inference(resolution,[],[f3432,f1967]) ).
fof(f65197,plain,
( spl0_1017
| ~ spl0_190
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f3770,f3431,f1950,f65195]) ).
fof(f65195,plain,
( spl0_1017
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f3770,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2) )
| ~ spl0_190
| ~ spl0_297 ),
inference(resolution,[],[f3432,f1951]) ).
fof(f65193,plain,
( spl0_1016
| ~ spl0_189
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f3769,f3431,f1946,f65191]) ).
fof(f65191,plain,
( spl0_1016
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f3769,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) )
| ~ spl0_189
| ~ spl0_297 ),
inference(resolution,[],[f3432,f1947]) ).
fof(f65189,plain,
( spl0_1015
| ~ spl0_188
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f3768,f3431,f1942,f65187]) ).
fof(f65187,plain,
( spl0_1015
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f3768,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) )
| ~ spl0_188
| ~ spl0_297 ),
inference(resolution,[],[f3432,f1943]) ).
fof(f65185,plain,
( spl0_1014
| ~ spl0_187
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f3767,f3431,f1938,f65183]) ).
fof(f65183,plain,
( spl0_1014
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f3767,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2) )
| ~ spl0_187
| ~ spl0_297 ),
inference(resolution,[],[f3432,f1939]) ).
fof(f65181,plain,
( spl0_1013
| ~ spl0_195
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f3730,f3423,f1970,f65179]) ).
fof(f65179,plain,
( spl0_1013
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f3423,plain,
( spl0_295
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f3730,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) )
| ~ spl0_195
| ~ spl0_295 ),
inference(resolution,[],[f3424,f1971]) ).
fof(f3424,plain,
( ! [X3,X0,X1,X13] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_295 ),
inference(avatar_component_clause,[],[f3423]) ).
fof(f65177,plain,
( spl0_1012
| ~ spl0_484
| ~ spl0_860 ),
inference(avatar_split_clause,[],[f40140,f39932,f12230,f65175]) ).
fof(f65175,plain,
( spl0_1012
<=> ! [X0,X1] :
( c_HOL_Oinverse__class_Oinverse(X0,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Odivide(X1,X1,t_a),X0,t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).
fof(f40140,plain,
( ! [X0,X1] :
( c_HOL_Oinverse__class_Oinverse(X0,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Odivide(X1,X1,t_a),X0,t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X1 )
| ~ spl0_484
| ~ spl0_860 ),
inference(superposition,[],[f39933,f12231]) ).
fof(f65173,plain,
( spl0_1011
| ~ spl0_194
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f3729,f3423,f1966,f65171]) ).
fof(f65171,plain,
( spl0_1011
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
fof(f3729,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2) )
| ~ spl0_194
| ~ spl0_295 ),
inference(resolution,[],[f3424,f1967]) ).
fof(f65169,plain,
( spl0_1010
| ~ spl0_190
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f3728,f3423,f1950,f65167]) ).
fof(f65167,plain,
( spl0_1010
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
fof(f3728,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2) )
| ~ spl0_190
| ~ spl0_295 ),
inference(resolution,[],[f3424,f1951]) ).
fof(f65165,plain,
( spl0_1009
| ~ spl0_189
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f3727,f3423,f1946,f65163]) ).
fof(f65163,plain,
( spl0_1009
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
fof(f3727,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) )
| ~ spl0_189
| ~ spl0_295 ),
inference(resolution,[],[f3424,f1947]) ).
fof(f65161,plain,
( spl0_1008
| ~ spl0_188
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f3726,f3423,f1942,f65159]) ).
fof(f65159,plain,
( spl0_1008
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
fof(f3726,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) )
| ~ spl0_188
| ~ spl0_295 ),
inference(resolution,[],[f3424,f1943]) ).
fof(f65157,plain,
( spl0_1007
| ~ spl0_187
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f3725,f3423,f1938,f65155]) ).
fof(f65155,plain,
( spl0_1007
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f3725,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),X4,X2) )
| ~ spl0_187
| ~ spl0_295 ),
inference(resolution,[],[f3424,f1939]) ).
fof(f65153,plain,
( spl0_1006
| ~ spl0_215
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2719,f2636,f2297,f65151]) ).
fof(f65151,plain,
( spl0_1006
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X3,tc_nat)
| ~ c_lessequals(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f2636,plain,
( spl0_235
<=> ! [X13,X1,X3] :
( ~ c_lessequals(X13,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X13,tc_nat),c_HOL_Ominus__class_Ominus(X3,X13,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f2719,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X3,tc_nat)
| ~ c_lessequals(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) )
| ~ spl0_215
| ~ spl0_235 ),
inference(superposition,[],[f2637,f2298]) ).
fof(f2637,plain,
( ! [X3,X1,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X13,tc_nat),c_HOL_Ominus__class_Ominus(X3,X13,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_lessequals(X13,X1,tc_nat) )
| ~ spl0_235 ),
inference(avatar_component_clause,[],[f2636]) ).
fof(f65149,plain,
( spl0_1005
| ~ spl0_215
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2701,f2632,f2297,f65147]) ).
fof(f65147,plain,
( spl0_1005
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X3,tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f2632,plain,
( spl0_234
<=> ! [X9,X21,X19] :
( ~ c_HOL_Oord__class_Oless(X19,X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(X19,X21,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X21,X9,tc_nat),c_HOL_Ominus__class_Ominus(X21,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f2701,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X3,tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) )
| ~ spl0_215
| ~ spl0_234 ),
inference(superposition,[],[f2633,f2298]) ).
fof(f2633,plain,
( ! [X21,X19,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X21,X9,tc_nat),c_HOL_Ominus__class_Ominus(X21,X19,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X19,X21,tc_nat)
| ~ c_HOL_Oord__class_Oless(X19,X9,tc_nat) )
| ~ spl0_234 ),
inference(avatar_component_clause,[],[f2632]) ).
fof(f65145,plain,
( spl0_1004
| ~ spl0_215
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2696,f2632,f2297,f65143]) ).
fof(f65143,plain,
( spl0_1004
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f2696,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) )
| ~ spl0_215
| ~ spl0_234 ),
inference(superposition,[],[f2633,f2298]) ).
fof(f64849,plain,
( spl0_1003
| ~ spl0_285
| ~ spl0_691
| ~ spl0_737 ),
inference(avatar_split_clause,[],[f28025,f24905,f21490,f3088,f64847]) ).
fof(f64847,plain,
( spl0_1003
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,t_a),X2,t_a) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X0,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f21490,plain,
( spl0_691
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,t_a),t_a) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X0,X2,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f24905,plain,
( spl0_737
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X1,X0,t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f28025,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,t_a),X2,t_a) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X0,t_a),t_a)
| ~ spl0_285
| ~ spl0_691
| ~ spl0_737 ),
inference(forward_demodulation,[],[f27601,f3089]) ).
fof(f27601,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X0,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,t_a),c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(t_a),t_a),t_a)
| ~ spl0_691
| ~ spl0_737 ),
inference(superposition,[],[f21491,f24906]) ).
fof(f24906,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X1,X0,t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,t_a),c_HOL_Oone__class_Oone(t_a),t_a)
| ~ spl0_737 ),
inference(avatar_component_clause,[],[f24905]) ).
fof(f21491,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,t_a),t_a) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X0,X2,t_a),t_a)
| ~ spl0_691 ),
inference(avatar_component_clause,[],[f21490]) ).
fof(f48832,plain,
( spl0_1002
| ~ spl0_47
| ~ spl0_55
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f4881,f4851,f961,f921,f48830]) ).
fof(f48830,plain,
( spl0_1002
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,X1,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(X2,tc_Int_Oint),tc_Int_Oint) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,c_Int_Onumber__class_Onumber__of(X2,tc_Int_Oint),tc_Int_Oint),c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
fof(f921,plain,
( spl0_47
<=> class_Ring__and__Field_Oring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f961,plain,
( spl0_55
<=> class_Int_Onumber(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f4851,plain,
( spl0_347
<=> ! [X20,X0,X3,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X3,X0),c_Int_Onumber__class_Onumber__of(X20,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X20,X0),X0),c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X20,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f4881,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(tc_Int_Oint)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,X1,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(X2,tc_Int_Oint),tc_Int_Oint) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,c_Int_Onumber__class_Onumber__of(X2,tc_Int_Oint),tc_Int_Oint),c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint) )
| ~ spl0_55
| ~ spl0_347 ),
inference(resolution,[],[f4852,f963]) ).
fof(f963,plain,
( class_Int_Onumber(tc_Int_Oint)
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f961]) ).
fof(f4852,plain,
( ! [X3,X0,X1,X20] :
( ~ class_Int_Onumber(X0)
| ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X3,X0),c_Int_Onumber__class_Onumber__of(X20,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X20,X0),X0),c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X20,X0),X0),X0) )
| ~ spl0_347 ),
inference(avatar_component_clause,[],[f4851]) ).
fof(f48772,plain,
( spl0_1001
| ~ spl0_47
| ~ spl0_55
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f4879,f4847,f961,f921,f48770]) ).
fof(f48770,plain,
( spl0_1001
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X0,tc_Int_Oint),c_HOL_Ominus__class_Ominus(X1,X2,tc_Int_Oint),tc_Int_Oint) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X0,tc_Int_Oint),X1,tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X0,tc_Int_Oint),X2,tc_Int_Oint),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f4847,plain,
( spl0_346
<=> ! [X13,X0,X3,X20] :
( ~ class_Ring__and__Field_Oring(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X20,X0),c_HOL_Ominus__class_Ominus(X3,X13,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X20,X0),X3,X0),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X20,X0),X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f4879,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(tc_Int_Oint)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X0,tc_Int_Oint),c_HOL_Ominus__class_Ominus(X1,X2,tc_Int_Oint),tc_Int_Oint) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X0,tc_Int_Oint),X1,tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X0,tc_Int_Oint),X2,tc_Int_Oint),tc_Int_Oint) )
| ~ spl0_55
| ~ spl0_346 ),
inference(resolution,[],[f4848,f963]) ).
fof(f4848,plain,
( ! [X3,X0,X13,X20] :
( ~ class_Int_Onumber(X0)
| ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X20,X0),c_HOL_Ominus__class_Ominus(X3,X13,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X20,X0),X3,X0),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X20,X0),X13,X0),X0) )
| ~ spl0_346 ),
inference(avatar_component_clause,[],[f4847]) ).
fof(f48768,plain,
( spl0_999
| ~ spl0_1000
| ~ spl0_22
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f4878,f4847,f796,f48765,f48762]) ).
fof(f48762,plain,
( spl0_999
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X0,tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X0,tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X0,tc_nat),X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f48765,plain,
( spl0_1000
<=> class_Ring__and__Field_Oring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f796,plain,
( spl0_22
<=> class_Int_Onumber(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f4878,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(tc_nat)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X0,tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X0,tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X0,tc_nat),X2,tc_nat),tc_nat) )
| ~ spl0_22
| ~ spl0_346 ),
inference(resolution,[],[f4848,f798]) ).
fof(f798,plain,
( class_Int_Onumber(tc_nat)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f796]) ).
fof(f48712,plain,
( ~ spl0_8
| spl0_998
| ~ spl0_97
| ~ spl0_341 ),
inference(avatar_split_clause,[],[f4797,f4767,f1159,f48710,f726]) ).
fof(f48710,plain,
( spl0_998
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X2,X1,tc_nat),c_Power_Opower__class_Opower(X2,X0,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
fof(f4797,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X2,X1,tc_nat),c_Power_Opower__class_Opower(X2,X0,tc_nat),tc_nat) )
| ~ spl0_97
| ~ spl0_341 ),
inference(resolution,[],[f4768,f1160]) ).
fof(f48607,plain,
( ~ spl0_8
| spl0_997
| ~ spl0_97
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f4777,f4763,f1159,f48605,f726]) ).
fof(f48605,plain,
( spl0_997
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X0,X2,tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f4777,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X0,X2,tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat) )
| ~ spl0_97
| ~ spl0_340 ),
inference(resolution,[],[f4764,f1160]) ).
fof(f48603,plain,
( spl0_996
| ~ spl0_136
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f4712,f4680,f1363,f48601]) ).
fof(f48601,plain,
( spl0_996
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
fof(f4712,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) )
| ~ spl0_136
| ~ spl0_335 ),
inference(resolution,[],[f4681,f1364]) ).
fof(f48599,plain,
( spl0_995
| ~ spl0_134
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f4711,f4680,f1355,f48597]) ).
fof(f48597,plain,
( spl0_995
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
fof(f4711,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) )
| ~ spl0_134
| ~ spl0_335 ),
inference(resolution,[],[f4681,f1356]) ).
fof(f48595,plain,
( spl0_994
| ~ spl0_136
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4688,f4676,f1363,f48593]) ).
fof(f48593,plain,
( spl0_994
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X2,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f4688,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X2,X0,X1),X1) )
| ~ spl0_136
| ~ spl0_334 ),
inference(resolution,[],[f4677,f1364]) ).
fof(f48591,plain,
( spl0_993
| ~ spl0_134
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4687,f4676,f1355,f48589]) ).
fof(f48589,plain,
( spl0_993
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X2,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
fof(f4687,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X2,X0,X1),X1) )
| ~ spl0_134
| ~ spl0_334 ),
inference(resolution,[],[f4677,f1356]) ).
fof(f48587,plain,
( spl0_992
| ~ spl0_193
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3369,f2994,f1962,f48585]) ).
fof(f48585,plain,
( spl0_992
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X1),X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f2994,plain,
( spl0_279
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f3369,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X1),X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1) )
| ~ spl0_193
| ~ spl0_279 ),
inference(resolution,[],[f2995,f1963]) ).
fof(f2995,plain,
( ! [X0,X1,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_279 ),
inference(avatar_component_clause,[],[f2994]) ).
fof(f48583,plain,
( spl0_991
| ~ spl0_192
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3368,f2994,f1958,f48581]) ).
fof(f48581,plain,
( spl0_991
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_HOL_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X2,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f3368,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_HOL_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X2,X0,X1),X1) )
| ~ spl0_192
| ~ spl0_279 ),
inference(resolution,[],[f2995,f1959]) ).
fof(f48579,plain,
( spl0_990
| ~ spl0_193
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f3361,f2990,f1962,f48577]) ).
fof(f48577,plain,
( spl0_990
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X0),X0),X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
fof(f2990,plain,
( spl0_278
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X9,X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X9,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f3361,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X0),X0),X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0) )
| ~ spl0_193
| ~ spl0_278 ),
inference(resolution,[],[f2991,f1963]) ).
fof(f2991,plain,
( ! [X0,X1,X9] :
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X9,X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X9,X0),X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_278 ),
inference(avatar_component_clause,[],[f2990]) ).
fof(f48575,plain,
( spl0_989
| ~ spl0_192
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f3360,f2990,f1958,f48573]) ).
fof(f48573,plain,
( spl0_989
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X1,X3,X0),X0)
| ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X3,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f3360,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X1,X3,X0),X0)
| ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X3,X0),X0),X0) )
| ~ spl0_192
| ~ spl0_278 ),
inference(resolution,[],[f2991,f1959]) ).
fof(f48571,plain,
( spl0_988
| ~ spl0_361
| ~ spl0_484
| ~ spl0_839 ),
inference(avatar_split_clause,[],[f45930,f33875,f12230,f5201,f48569]) ).
fof(f48569,plain,
( spl0_988
<=> ! [X2,X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Odivide(X1,X2,t_a),X0,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Odivide(X1,X0,t_a),X2,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f45930,plain,
( ! [X2,X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Odivide(X1,X2,t_a),X0,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Odivide(X1,X0,t_a),X2,t_a)
| ~ spl0_361
| ~ spl0_484
| ~ spl0_839 ),
inference(forward_demodulation,[],[f45583,f5202]) ).
fof(f45583,plain,
( ! [X2,X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Odivide(X1,X2,t_a),X0,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X0,t_a),t_a),X2,t_a)
| ~ spl0_484
| ~ spl0_839 ),
inference(superposition,[],[f33876,f12231]) ).
fof(f48567,plain,
( spl0_987
| ~ spl0_193
| ~ spl0_277 ),
inference(avatar_split_clause,[],[f3353,f2986,f1962,f48565]) ).
fof(f48565,plain,
( spl0_987
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f2986,plain,
( spl0_277
<=> ! [X9,X0,X19] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X19,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X19,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f3353,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0) )
| ~ spl0_193
| ~ spl0_277 ),
inference(resolution,[],[f2987,f1963]) ).
fof(f2987,plain,
( ! [X0,X19,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X19,X9,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X19,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X9,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_277 ),
inference(avatar_component_clause,[],[f2986]) ).
fof(f48563,plain,
( spl0_986
| ~ spl0_192
| ~ spl0_277 ),
inference(avatar_split_clause,[],[f3352,f2986,f1958,f48561]) ).
fof(f48561,plain,
( spl0_986
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f3352,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) )
| ~ spl0_192
| ~ spl0_277 ),
inference(resolution,[],[f2987,f1959]) ).
fof(f48559,plain,
( spl0_985
| ~ spl0_195
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f3338,f2982,f1970,f48557]) ).
fof(f48557,plain,
( spl0_985
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f3338,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_195
| ~ spl0_276 ),
inference(resolution,[],[f2983,f1971]) ).
fof(f48555,plain,
( spl0_984
| ~ spl0_194
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f3337,f2982,f1966,f48553]) ).
fof(f48553,plain,
( spl0_984
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f3337,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1) )
| ~ spl0_194
| ~ spl0_276 ),
inference(resolution,[],[f2983,f1967]) ).
fof(f48551,plain,
( spl0_983
| ~ spl0_190
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f3336,f2982,f1950,f48549]) ).
fof(f48549,plain,
( spl0_983
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f3336,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1) )
| ~ spl0_190
| ~ spl0_276 ),
inference(resolution,[],[f2983,f1951]) ).
fof(f48547,plain,
( spl0_982
| ~ spl0_189
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f3335,f2982,f1946,f48545]) ).
fof(f48545,plain,
( spl0_982
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f3335,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_189
| ~ spl0_276 ),
inference(resolution,[],[f2983,f1947]) ).
fof(f48543,plain,
( spl0_981
| ~ spl0_188
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f3334,f2982,f1942,f48541]) ).
fof(f48541,plain,
( spl0_981
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f3334,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_188
| ~ spl0_276 ),
inference(resolution,[],[f2983,f1943]) ).
fof(f48539,plain,
( spl0_980
| ~ spl0_187
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f3333,f2982,f1938,f48537]) ).
fof(f48537,plain,
( spl0_980
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f3333,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1) )
| ~ spl0_187
| ~ spl0_276 ),
inference(resolution,[],[f2983,f1939]) ).
fof(f48535,plain,
( spl0_979
| ~ spl0_195
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f3316,f2978,f1970,f48533]) ).
fof(f48533,plain,
( spl0_979
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f3316,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_195
| ~ spl0_275 ),
inference(resolution,[],[f2979,f1971]) ).
fof(f48531,plain,
( spl0_978
| ~ spl0_194
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f3315,f2978,f1966,f48529]) ).
fof(f48529,plain,
( spl0_978
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X0,X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f3315,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X0,X1),X3,X1) )
| ~ spl0_194
| ~ spl0_275 ),
inference(resolution,[],[f2979,f1967]) ).
fof(f48527,plain,
( spl0_977
| ~ spl0_283
| ~ spl0_735
| ~ spl0_838 ),
inference(avatar_split_clause,[],[f44530,f32647,f22784,f3010,f48525]) ).
fof(f48525,plain,
( spl0_977
<=> ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X0,t_a),c_HOL_Oinverse__class_Oinverse(X0,t_a),t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f3010,plain,
( spl0_283
<=> ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),X0,t_a) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f32647,plain,
( spl0_838
<=> ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Otimes__class_Otimes(X1,X0,t_a),t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f44530,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X0,t_a),c_HOL_Oinverse__class_Oinverse(X0,t_a),t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_283
| ~ spl0_735
| ~ spl0_838 ),
inference(forward_demodulation,[],[f44223,f3011]) ).
fof(f3011,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),X0,t_a) = X0
| ~ spl0_283 ),
inference(avatar_component_clause,[],[f3010]) ).
fof(f44223,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),X1,t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X0,t_a),c_HOL_Oinverse__class_Oinverse(X0,t_a),t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_735
| ~ spl0_838 ),
inference(superposition,[],[f22785,f32648]) ).
fof(f32648,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Otimes__class_Otimes(X1,X0,t_a),t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_838 ),
inference(avatar_component_clause,[],[f32647]) ).
fof(f48523,plain,
( spl0_976
| ~ spl0_190
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f3314,f2978,f1950,f48521]) ).
fof(f48521,plain,
( spl0_976
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f3314,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,X1),X3,X1) )
| ~ spl0_190
| ~ spl0_275 ),
inference(resolution,[],[f2979,f1951]) ).
fof(f48519,plain,
( spl0_975
| ~ spl0_189
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f3313,f2978,f1946,f48517]) ).
fof(f48517,plain,
( spl0_975
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f3313,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_189
| ~ spl0_275 ),
inference(resolution,[],[f2979,f1947]) ).
fof(f48515,plain,
( spl0_974
| ~ spl0_188
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f3312,f2978,f1942,f48513]) ).
fof(f48513,plain,
( spl0_974
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f3312,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_188
| ~ spl0_275 ),
inference(resolution,[],[f2979,f1943]) ).
fof(f48511,plain,
( spl0_973
| ~ spl0_187
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f3311,f2978,f1938,f48509]) ).
fof(f48509,plain,
( spl0_973
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f3311,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,X1),X3,X1) )
| ~ spl0_187
| ~ spl0_275 ),
inference(resolution,[],[f2979,f1939]) ).
fof(f48507,plain,
( spl0_972
| ~ spl0_195
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3292,f2974,f1970,f48505]) ).
fof(f48505,plain,
( spl0_972
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f3292,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_195
| ~ spl0_274 ),
inference(resolution,[],[f2975,f1971]) ).
fof(f48503,plain,
( spl0_971
| ~ spl0_194
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3291,f2974,f1966,f48501]) ).
fof(f48501,plain,
( spl0_971
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f3291,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1) )
| ~ spl0_194
| ~ spl0_274 ),
inference(resolution,[],[f2975,f1967]) ).
fof(f48499,plain,
( spl0_970
| ~ spl0_190
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3290,f2974,f1950,f48497]) ).
fof(f48497,plain,
( spl0_970
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f3290,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1) )
| ~ spl0_190
| ~ spl0_274 ),
inference(resolution,[],[f2975,f1951]) ).
fof(f48495,plain,
( spl0_969
| ~ spl0_189
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3289,f2974,f1946,f48493]) ).
fof(f48493,plain,
( spl0_969
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
fof(f3289,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_189
| ~ spl0_274 ),
inference(resolution,[],[f2975,f1947]) ).
fof(f48491,plain,
( spl0_968
| ~ spl0_188
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3288,f2974,f1942,f48489]) ).
fof(f48489,plain,
( spl0_968
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).
fof(f3288,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_188
| ~ spl0_274 ),
inference(resolution,[],[f2975,f1943]) ).
fof(f48487,plain,
( spl0_967
| ~ spl0_187
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3287,f2974,f1938,f48485]) ).
fof(f48485,plain,
( spl0_967
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f3287,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1) )
| ~ spl0_187
| ~ spl0_274 ),
inference(resolution,[],[f2975,f1939]) ).
fof(f48483,plain,
( spl0_966
| ~ spl0_283
| ~ spl0_735
| ~ spl0_835 ),
inference(avatar_split_clause,[],[f39862,f28834,f22784,f3010,f48481]) ).
fof(f48481,plain,
( spl0_966
<=> ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,t_a),c_HOL_Oinverse__class_Oinverse(X0,t_a),t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f28834,plain,
( spl0_835
<=> ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Otimes__class_Otimes(X0,X1,t_a),t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f39862,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,t_a),c_HOL_Oinverse__class_Oinverse(X0,t_a),t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_283
| ~ spl0_735
| ~ spl0_835 ),
inference(forward_demodulation,[],[f39559,f3011]) ).
fof(f39559,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),X1,t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,t_a),c_HOL_Oinverse__class_Oinverse(X0,t_a),t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_735
| ~ spl0_835 ),
inference(superposition,[],[f22785,f28835]) ).
fof(f28835,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Otimes__class_Otimes(X0,X1,t_a),t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_835 ),
inference(avatar_component_clause,[],[f28834]) ).
fof(f48479,plain,
( spl0_965
| ~ spl0_195
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f3268,f2970,f1970,f48477]) ).
fof(f48477,plain,
( spl0_965
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f3268,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_195
| ~ spl0_273 ),
inference(resolution,[],[f2971,f1971]) ).
fof(f48475,plain,
( spl0_964
| ~ spl0_194
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f3267,f2970,f1966,f48473]) ).
fof(f48473,plain,
( spl0_964
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X0,X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f3267,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X0,X1),X3,X1) )
| ~ spl0_194
| ~ spl0_273 ),
inference(resolution,[],[f2971,f1967]) ).
fof(f48471,plain,
( spl0_963
| ~ spl0_190
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f3266,f2970,f1950,f48469]) ).
fof(f48469,plain,
( spl0_963
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f3266,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,X1),X3,X1) )
| ~ spl0_190
| ~ spl0_273 ),
inference(resolution,[],[f2971,f1951]) ).
fof(f48467,plain,
( spl0_962
| ~ spl0_189
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f3265,f2970,f1946,f48465]) ).
fof(f48465,plain,
( spl0_962
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f3265,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_189
| ~ spl0_273 ),
inference(resolution,[],[f2971,f1947]) ).
fof(f48463,plain,
( spl0_961
| ~ spl0_188
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f3264,f2970,f1942,f48461]) ).
fof(f48461,plain,
( spl0_961
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f3264,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_188
| ~ spl0_273 ),
inference(resolution,[],[f2971,f1943]) ).
fof(f48459,plain,
( spl0_960
| ~ spl0_187
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f3263,f2970,f1938,f48457]) ).
fof(f48457,plain,
( spl0_960
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f3263,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,X1),X3,X1) )
| ~ spl0_187
| ~ spl0_273 ),
inference(resolution,[],[f2971,f1939]) ).
fof(f48455,plain,
( spl0_959
| ~ spl0_195
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f3200,f2946,f1970,f48453]) ).
fof(f48453,plain,
( spl0_959
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f3200,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) )
| ~ spl0_195
| ~ spl0_267 ),
inference(resolution,[],[f2947,f1971]) ).
fof(f48451,plain,
( spl0_958
| ~ spl0_194
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f3199,f2946,f1966,f48449]) ).
fof(f48449,plain,
( spl0_958
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f3199,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0) )
| ~ spl0_194
| ~ spl0_267 ),
inference(resolution,[],[f2947,f1967]) ).
fof(f48447,plain,
( spl0_957
| ~ spl0_190
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f3198,f2946,f1950,f48445]) ).
fof(f48445,plain,
( spl0_957
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f3198,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) )
| ~ spl0_190
| ~ spl0_267 ),
inference(resolution,[],[f2947,f1951]) ).
fof(f48443,plain,
( spl0_956
| ~ spl0_189
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f3197,f2946,f1946,f48441]) ).
fof(f48441,plain,
( spl0_956
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f3197,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) )
| ~ spl0_189
| ~ spl0_267 ),
inference(resolution,[],[f2947,f1947]) ).
fof(f48439,plain,
( spl0_955
| ~ spl0_449
| ~ spl0_812 ),
inference(avatar_split_clause,[],[f36584,f28172,f9464,f48437]) ).
fof(f48437,plain,
( spl0_955
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X0,X1,t_a),t_a) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X0,X2,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f9464,plain,
( spl0_449
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,t_a) = c_HOL_Otimes__class_Otimes(X1,X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f28172,plain,
( spl0_812
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X0,t_a),X2,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f36584,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X0,X1,t_a),t_a) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X0,X2,t_a),t_a)
| ~ spl0_449
| ~ spl0_812 ),
inference(superposition,[],[f28173,f9465]) ).
fof(f9465,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,t_a) = c_HOL_Otimes__class_Otimes(X1,X0,t_a)
| ~ spl0_449 ),
inference(avatar_component_clause,[],[f9464]) ).
fof(f28173,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X0,t_a),X2,t_a)
| ~ spl0_812 ),
inference(avatar_component_clause,[],[f28172]) ).
fof(f48435,plain,
( spl0_954
| ~ spl0_188
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f3196,f2946,f1942,f48433]) ).
fof(f48433,plain,
( spl0_954
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f3196,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) )
| ~ spl0_188
| ~ spl0_267 ),
inference(resolution,[],[f2947,f1943]) ).
fof(f48431,plain,
( spl0_953
| ~ spl0_187
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f3195,f2946,f1938,f48429]) ).
fof(f48429,plain,
( spl0_953
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f3195,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) )
| ~ spl0_187
| ~ spl0_267 ),
inference(resolution,[],[f2947,f1939]) ).
fof(f48427,plain,
( spl0_952
| ~ spl0_195
| ~ spl0_266 ),
inference(avatar_split_clause,[],[f3182,f2942,f1970,f48425]) ).
fof(f48425,plain,
( spl0_952
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f3182,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) )
| ~ spl0_195
| ~ spl0_266 ),
inference(resolution,[],[f2943,f1971]) ).
fof(f48423,plain,
( spl0_951
| ~ spl0_194
| ~ spl0_266 ),
inference(avatar_split_clause,[],[f3181,f2942,f1966,f48421]) ).
fof(f48421,plain,
( spl0_951
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f3181,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) )
| ~ spl0_194
| ~ spl0_266 ),
inference(resolution,[],[f2943,f1967]) ).
fof(f48419,plain,
( spl0_950
| ~ spl0_190
| ~ spl0_266 ),
inference(avatar_split_clause,[],[f3180,f2942,f1950,f48417]) ).
fof(f48417,plain,
( spl0_950
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f3180,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) )
| ~ spl0_190
| ~ spl0_266 ),
inference(resolution,[],[f2943,f1951]) ).
fof(f48415,plain,
( spl0_949
| ~ spl0_189
| ~ spl0_266 ),
inference(avatar_split_clause,[],[f3179,f2942,f1946,f48413]) ).
fof(f48413,plain,
( spl0_949
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f3179,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) )
| ~ spl0_189
| ~ spl0_266 ),
inference(resolution,[],[f2943,f1947]) ).
fof(f48411,plain,
( spl0_948
| ~ spl0_188
| ~ spl0_266 ),
inference(avatar_split_clause,[],[f3178,f2942,f1942,f48409]) ).
fof(f48409,plain,
( spl0_948
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f3178,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) )
| ~ spl0_188
| ~ spl0_266 ),
inference(resolution,[],[f2943,f1943]) ).
fof(f48407,plain,
( spl0_947
| ~ spl0_187
| ~ spl0_266 ),
inference(avatar_split_clause,[],[f3177,f2942,f1938,f48405]) ).
fof(f48405,plain,
( spl0_947
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f3177,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) )
| ~ spl0_187
| ~ spl0_266 ),
inference(resolution,[],[f2943,f1939]) ).
fof(f48403,plain,
( spl0_946
| ~ spl0_195
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f3164,f2938,f1970,f48401]) ).
fof(f48401,plain,
( spl0_946
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f3164,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) )
| ~ spl0_195
| ~ spl0_265 ),
inference(resolution,[],[f2939,f1971]) ).
fof(f48399,plain,
( spl0_945
| ~ spl0_194
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f3163,f2938,f1966,f48397]) ).
fof(f48397,plain,
( spl0_945
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f3163,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0) )
| ~ spl0_194
| ~ spl0_265 ),
inference(resolution,[],[f2939,f1967]) ).
fof(f48395,plain,
( spl0_944
| ~ spl0_484
| ~ spl0_680 ),
inference(avatar_split_clause,[],[f22152,f21446,f12230,f48393]) ).
fof(f48393,plain,
( spl0_944
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X0,t_a),X2,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X1,t_a),X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f21446,plain,
( spl0_680
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,t_a),X2,t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,X1,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f22152,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X0,t_a),X2,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X1,t_a),X0,t_a)
| ~ spl0_484
| ~ spl0_680 ),
inference(forward_demodulation,[],[f21993,f12231]) ).
fof(f21993,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X0,t_a),X2,t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Otimes__class_Otimes(X2,X1,t_a),t_a)
| ~ spl0_484
| ~ spl0_680 ),
inference(superposition,[],[f21447,f12231]) ).
fof(f21447,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,t_a),X2,t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,X1,t_a),t_a)
| ~ spl0_680 ),
inference(avatar_component_clause,[],[f21446]) ).
fof(f48391,plain,
( spl0_943
| ~ spl0_190
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f3162,f2938,f1950,f48389]) ).
fof(f48389,plain,
( spl0_943
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f3162,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) )
| ~ spl0_190
| ~ spl0_265 ),
inference(resolution,[],[f2939,f1951]) ).
fof(f48387,plain,
( spl0_942
| ~ spl0_189
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f3161,f2938,f1946,f48385]) ).
fof(f48385,plain,
( spl0_942
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f3161,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) )
| ~ spl0_189
| ~ spl0_265 ),
inference(resolution,[],[f2939,f1947]) ).
fof(f48383,plain,
( spl0_941
| ~ spl0_188
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f3160,f2938,f1942,f48381]) ).
fof(f48381,plain,
( spl0_941
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f3160,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) )
| ~ spl0_188
| ~ spl0_265 ),
inference(resolution,[],[f2939,f1943]) ).
fof(f48379,plain,
( spl0_940
| ~ spl0_187
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f3159,f2938,f1938,f48377]) ).
fof(f48377,plain,
( spl0_940
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f3159,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) )
| ~ spl0_187
| ~ spl0_265 ),
inference(resolution,[],[f2939,f1939]) ).
fof(f48375,plain,
( spl0_939
| ~ spl0_195
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f3146,f2934,f1970,f48373]) ).
fof(f48373,plain,
( spl0_939
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f3146,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) )
| ~ spl0_195
| ~ spl0_264 ),
inference(resolution,[],[f2935,f1971]) ).
fof(f48371,plain,
( spl0_938
| ~ spl0_194
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f3145,f2934,f1966,f48369]) ).
fof(f48369,plain,
( spl0_938
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f3145,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) )
| ~ spl0_194
| ~ spl0_264 ),
inference(resolution,[],[f2935,f1967]) ).
fof(f48367,plain,
( spl0_937
| ~ spl0_190
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f3144,f2934,f1950,f48365]) ).
fof(f48365,plain,
( spl0_937
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f3144,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) )
| ~ spl0_190
| ~ spl0_264 ),
inference(resolution,[],[f2935,f1951]) ).
fof(f48363,plain,
( spl0_936
| ~ spl0_189
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f3143,f2934,f1946,f48361]) ).
fof(f48361,plain,
( spl0_936
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f3143,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) )
| ~ spl0_189
| ~ spl0_264 ),
inference(resolution,[],[f2935,f1947]) ).
fof(f48359,plain,
( spl0_935
| ~ spl0_188
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f3142,f2934,f1942,f48357]) ).
fof(f48357,plain,
( spl0_935
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f3142,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) )
| ~ spl0_188
| ~ spl0_264 ),
inference(resolution,[],[f2935,f1943]) ).
fof(f48355,plain,
( spl0_934
| ~ spl0_187
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f3141,f2934,f1938,f48353]) ).
fof(f48353,plain,
( spl0_934
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f3141,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) )
| ~ spl0_187
| ~ spl0_264 ),
inference(resolution,[],[f2935,f1939]) ).
fof(f48351,plain,
( spl0_933
| ~ spl0_361
| ~ spl0_484
| ~ spl0_669 ),
inference(avatar_split_clause,[],[f21694,f21402,f12230,f5201,f48349]) ).
fof(f21402,plain,
( spl0_669
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,t_a),X2,t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f21694,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(X2,X0,t_a),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X2,t_a),X0,t_a)
| ~ spl0_361
| ~ spl0_484
| ~ spl0_669 ),
inference(forward_demodulation,[],[f21693,f12231]) ).
fof(f21693,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Otimes__class_Otimes(X1,X2,t_a),t_a) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(X2,X0,t_a),t_a)
| ~ spl0_361
| ~ spl0_484
| ~ spl0_669 ),
inference(forward_demodulation,[],[f21542,f21687]) ).
fof(f21687,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X0,X1,t_a),X2,t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Odivide(X2,X1,t_a),t_a)
| ~ spl0_361
| ~ spl0_484
| ~ spl0_669 ),
inference(forward_demodulation,[],[f21537,f12231]) ).
fof(f21537,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,t_a),X2,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X0,X1,t_a),X2,t_a)
| ~ spl0_361
| ~ spl0_669 ),
inference(superposition,[],[f21403,f5202]) ).
fof(f21403,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,t_a),X2,t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,t_a),t_a)
| ~ spl0_669 ),
inference(avatar_component_clause,[],[f21402]) ).
fof(f21542,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Otimes__class_Otimes(X1,X2,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X0,t_a),X2,t_a)
| ~ spl0_484
| ~ spl0_669 ),
inference(superposition,[],[f21403,f12231]) ).
fof(f48347,plain,
( spl0_932
| ~ spl0_195
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f3128,f2930,f1970,f48345]) ).
fof(f48345,plain,
( spl0_932
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f3128,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) )
| ~ spl0_195
| ~ spl0_263 ),
inference(resolution,[],[f2931,f1971]) ).
fof(f48343,plain,
( spl0_931
| ~ spl0_194
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f3127,f2930,f1966,f48341]) ).
fof(f48341,plain,
( spl0_931
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f3127,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0) )
| ~ spl0_194
| ~ spl0_263 ),
inference(resolution,[],[f2931,f1967]) ).
fof(f48339,plain,
( spl0_930
| ~ spl0_190
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f3126,f2930,f1950,f48337]) ).
fof(f48337,plain,
( spl0_930
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f3126,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) )
| ~ spl0_190
| ~ spl0_263 ),
inference(resolution,[],[f2931,f1951]) ).
fof(f48335,plain,
( spl0_929
| ~ spl0_189
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f3125,f2930,f1946,f48333]) ).
fof(f48333,plain,
( spl0_929
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f3125,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) )
| ~ spl0_189
| ~ spl0_263 ),
inference(resolution,[],[f2931,f1947]) ).
fof(f48331,plain,
( spl0_928
| ~ spl0_188
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f3124,f2930,f1942,f48329]) ).
fof(f48329,plain,
( spl0_928
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f3124,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) )
| ~ spl0_188
| ~ spl0_263 ),
inference(resolution,[],[f2931,f1943]) ).
fof(f48327,plain,
( spl0_927
| ~ spl0_187
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f3123,f2930,f1938,f48325]) ).
fof(f48325,plain,
( spl0_927
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f3123,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) )
| ~ spl0_187
| ~ spl0_263 ),
inference(resolution,[],[f2931,f1939]) ).
fof(f48323,plain,
( spl0_926
| ~ spl0_193
| ~ spl0_258 ),
inference(avatar_split_clause,[],[f3100,f2909,f1962,f48321]) ).
fof(f48321,plain,
( spl0_926
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f2909,plain,
( spl0_258
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f3100,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X0,X1),X3,X1) )
| ~ spl0_193
| ~ spl0_258 ),
inference(resolution,[],[f2910,f1963]) ).
fof(f2910,plain,
( ! [X3,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0) )
| ~ spl0_258 ),
inference(avatar_component_clause,[],[f2909]) ).
fof(f48319,plain,
( spl0_925
| ~ spl0_192
| ~ spl0_258 ),
inference(avatar_split_clause,[],[f3099,f2909,f1958,f48317]) ).
fof(f48317,plain,
( spl0_925
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f3099,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_192
| ~ spl0_258 ),
inference(resolution,[],[f2910,f1959]) ).
fof(f48315,plain,
( spl0_924
| ~ spl0_193
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f3086,f2905,f1962,f48313]) ).
fof(f48313,plain,
( spl0_924
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f2905,plain,
( spl0_257
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f3086,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1) )
| ~ spl0_193
| ~ spl0_257 ),
inference(resolution,[],[f2906,f1963]) ).
fof(f2906,plain,
( ! [X3,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0) )
| ~ spl0_257 ),
inference(avatar_component_clause,[],[f2905]) ).
fof(f48311,plain,
( spl0_923
| ~ spl0_192
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f3085,f2905,f1958,f48309]) ).
fof(f48309,plain,
( spl0_923
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f3085,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_192
| ~ spl0_257 ),
inference(resolution,[],[f2906,f1959]) ).
fof(f48307,plain,
( spl0_922
| ~ spl0_363
| ~ spl0_484 ),
inference(avatar_split_clause,[],[f12564,f12230,f5479,f48305]) ).
fof(f48305,plain,
( spl0_922
<=> ! [X0,X1] :
( c_HOL_Oinverse__class_Oinverse(X0,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Odivide(X1,X0,t_a),X1,t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f12564,plain,
( ! [X0,X1] :
( c_HOL_Oinverse__class_Oinverse(X0,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Odivide(X1,X0,t_a),X1,t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X1 )
| ~ spl0_363
| ~ spl0_484 ),
inference(superposition,[],[f5480,f12231]) ).
fof(f48303,plain,
( spl0_921
| ~ spl0_193
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f3052,f2893,f1962,f48301]) ).
fof(f48301,plain,
( spl0_921
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f2893,plain,
( spl0_254
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f3052,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) )
| ~ spl0_193
| ~ spl0_254 ),
inference(resolution,[],[f2894,f1963]) ).
fof(f2894,plain,
( ! [X3,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0) )
| ~ spl0_254 ),
inference(avatar_component_clause,[],[f2893]) ).
fof(f48299,plain,
( spl0_920
| ~ spl0_192
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f3051,f2893,f1958,f48297]) ).
fof(f48297,plain,
( spl0_920
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f3051,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) )
| ~ spl0_192
| ~ spl0_254 ),
inference(resolution,[],[f2894,f1959]) ).
fof(f48295,plain,
( spl0_919
| ~ spl0_193
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3044,f2889,f1962,f48293]) ).
fof(f48293,plain,
( spl0_919
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f2889,plain,
( spl0_253
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f3044,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) )
| ~ spl0_193
| ~ spl0_253 ),
inference(resolution,[],[f2890,f1963]) ).
fof(f2890,plain,
( ! [X3,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_253 ),
inference(avatar_component_clause,[],[f2889]) ).
fof(f48291,plain,
( spl0_918
| ~ spl0_192
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3043,f2889,f1958,f48289]) ).
fof(f48289,plain,
( spl0_918
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f3043,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) )
| ~ spl0_192
| ~ spl0_253 ),
inference(resolution,[],[f2890,f1959]) ).
fof(f48287,plain,
( spl0_917
| ~ spl0_215
| ~ spl0_231 ),
inference(avatar_split_clause,[],[f2620,f2566,f2297,f48285]) ).
fof(f48285,plain,
( spl0_917
<=> ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f2566,plain,
( spl0_231
<=> ! [X9,X19] :
( X9 = X19
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X19,X9,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X9,X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f2620,plain,
( ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) )
| ~ spl0_215
| ~ spl0_231 ),
inference(superposition,[],[f2567,f2298]) ).
fof(f2567,plain,
( ! [X19,X9] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X19,X9,tc_nat)
| X9 = X19
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X9,X19,tc_nat) )
| ~ spl0_231 ),
inference(avatar_component_clause,[],[f2566]) ).
fof(f48283,plain,
( spl0_916
| ~ spl0_215
| ~ spl0_228 ),
inference(avatar_split_clause,[],[f2602,f2554,f2297,f48281]) ).
fof(f48281,plain,
( spl0_916
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f2554,plain,
( spl0_228
<=> ! [X9,X19] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X19,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X19,X9,tc_nat),X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f2602,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) )
| ~ spl0_215
| ~ spl0_228 ),
inference(superposition,[],[f2555,f2298]) ).
fof(f2555,plain,
( ! [X19,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X19,X9,tc_nat),X19,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X19,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat) )
| ~ spl0_228 ),
inference(avatar_component_clause,[],[f2554]) ).
fof(f47954,plain,
( spl0_915
| ~ spl0_459
| ~ spl0_484 ),
inference(avatar_split_clause,[],[f12545,f12230,f11244,f47952]) ).
fof(f47952,plain,
( spl0_915
<=> ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X0,X1,t_a) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oinverse__class_Oinverse(X0,t_a),t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f11244,plain,
( spl0_459
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(t_a) = X0
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X0,t_a),t_a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f12545,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X0,X1,t_a) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oinverse__class_Oinverse(X0,t_a),t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_459
| ~ spl0_484 ),
inference(superposition,[],[f12231,f11245]) ).
fof(f11245,plain,
( ! [X0] :
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X0,t_a),t_a) = X0
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_459 ),
inference(avatar_component_clause,[],[f11244]) ).
fof(f46637,plain,
( spl0_913
| spl0_914
| ~ spl0_317
| ~ spl0_342 ),
inference(avatar_split_clause,[],[f4833,f4771,f3576,f46635,f46632]) ).
fof(f46632,plain,
( spl0_913
<=> ! [X2,X3] :
( ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f46635,plain,
( spl0_914
<=> ! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f3576,plain,
( spl0_317
<=> ! [X19,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(X19,X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X19,X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f4833,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3) )
| ~ spl0_317
| ~ spl0_342 ),
inference(duplicate_literal_removal,[],[f4812]) ).
fof(f4812,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) )
| ~ spl0_317
| ~ spl0_342 ),
inference(resolution,[],[f4772,f3577]) ).
fof(f3577,plain,
( ! [X0,X1,X19,X9] :
( ~ c_lessequals(c_Power_Opower__class_Opower(X1,X19,X0),c_Power_Opower__class_Opower(X1,X9,X0),X0)
| c_lessequals(X19,X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_317 ),
inference(avatar_component_clause,[],[f3576]) ).
fof(f46586,plain,
( spl0_911
| spl0_912
| ~ spl0_323
| ~ spl0_341 ),
inference(avatar_split_clause,[],[f4810,f4767,f3600,f46584,f46581]) ).
fof(f46581,plain,
( spl0_911
<=> ! [X2,X3] :
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f46584,plain,
( spl0_912
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f4810,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3) )
| ~ spl0_323
| ~ spl0_341 ),
inference(duplicate_literal_removal,[],[f4795]) ).
fof(f4795,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) )
| ~ spl0_323
| ~ spl0_341 ),
inference(resolution,[],[f4768,f3601]) ).
fof(f46526,plain,
( spl0_909
| spl0_910
| ~ spl0_323
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f4790,f4763,f3600,f46524,f46521]) ).
fof(f46521,plain,
( spl0_909
<=> ! [X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f46524,plain,
( spl0_910
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f4790,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_HOL_Oord__class_Oless(X2,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X0,X1) )
| ~ spl0_323
| ~ spl0_340 ),
inference(duplicate_literal_removal,[],[f4775]) ).
fof(f4775,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_HOL_Oord__class_Oless(X2,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) )
| ~ spl0_323
| ~ spl0_340 ),
inference(resolution,[],[f4764,f3601]) ).
fof(f46480,plain,
( ~ spl0_8
| spl0_908
| ~ spl0_97
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f4751,f4743,f1159,f46478,f726]) ).
fof(f46478,plain,
( spl0_908
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X1,tc_nat),tc_nat),c_Power_Opower__class_Opower(X0,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f4751,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X1,tc_nat),tc_nat),c_Power_Opower__class_Opower(X0,X1,tc_nat),tc_nat) )
| ~ spl0_97
| ~ spl0_338 ),
inference(resolution,[],[f4744,f1160]) ).
fof(f46430,plain,
( ~ spl0_8
| spl0_907
| ~ spl0_164
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4407,f3604,f1652,f46428,f726]) ).
fof(f46428,plain,
( spl0_907
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X0,X2,tc_nat),X3,tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X2,tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f4407,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X2,tc_nat),X3,tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X0,X2,tc_nat),X3,tc_nat) )
| ~ spl0_164
| ~ spl0_324 ),
inference(resolution,[],[f3605,f1653]) ).
fof(f46300,plain,
( ~ spl0_8
| spl0_906
| ~ spl0_164
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4359,f3592,f1652,f46298,f726]) ).
fof(f46298,plain,
( spl0_906
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X2,X0,tc_nat),X3,tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X1,tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f4359,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X1,tc_nat),X3,tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X2,X0,tc_nat),X3,tc_nat) )
| ~ spl0_164
| ~ spl0_321 ),
inference(resolution,[],[f3593,f1653]) ).
fof(f46242,plain,
( ~ spl0_8
| spl0_905
| ~ spl0_164
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f4296,f3580,f1652,f46240,f726]) ).
fof(f46240,plain,
( spl0_905
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X2,X0,tc_nat),X3,tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X1,tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f4296,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X1,tc_nat),X3,tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X2,X0,tc_nat),X3,tc_nat) )
| ~ spl0_164
| ~ spl0_318 ),
inference(resolution,[],[f3581,f1653]) ).
fof(f46140,plain,
( ~ spl0_16
| spl0_904
| ~ spl0_164
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f4190,f3523,f1652,f46138,f766]) ).
fof(f46138,plain,
( spl0_904
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f4190,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Omult__mono(tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),X3,tc_nat) )
| ~ spl0_164
| ~ spl0_313 ),
inference(resolution,[],[f3524,f1653]) ).
fof(f46035,plain,
( ~ spl0_14
| spl0_903
| ~ spl0_164
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f4138,f3515,f1652,f46033,f756]) ).
fof(f46033,plain,
( spl0_903
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X0,tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f4138,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Omult__mono1(tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X3,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X0,tc_nat),X3,tc_nat) )
| ~ spl0_164
| ~ spl0_311 ),
inference(resolution,[],[f3516,f1653]) ).
fof(f46031,plain,
( spl0_902
| ~ spl0_195
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f2832,f2793,f1970,f46029]) ).
fof(f46029,plain,
( spl0_902
<=> ! [X4,X0,X3,X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(X4,c_Power_Opower__class_Opower(X1,X0,X3),X3)
| ~ class_Orderings_Opreorder(X3)
| c_lessequals(X4,c_Power_Opower__class_Opower(X2,X0,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f2832,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(X4,c_Power_Opower__class_Opower(X1,X0,X3),X3)
| ~ class_Orderings_Opreorder(X3)
| c_lessequals(X4,c_Power_Opower__class_Opower(X2,X0,X3),X3) )
| ~ spl0_195
| ~ spl0_241 ),
inference(resolution,[],[f2794,f1971]) ).
fof(f46027,plain,
( spl0_901
| ~ spl0_194
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f2831,f2793,f1966,f46025]) ).
fof(f46025,plain,
( spl0_901
<=> ! [X4,X0,X3,X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X0,X3),X4,X3)
| ~ class_Orderings_Oorder(X3)
| c_lessequals(c_Power_Opower__class_Opower(X1,X0,X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f2831,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X0,X3),X4,X3)
| ~ class_Orderings_Oorder(X3)
| c_lessequals(c_Power_Opower__class_Opower(X1,X0,X3),X4,X3) )
| ~ spl0_194
| ~ spl0_241 ),
inference(resolution,[],[f2794,f1967]) ).
fof(f46023,plain,
( spl0_900
| ~ spl0_190
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f2830,f2793,f1950,f46021]) ).
fof(f46021,plain,
( spl0_900
<=> ! [X4,X0,X3,X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X3),X4,X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X0,X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f2830,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X3),X4,X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X0,X3),X4,X3) )
| ~ spl0_190
| ~ spl0_241 ),
inference(resolution,[],[f2794,f1951]) ).
fof(f46019,plain,
( spl0_899
| ~ spl0_251
| ~ spl0_839 ),
inference(avatar_split_clause,[],[f45560,f33875,f2881,f46017]) ).
fof(f46017,plain,
( spl0_899
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X1,X0,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X0,X1,t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f2881,plain,
( spl0_251
<=> ! [X0] : c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(t_a),t_a) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f45560,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X1,X0,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X0,X1,t_a),c_HOL_Oone__class_Oone(t_a),t_a)
| ~ spl0_251
| ~ spl0_839 ),
inference(superposition,[],[f33876,f2882]) ).
fof(f2882,plain,
( ! [X0] : c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(t_a),t_a) = X0
| ~ spl0_251 ),
inference(avatar_component_clause,[],[f2881]) ).
fof(f46015,plain,
( spl0_898
| ~ spl0_189
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f2829,f2793,f1946,f46013]) ).
fof(f46013,plain,
( spl0_898
<=> ! [X4,X0,X3,X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X1,X0,X3),X3)
| c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X2,X0,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f2829,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X1,X0,X3),X3)
| c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X2,X0,X3),X3) )
| ~ spl0_189
| ~ spl0_241 ),
inference(resolution,[],[f2794,f1947]) ).
fof(f46011,plain,
( spl0_897
| ~ spl0_188
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f2828,f2793,f1942,f46009]) ).
fof(f46009,plain,
( spl0_897
<=> ! [X4,X0,X3,X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X1,X0,X3),X3)
| c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X2,X0,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f2828,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X1,X0,X3),X3)
| c_HOL_Oord__class_Oless(X4,c_Power_Opower__class_Opower(X2,X0,X3),X3) )
| ~ spl0_188
| ~ spl0_241 ),
inference(resolution,[],[f2794,f1943]) ).
fof(f46007,plain,
( spl0_896
| ~ spl0_187
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f2827,f2793,f1938,f46005]) ).
fof(f46005,plain,
( spl0_896
<=> ! [X4,X0,X3,X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X3),X4,X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X0,X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f2827,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X3),X4,X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X0,X3),X4,X3) )
| ~ spl0_187
| ~ spl0_241 ),
inference(resolution,[],[f2794,f1939]) ).
fof(f46003,plain,
( spl0_895
| ~ spl0_215
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2512,f2480,f2297,f46001]) ).
fof(f46001,plain,
( spl0_895
<=> ! [X2,X0,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f2480,plain,
( spl0_218
<=> ! [X2,X4] :
( ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
| c_HOL_Oord__class_Oless(X2,X4,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X2,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f2512,plain,
( ! [X2,X0,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) )
| ~ spl0_215
| ~ spl0_218 ),
inference(superposition,[],[f2481,f2298]) ).
fof(f2481,plain,
( ! [X2,X4] :
( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X2,X4,tc_nat),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
| c_HOL_Oord__class_Oless(X2,X4,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) )
| ~ spl0_218 ),
inference(avatar_component_clause,[],[f2480]) ).
fof(f45999,plain,
( spl0_894
| ~ spl0_215
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2498,f2476,f2297,f45997]) ).
fof(f45997,plain,
( spl0_894
<=> ! [X2,X0,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f2476,plain,
( spl0_217
<=> ! [X4,X2] :
( ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X4,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X2,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f2498,plain,
( ! [X2,X0,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) )
| ~ spl0_215
| ~ spl0_217 ),
inference(superposition,[],[f2477,f2298]) ).
fof(f2477,plain,
( ! [X2,X4] :
( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X2,X4,tc_nat),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X4,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat) )
| ~ spl0_217 ),
inference(avatar_component_clause,[],[f2476]) ).
fof(f45995,plain,
( spl0_893
| ~ spl0_186
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2394,f2293,f1927,f45993]) ).
fof(f45993,plain,
( spl0_893
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f2293,plain,
( spl0_214
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f2394,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) )
| ~ spl0_186
| ~ spl0_214 ),
inference(resolution,[],[f2294,f1928]) ).
fof(f2294,plain,
( ! [X0,X1,X9] :
( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_214 ),
inference(avatar_component_clause,[],[f2293]) ).
fof(f45991,plain,
( spl0_892
| ~ spl0_186
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2376,f2289,f1927,f45989]) ).
fof(f45989,plain,
( spl0_892
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f2289,plain,
( spl0_213
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f2376,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) )
| ~ spl0_186
| ~ spl0_213 ),
inference(resolution,[],[f2290,f1928]) ).
fof(f2290,plain,
( ! [X0,X1,X9] :
( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_213 ),
inference(avatar_component_clause,[],[f2289]) ).
fof(f45987,plain,
( spl0_891
| ~ spl0_186
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2340,f2281,f1927,f45985]) ).
fof(f45985,plain,
( spl0_891
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f2281,plain,
( spl0_211
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f2340,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) )
| ~ spl0_186
| ~ spl0_211 ),
inference(resolution,[],[f2282,f1928]) ).
fof(f2282,plain,
( ! [X0,X1,X9] :
( c_lessequals(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_211 ),
inference(avatar_component_clause,[],[f2281]) ).
fof(f45983,plain,
( spl0_890
| ~ spl0_179
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2210,f1986,f1763,f45981]) ).
fof(f45981,plain,
( spl0_890
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f1763,plain,
( spl0_179
<=> ! [X9,X27] :
( ~ c_lessequals(X27,X9,tc_nat)
| c_HOL_Ominus__class_Ominus(X9,c_HOL_Ominus__class_Ominus(X9,X27,tc_nat),tc_nat) = X27 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f1986,plain,
( spl0_199
<=> ! [X9,X21,X19] :
( ~ c_lessequals(X19,X9,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X21,X9,tc_nat),c_HOL_Ominus__class_Ominus(X21,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f2210,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat),tc_nat) )
| ~ spl0_179
| ~ spl0_199 ),
inference(resolution,[],[f1987,f1764]) ).
fof(f1764,plain,
( ! [X9,X27] :
( ~ c_lessequals(X27,X9,tc_nat)
| c_HOL_Ominus__class_Ominus(X9,c_HOL_Ominus__class_Ominus(X9,X27,tc_nat),tc_nat) = X27 )
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f1763]) ).
fof(f1987,plain,
( ! [X21,X19,X9] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X21,X9,tc_nat),c_HOL_Ominus__class_Ominus(X21,X19,tc_nat),tc_nat)
| ~ c_lessequals(X19,X9,tc_nat) )
| ~ spl0_199 ),
inference(avatar_component_clause,[],[f1986]) ).
fof(f45979,plain,
( spl0_889
| ~ spl0_179
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2186,f1982,f1763,f45977]) ).
fof(f45977,plain,
( spl0_889
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f1982,plain,
( spl0_198
<=> ! [X9,X21,X19] :
( ~ c_lessequals(X19,X9,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X19,X21,tc_nat),c_HOL_Ominus__class_Ominus(X9,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f2186,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat),tc_nat) )
| ~ spl0_179
| ~ spl0_198 ),
inference(resolution,[],[f1983,f1764]) ).
fof(f1983,plain,
( ! [X21,X19,X9] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X19,X21,tc_nat),c_HOL_Ominus__class_Ominus(X9,X21,tc_nat),tc_nat)
| ~ c_lessequals(X19,X9,tc_nat) )
| ~ spl0_198 ),
inference(avatar_component_clause,[],[f1982]) ).
fof(f41186,plain,
( spl0_888
| ~ spl0_289
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f5018,f4963,f3399,f41184]) ).
fof(f41184,plain,
( spl0_888
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,X3,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| c_HOL_Oord__class_Oless(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f5018,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,X3,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| c_HOL_Oord__class_Oless(X0,X1,X2) )
| ~ spl0_289
| ~ spl0_351 ),
inference(duplicate_literal_removal,[],[f4987]) ).
fof(f4987,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,X3,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) )
| ~ spl0_289
| ~ spl0_351 ),
inference(resolution,[],[f4964,f3400]) ).
fof(f41182,plain,
( spl0_887
| ~ spl0_136
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f4536,f4437,f1363,f41180]) ).
fof(f41180,plain,
( spl0_887
<=> ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X1,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f4536,plain,
( ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X1,X0,X2),X2) )
| ~ spl0_136
| ~ spl0_330 ),
inference(resolution,[],[f4438,f1364]) ).
fof(f41178,plain,
( spl0_886
| ~ spl0_134
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f4535,f4437,f1355,f41176]) ).
fof(f41176,plain,
( spl0_886
<=> ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X1,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f4535,plain,
( ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X1,X0,X2),X2) )
| ~ spl0_134
| ~ spl0_330 ),
inference(resolution,[],[f4438,f1356]) ).
fof(f41174,plain,
( spl0_885
| ~ spl0_135
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f4499,f4425,f1359,f41172]) ).
fof(f41172,plain,
( spl0_885
<=> ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_Power_Opower__class_Opower(X2,X0,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f1359,plain,
( spl0_135
<=> ! [X2,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X4,X2,X0)
| c_HOL_Oord__class_Oless(X2,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f4425,plain,
( spl0_327
<=> ! [X9,X0,X2] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X9
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f4499,plain,
( ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_Power_Opower__class_Opower(X2,X0,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_135
| ~ spl0_327 ),
inference(resolution,[],[f4426,f1360]) ).
fof(f1360,plain,
( ! [X2,X0,X4] :
( c_HOL_Oord__class_Oless(X2,X4,X0)
| c_lessequals(X4,X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_135 ),
inference(avatar_component_clause,[],[f1359]) ).
fof(f4426,plain,
( ! [X2,X0,X9] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X9,X0),X0)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X9
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_327 ),
inference(avatar_component_clause,[],[f4425]) ).
fof(f41170,plain,
( spl0_884
| ~ spl0_135
| ~ spl0_326 ),
inference(avatar_split_clause,[],[f4478,f4421,f1359,f41168]) ).
fof(f41168,plain,
( spl0_884
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X0,X1),c_HOL_Otimes__class_Otimes(X3,X0,X1),X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f4421,plain,
( spl0_326
<=> ! [X13,X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f4478,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X0,X1),c_HOL_Otimes__class_Otimes(X3,X0,X1),X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_135
| ~ spl0_326 ),
inference(resolution,[],[f4422,f1360]) ).
fof(f4422,plain,
( ! [X3,X0,X1,X13] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0)
| c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_326 ),
inference(avatar_component_clause,[],[f4421]) ).
fof(f41166,plain,
( spl0_883
| ~ spl0_135
| ~ spl0_325 ),
inference(avatar_split_clause,[],[f4455,f4417,f1359,f41164]) ).
fof(f41164,plain,
( spl0_883
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Otimes__class_Otimes(X0,X3,X1),X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f4417,plain,
( spl0_325
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f4455,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Otimes__class_Otimes(X0,X3,X1),X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_135
| ~ spl0_325 ),
inference(resolution,[],[f4418,f1360]) ).
fof(f4418,plain,
( ! [X3,X0,X1,X13] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0)
| c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_325 ),
inference(avatar_component_clause,[],[f4417]) ).
fof(f40718,plain,
( ~ spl0_8
| spl0_882
| ~ spl0_156
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4409,f3604,f1526,f40716,f726]) ).
fof(f40716,plain,
( spl0_882
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(X0,X2,tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f4409,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(X0,X2,tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat) )
| ~ spl0_156
| ~ spl0_324 ),
inference(resolution,[],[f3605,f1527]) ).
fof(f40678,plain,
( ~ spl0_8
| spl0_881
| ~ spl0_156
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4361,f3592,f1526,f40676,f726]) ).
fof(f40676,plain,
( spl0_881
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(X2,X0,tc_nat),c_Power_Opower__class_Opower(X2,X1,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f4361,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(X2,X0,tc_nat),c_Power_Opower__class_Opower(X2,X1,tc_nat),tc_nat) )
| ~ spl0_156
| ~ spl0_321 ),
inference(resolution,[],[f3593,f1527]) ).
fof(f40645,plain,
( ~ spl0_8
| spl0_880
| ~ spl0_156
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f4298,f3580,f1526,f40643,f726]) ).
fof(f40643,plain,
( spl0_880
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(X2,X0,tc_nat),c_Power_Opower__class_Opower(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f4298,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(X2,X0,tc_nat),c_Power_Opower__class_Opower(X2,X1,tc_nat),tc_nat) )
| ~ spl0_156
| ~ spl0_318 ),
inference(resolution,[],[f3581,f1527]) ).
fof(f40641,plain,
( ~ spl0_878
| spl0_879
| ~ spl0_156
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f4218,f3527,f1526,f40639,f40635]) ).
fof(f40635,plain,
( spl0_878
<=> class_Ring__and__Field_Opordered__ring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f40639,plain,
( spl0_879
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X2,X0,tc_nat),tc_nat)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f4218,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ class_Ring__and__Field_Opordered__ring(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X2,X0,tc_nat),tc_nat) )
| ~ spl0_156
| ~ spl0_314 ),
inference(resolution,[],[f3528,f1527]) ).
fof(f40586,plain,
( ~ spl0_16
| spl0_877
| ~ spl0_156
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f4192,f3523,f1526,f40584,f766]) ).
fof(f40584,plain,
( spl0_877
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f4192,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Omult__mono(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) )
| ~ spl0_156
| ~ spl0_313 ),
inference(resolution,[],[f3524,f1527]) ).
fof(f40582,plain,
( spl0_876
| ~ spl0_449
| ~ spl0_860 ),
inference(avatar_split_clause,[],[f40133,f39932,f9464,f40580]) ).
fof(f40580,plain,
( spl0_876
<=> ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X1,t_a),X0,t_a) = X0
| c_HOL_Ozero__class_Ozero(t_a) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f40133,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X1,t_a),X0,t_a) = X0
| c_HOL_Ozero__class_Ozero(t_a) = X1 )
| ~ spl0_449
| ~ spl0_860 ),
inference(superposition,[],[f39933,f9465]) ).
fof(f40531,plain,
( ~ spl0_14
| spl0_875
| ~ spl0_156
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f4140,f3515,f1526,f40529,f756]) ).
fof(f40529,plain,
( spl0_875
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X0,tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f4140,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Omult__mono1(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X0,tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) )
| ~ spl0_156
| ~ spl0_311 ),
inference(resolution,[],[f3516,f1527]) ).
fof(f40527,plain,
( spl0_874
| ~ spl0_195
| ~ spl0_240 ),
inference(avatar_split_clause,[],[f2781,f2656,f1970,f40525]) ).
fof(f40525,plain,
( spl0_874
<=> ! [X2,X0,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X2,c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X0,X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f2656,plain,
( spl0_240
<=> ! [X9,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X9
| c_lessequals(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f2781,plain,
( ! [X2,X0,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X2,c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X0,X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_195
| ~ spl0_240 ),
inference(resolution,[],[f2657,f1971]) ).
fof(f2657,plain,
( ! [X0,X9] :
( c_lessequals(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X9,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X9
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_240 ),
inference(avatar_component_clause,[],[f2656]) ).
fof(f40523,plain,
( spl0_873
| ~ spl0_194
| ~ spl0_240 ),
inference(avatar_split_clause,[],[f2780,f2656,f1966,f40521]) ).
fof(f40521,plain,
( spl0_873
<=> ! [X2,X0,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X0,X1),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f2780,plain,
( ! [X2,X0,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X0,X1),X2,X1) )
| ~ spl0_194
| ~ spl0_240 ),
inference(resolution,[],[f2657,f1967]) ).
fof(f40519,plain,
( spl0_872
| ~ spl0_190
| ~ spl0_240 ),
inference(avatar_split_clause,[],[f2779,f2656,f1950,f40517]) ).
fof(f40517,plain,
( spl0_872
<=> ! [X2,X0,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X0,X1),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f2779,plain,
( ! [X2,X0,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X0,X1),X2,X1) )
| ~ spl0_190
| ~ spl0_240 ),
inference(resolution,[],[f2657,f1951]) ).
fof(f40515,plain,
( spl0_871
| ~ spl0_189
| ~ spl0_240 ),
inference(avatar_split_clause,[],[f2778,f2656,f1946,f40513]) ).
fof(f40513,plain,
( spl0_871
<=> ! [X2,X0,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X0,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f2778,plain,
( ! [X2,X0,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X0,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_189
| ~ spl0_240 ),
inference(resolution,[],[f2657,f1947]) ).
fof(f40511,plain,
( spl0_870
| ~ spl0_188
| ~ spl0_240 ),
inference(avatar_split_clause,[],[f2777,f2656,f1942,f40509]) ).
fof(f40509,plain,
( spl0_870
<=> ! [X2,X0,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X0,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f2777,plain,
( ! [X2,X0,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X0,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_188
| ~ spl0_240 ),
inference(resolution,[],[f2657,f1943]) ).
fof(f40507,plain,
( spl0_869
| ~ spl0_187
| ~ spl0_240 ),
inference(avatar_split_clause,[],[f2776,f2656,f1938,f40505]) ).
fof(f40505,plain,
( spl0_869
<=> ! [X2,X0,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X0,X1),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f2776,plain,
( ! [X2,X0,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X0,X1),X2,X1) )
| ~ spl0_187
| ~ spl0_240 ),
inference(resolution,[],[f2657,f1939]) ).
fof(f40503,plain,
( spl0_868
| ~ spl0_193
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f2764,f2652,f1962,f40501]) ).
fof(f40501,plain,
( spl0_868
<=> ! [X0,X3,X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X1),X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f2652,plain,
( spl0_239
<=> ! [X9,X0,X2] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f2764,plain,
( ! [X2,X3,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X1),X3,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) )
| ~ spl0_193
| ~ spl0_239 ),
inference(resolution,[],[f2653,f1963]) ).
fof(f2653,plain,
( ! [X2,X0,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X9,X0),X0)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_239 ),
inference(avatar_component_clause,[],[f2652]) ).
fof(f40499,plain,
( spl0_867
| ~ spl0_192
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f2763,f2652,f1958,f40497]) ).
fof(f40497,plain,
( spl0_867
<=> ! [X0,X3,X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_HOL_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X2,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f2763,plain,
( ! [X2,X3,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_HOL_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X2,X0,X1),X1) )
| ~ spl0_192
| ~ spl0_239 ),
inference(resolution,[],[f2653,f1959]) ).
fof(f40126,plain,
( spl0_866
| ~ spl0_193
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f2753,f2648,f1962,f40124]) ).
fof(f40124,plain,
( spl0_866
<=> ! [X0,X3,X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X0,X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f2648,plain,
( spl0_238
<=> ! [X9,X0,X2] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f2753,plain,
( ! [X2,X3,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X0,X2),X3,X2) )
| ~ spl0_193
| ~ spl0_238 ),
inference(resolution,[],[f2649,f1963]) ).
fof(f2649,plain,
( ! [X2,X0,X9] :
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_238 ),
inference(avatar_component_clause,[],[f2648]) ).
fof(f40122,plain,
( spl0_865
| ~ spl0_192
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f2752,f2648,f1958,f40120]) ).
fof(f40120,plain,
( spl0_865
<=> ! [X0,X3,X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X1,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f2752,plain,
( ! [X2,X3,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X1,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2) )
| ~ spl0_192
| ~ spl0_238 ),
inference(resolution,[],[f2649,f1959]) ).
fof(f40118,plain,
( spl0_864
| ~ spl0_215
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2724,f2636,f2297,f40116]) ).
fof(f40116,plain,
( spl0_864
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f2724,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) )
| ~ spl0_215
| ~ spl0_235 ),
inference(superposition,[],[f2637,f2298]) ).
fof(f40067,plain,
( ~ spl0_20
| spl0_863
| ~ spl0_193
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2715,f2636,f1962,f40065,f786]) ).
fof(f786,plain,
( spl0_20
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f40065,plain,
( spl0_863
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
| ~ c_lessequals(X2,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f2715,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_lessequals(X2,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
| ~ class_Orderings_Oorder(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X3,tc_nat) )
| ~ spl0_193
| ~ spl0_235 ),
inference(resolution,[],[f2637,f1963]) ).
fof(f40026,plain,
( ~ spl0_18
| spl0_862
| ~ spl0_192
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2714,f2636,f1958,f40024,f776]) ).
fof(f776,plain,
( spl0_18
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f40024,plain,
( spl0_862
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat)
| ~ c_lessequals(X2,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f2714,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_lessequals(X2,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) )
| ~ spl0_192
| ~ spl0_235 ),
inference(resolution,[],[f2637,f1959]) ).
fof(f39975,plain,
( ~ spl0_20
| spl0_861
| ~ spl0_193
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2692,f2632,f1962,f39973,f786]) ).
fof(f39973,plain,
( spl0_861
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f2692,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X3,tc_nat)
| ~ class_Orderings_Oorder(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) )
| ~ spl0_193
| ~ spl0_234 ),
inference(resolution,[],[f2633,f1963]) ).
fof(f39934,plain,
( spl0_860
| ~ spl0_361
| ~ spl0_449
| ~ spl0_823
| ~ spl0_835 ),
inference(avatar_split_clause,[],[f39851,f28834,f28216,f9464,f5201,f39932]) ).
fof(f28216,plain,
( spl0_823
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,t_a),t_a) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X0,X1,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f39851,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(X0,X0,t_a),t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_361
| ~ spl0_449
| ~ spl0_823
| ~ spl0_835 ),
inference(forward_demodulation,[],[f39850,f5202]) ).
fof(f39850,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X0,t_a),t_a),t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_449
| ~ spl0_823
| ~ spl0_835 ),
inference(forward_demodulation,[],[f39540,f9465]) ).
fof(f39540,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,t_a),X0,t_a),t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_823
| ~ spl0_835 ),
inference(superposition,[],[f28835,f28217]) ).
fof(f28217,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,t_a),t_a) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X0,X1,t_a),t_a)
| ~ spl0_823 ),
inference(avatar_component_clause,[],[f28216]) ).
fof(f39930,plain,
( ~ spl0_18
| spl0_859
| ~ spl0_192
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2691,f2632,f1958,f39928,f776]) ).
fof(f39928,plain,
( spl0_859
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f2691,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) )
| ~ spl0_192
| ~ spl0_234 ),
inference(resolution,[],[f2633,f1959]) ).
fof(f39926,plain,
( spl0_858
| ~ spl0_193
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2666,f2624,f1962,f39924]) ).
fof(f39924,plain,
( spl0_858
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X0),X0),X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f2624,plain,
( spl0_232
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X9,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f2666,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X0),X0),X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0) )
| ~ spl0_193
| ~ spl0_232 ),
inference(resolution,[],[f2625,f1963]) ).
fof(f2625,plain,
( ! [X0,X1,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X9,X0),X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_232 ),
inference(avatar_component_clause,[],[f2624]) ).
fof(f39922,plain,
( spl0_857
| ~ spl0_192
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2665,f2624,f1958,f39920]) ).
fof(f39920,plain,
( spl0_857
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X3,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f2665,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X3,X0),X0),X0) )
| ~ spl0_192
| ~ spl0_232 ),
inference(resolution,[],[f2625,f1959]) ).
fof(f39918,plain,
( spl0_856
| ~ spl0_209
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2433,f2297,f2273,f39916]) ).
fof(f39916,plain,
( spl0_856
<=> ! [X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f2273,plain,
( spl0_209
<=> ! [X9] :
( c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X9,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f2433,plain,
( ! [X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) )
| ~ spl0_209
| ~ spl0_215 ),
inference(superposition,[],[f2274,f2298]) ).
fof(f2274,plain,
( ! [X9] :
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X9,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) )
| ~ spl0_209 ),
inference(avatar_component_clause,[],[f2273]) ).
fof(f39914,plain,
( spl0_855
| ~ spl0_210
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2432,f2297,f2277,f39912]) ).
fof(f39912,plain,
( spl0_855
<=> ! [X0,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f2277,plain,
( spl0_210
<=> ! [X9] :
( ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X9,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f2432,plain,
( ! [X0,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) )
| ~ spl0_210
| ~ spl0_215 ),
inference(superposition,[],[f2278,f2298]) ).
fof(f2278,plain,
( ! [X9] :
( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X9,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) )
| ~ spl0_210 ),
inference(avatar_component_clause,[],[f2277]) ).
fof(f39910,plain,
( spl0_854
| ~ spl0_181
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2393,f2293,f1771,f39908]) ).
fof(f39908,plain,
( spl0_854
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(X1,X2,X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f2393,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(X1,X2,X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_181
| ~ spl0_214 ),
inference(resolution,[],[f2294,f1772]) ).
fof(f39906,plain,
( spl0_853
| ~ spl0_175
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2392,f2293,f1745,f39904]) ).
fof(f39904,plain,
( spl0_853
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f2392,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) )
| ~ spl0_175
| ~ spl0_214 ),
inference(resolution,[],[f2294,f1746]) ).
fof(f39902,plain,
( spl0_852
| ~ spl0_174
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2391,f2293,f1741,f39900]) ).
fof(f39900,plain,
( spl0_852
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f2391,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) )
| ~ spl0_174
| ~ spl0_214 ),
inference(resolution,[],[f2294,f1742]) ).
fof(f39898,plain,
( spl0_851
| ~ spl0_181
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2375,f2289,f1771,f39896]) ).
fof(f39896,plain,
( spl0_851
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(X1,X2,X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f2375,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(X1,X2,X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_181
| ~ spl0_213 ),
inference(resolution,[],[f2290,f1772]) ).
fof(f39894,plain,
( spl0_850
| ~ spl0_175
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2374,f2289,f1745,f39892]) ).
fof(f39892,plain,
( spl0_850
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f2374,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) )
| ~ spl0_175
| ~ spl0_213 ),
inference(resolution,[],[f2290,f1746]) ).
fof(f39513,plain,
( spl0_849
| ~ spl0_174
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2373,f2289,f1741,f39511]) ).
fof(f39511,plain,
( spl0_849
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f2373,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) )
| ~ spl0_174
| ~ spl0_213 ),
inference(resolution,[],[f2290,f1742]) ).
fof(f39509,plain,
( spl0_848
| ~ spl0_181
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2356,f2285,f1771,f39507]) ).
fof(f39507,plain,
( spl0_848
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(X2,X1,X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f2285,plain,
( spl0_212
<=> ! [X9,X0,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f2356,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(X2,X1,X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_181
| ~ spl0_212 ),
inference(resolution,[],[f2286,f1772]) ).
fof(f2286,plain,
( ! [X2,X0,X9] :
( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X9,X0),X0)
| ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_212 ),
inference(avatar_component_clause,[],[f2285]) ).
fof(f39505,plain,
( spl0_847
| ~ spl0_175
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2355,f2285,f1745,f39503]) ).
fof(f39503,plain,
( spl0_847
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(X2,X1,X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f2355,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(X2,X1,X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X1,X0),X0) )
| ~ spl0_175
| ~ spl0_212 ),
inference(resolution,[],[f2286,f1746]) ).
fof(f39501,plain,
( spl0_846
| ~ spl0_174
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2354,f2285,f1741,f39499]) ).
fof(f39499,plain,
( spl0_846
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(X2,X1,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f2354,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(X2,X1,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X1,X0),X0) )
| ~ spl0_174
| ~ spl0_212 ),
inference(resolution,[],[f2286,f1742]) ).
fof(f39461,plain,
( ~ spl0_8
| spl0_845
| ~ spl0_179
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2347,f2281,f1763,f39459,f726]) ).
fof(f39459,plain,
( spl0_845
<=> ! [X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(X0,X1,tc_nat),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(X0,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f2347,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(X0,X1,tc_nat),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(X0,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) )
| ~ spl0_179
| ~ spl0_211 ),
inference(resolution,[],[f2282,f1764]) ).
fof(f39457,plain,
( spl0_844
| ~ spl0_181
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2339,f2281,f1771,f39455]) ).
fof(f39455,plain,
( spl0_844
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,X2,X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f2339,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,X2,X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_181
| ~ spl0_211 ),
inference(resolution,[],[f2282,f1772]) ).
fof(f39453,plain,
( spl0_843
| ~ spl0_175
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2338,f2281,f1745,f39451]) ).
fof(f39451,plain,
( spl0_843
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f2338,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) )
| ~ spl0_175
| ~ spl0_211 ),
inference(resolution,[],[f2282,f1746]) ).
fof(f39449,plain,
( spl0_842
| ~ spl0_174
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2337,f2281,f1741,f39447]) ).
fof(f39447,plain,
( spl0_842
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f2337,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) )
| ~ spl0_174
| ~ spl0_211 ),
inference(resolution,[],[f2282,f1742]) ).
fof(f39445,plain,
( spl0_841
| ~ spl0_186
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2168,f1978,f1927,f39443]) ).
fof(f39443,plain,
( spl0_841
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f1978,plain,
( spl0_197
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,X3,X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f2168,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) )
| ~ spl0_186
| ~ spl0_197 ),
inference(resolution,[],[f1979,f1928]) ).
fof(f1979,plain,
( ! [X3,X0,X1] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,X3,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
| ~ spl0_197 ),
inference(avatar_component_clause,[],[f1978]) ).
fof(f39441,plain,
( spl0_840
| ~ spl0_361
| ~ spl0_484
| ~ spl0_669
| ~ spl0_834 ),
inference(avatar_split_clause,[],[f28263,f28260,f21402,f12230,f5201,f39439]) ).
fof(f39439,plain,
( spl0_840
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X0,X1,t_a),X2,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X0,X2,t_a),X1,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f28260,plain,
( spl0_834
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X0,X1,t_a),X2,t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Odivide(X2,X1,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f28263,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X0,X1,t_a),X2,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X0,X2,t_a),X1,t_a)
| ~ spl0_361
| ~ spl0_484
| ~ spl0_669
| ~ spl0_834 ),
inference(forward_demodulation,[],[f28261,f21694]) ).
fof(f28261,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X0,X1,t_a),X2,t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Odivide(X2,X1,t_a),t_a)
| ~ spl0_834 ),
inference(avatar_component_clause,[],[f28260]) ).
fof(f33877,plain,
( spl0_839
| ~ spl0_361
| ~ spl0_484
| ~ spl0_669
| ~ spl0_691 ),
inference(avatar_split_clause,[],[f28021,f21490,f21402,f12230,f5201,f33875]) ).
fof(f28021,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Odivide(X0,X1,t_a),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X0,X2,t_a),X1,t_a)
| ~ spl0_361
| ~ spl0_484
| ~ spl0_669
| ~ spl0_691 ),
inference(forward_demodulation,[],[f28020,f21694]) ).
fof(f28020,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Odivide(X0,X1,t_a),t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Odivide(X2,X1,t_a),t_a)
| ~ spl0_361
| ~ spl0_691 ),
inference(forward_demodulation,[],[f27596,f5202]) ).
fof(f27596,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Odivide(X0,X1,t_a),t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X1,t_a),t_a),t_a)
| ~ spl0_361
| ~ spl0_691 ),
inference(superposition,[],[f21491,f5202]) ).
fof(f32649,plain,
( spl0_838
| ~ spl0_283
| ~ spl0_531
| ~ spl0_680 ),
inference(avatar_split_clause,[],[f22153,f21446,f14012,f3010,f32647]) ).
fof(f14012,plain,
( spl0_531
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(t_a) = X0
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,t_a),X0,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f22153,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Otimes__class_Otimes(X1,X0,t_a),t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_283
| ~ spl0_531
| ~ spl0_680 ),
inference(forward_demodulation,[],[f21994,f3011]) ).
fof(f21994,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),X1,t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Otimes__class_Otimes(X1,X0,t_a),t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_531
| ~ spl0_680 ),
inference(superposition,[],[f21447,f14013]) ).
fof(f14013,plain,
( ! [X0] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,t_a),X0,t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_531 ),
inference(avatar_component_clause,[],[f14012]) ).
fof(f31334,plain,
( spl0_837
| ~ spl0_669
| ~ spl0_680 ),
inference(avatar_split_clause,[],[f21995,f21446,f21402,f31332]) ).
fof(f31332,plain,
( spl0_837
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,t_a),t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,X1,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f21995,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,t_a),t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,X1,t_a),t_a)
| ~ spl0_669
| ~ spl0_680 ),
inference(superposition,[],[f21447,f21403]) ).
fof(f30054,plain,
( spl0_836
| ~ spl0_449
| ~ spl0_680 ),
inference(avatar_split_clause,[],[f21982,f21446,f9464,f30052]) ).
fof(f30052,plain,
( spl0_836
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,X1,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X0,t_a),X2,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f21982,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,X1,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X0,t_a),X2,t_a)
| ~ spl0_449
| ~ spl0_680 ),
inference(superposition,[],[f21447,f9465]) ).
fof(f28836,plain,
( spl0_835
| ~ spl0_283
| ~ spl0_531
| ~ spl0_669 ),
inference(avatar_split_clause,[],[f21695,f21402,f14012,f3010,f28834]) ).
fof(f21695,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Otimes__class_Otimes(X0,X1,t_a),t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_283
| ~ spl0_531
| ~ spl0_669 ),
inference(forward_demodulation,[],[f21543,f3011]) ).
fof(f21543,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),X1,t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Otimes__class_Otimes(X0,X1,t_a),t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_531
| ~ spl0_669 ),
inference(superposition,[],[f21403,f14013]) ).
fof(f28262,plain,
( spl0_834
| ~ spl0_361
| ~ spl0_484
| ~ spl0_669 ),
inference(avatar_split_clause,[],[f21687,f21402,f12230,f5201,f28260]) ).
fof(f28258,plain,
( spl0_833
| ~ spl0_102
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4607,f4590,f1180,f28256]) ).
fof(f28256,plain,
( spl0_833
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat)
| c_lessequals(X2,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f4607,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat)
| c_lessequals(X2,X0,tc_nat) )
| ~ spl0_102
| ~ spl0_333 ),
inference(resolution,[],[f4591,f1181]) ).
fof(f28254,plain,
( spl0_832
| ~ spl0_136
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4395,f3604,f1363,f28252]) ).
fof(f28252,plain,
( spl0_832
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X2),c_Power_Opower__class_Opower(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f4395,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X2),c_Power_Opower__class_Opower(X0,X3,X2),X2) )
| ~ spl0_136
| ~ spl0_324 ),
inference(resolution,[],[f3605,f1364]) ).
fof(f28250,plain,
( spl0_831
| ~ spl0_134
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4394,f3604,f1355,f28248]) ).
fof(f28248,plain,
( spl0_831
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X2),c_Power_Opower__class_Opower(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f4394,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X2),c_Power_Opower__class_Opower(X0,X3,X2),X2) )
| ~ spl0_134
| ~ spl0_324 ),
inference(resolution,[],[f3605,f1356]) ).
fof(f28246,plain,
( spl0_830
| ~ spl0_135
| ~ spl0_323 ),
inference(avatar_split_clause,[],[f4387,f3600,f1359,f28244]) ).
fof(f28244,plain,
( spl0_830
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_lessequals(c_Power_Opower__class_Opower(X3,X1,X2),c_Power_Opower__class_Opower(X3,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f4387,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_lessequals(c_Power_Opower__class_Opower(X3,X1,X2),c_Power_Opower__class_Opower(X3,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_135
| ~ spl0_323 ),
inference(resolution,[],[f3601,f1360]) ).
fof(f28242,plain,
( spl0_829
| ~ spl0_142
| ~ spl0_322 ),
inference(avatar_split_clause,[],[f4376,f3596,f1387,f28240]) ).
fof(f28240,plain,
( spl0_829
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,X2),c_Power_Opower__class_Opower(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f4376,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,X2),c_Power_Opower__class_Opower(X3,X0,X2),X2) )
| ~ spl0_142
| ~ spl0_322 ),
inference(resolution,[],[f3597,f1388]) ).
fof(f28238,plain,
( spl0_828
| ~ spl0_141
| ~ spl0_322 ),
inference(avatar_split_clause,[],[f4375,f3596,f1383,f28236]) ).
fof(f28236,plain,
( spl0_828
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,X2),c_Power_Opower__class_Opower(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f4375,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,X2),c_Power_Opower__class_Opower(X3,X0,X2),X2) )
| ~ spl0_141
| ~ spl0_322 ),
inference(resolution,[],[f3597,f1384]) ).
fof(f28234,plain,
( spl0_827
| ~ spl0_140
| ~ spl0_322 ),
inference(avatar_split_clause,[],[f4374,f3596,f1379,f28232]) ).
fof(f28232,plain,
( spl0_827
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,X2),c_Power_Opower__class_Opower(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f4374,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,X2),c_Power_Opower__class_Opower(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_140
| ~ spl0_322 ),
inference(resolution,[],[f3597,f1380]) ).
fof(f28230,plain,
( spl0_826
| ~ spl0_138
| ~ spl0_322 ),
inference(avatar_split_clause,[],[f4373,f3596,f1371,f28228]) ).
fof(f28228,plain,
( spl0_826
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(c_Power_Opower__class_Opower(X3,X0,X2),c_Power_Opower__class_Opower(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f4373,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(c_Power_Opower__class_Opower(X3,X0,X2),c_Power_Opower__class_Opower(X3,X1,X2),X2) )
| ~ spl0_138
| ~ spl0_322 ),
inference(resolution,[],[f3597,f1372]) ).
fof(f28226,plain,
( spl0_825
| ~ spl0_137
| ~ spl0_322 ),
inference(avatar_split_clause,[],[f4372,f3596,f1367,f28224]) ).
fof(f28224,plain,
( spl0_825
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_Power_Opower__class_Opower(X3,X0,X2),c_Power_Opower__class_Opower(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f4372,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_Power_Opower__class_Opower(X3,X0,X2),c_Power_Opower__class_Opower(X3,X1,X2),X2) )
| ~ spl0_137
| ~ spl0_322 ),
inference(resolution,[],[f3597,f1368]) ).
fof(f28222,plain,
( spl0_824
| ~ spl0_136
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4347,f3592,f1363,f28220]) ).
fof(f28220,plain,
( spl0_824
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,X2),c_Power_Opower__class_Opower(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f4347,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,X2),c_Power_Opower__class_Opower(X3,X0,X2),X2) )
| ~ spl0_136
| ~ spl0_321 ),
inference(resolution,[],[f3593,f1364]) ).
fof(f28218,plain,
( spl0_823
| ~ spl0_449
| ~ spl0_669 ),
inference(avatar_split_clause,[],[f21544,f21402,f9464,f28216]) ).
fof(f21544,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,t_a),t_a) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X0,X1,t_a),t_a)
| ~ spl0_449
| ~ spl0_669 ),
inference(superposition,[],[f21403,f9465]) ).
fof(f28214,plain,
( spl0_822
| ~ spl0_134
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4346,f3592,f1355,f28212]) ).
fof(f28212,plain,
( spl0_822
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,X2),c_Power_Opower__class_Opower(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f4346,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,X2),c_Power_Opower__class_Opower(X3,X0,X2),X2) )
| ~ spl0_134
| ~ spl0_321 ),
inference(resolution,[],[f3593,f1356]) ).
fof(f28210,plain,
( spl0_821
| ~ spl0_135
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f4338,f3588,f1359,f28208]) ).
fof(f28208,plain,
( spl0_821
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X0,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f3588,plain,
( spl0_320
<=> ! [X9,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X9
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f4338,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X0,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_135
| ~ spl0_320 ),
inference(resolution,[],[f3589,f1360]) ).
fof(f3589,plain,
( ! [X0,X9] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X9,X0),X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X9
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_320 ),
inference(avatar_component_clause,[],[f3588]) ).
fof(f28206,plain,
( spl0_820
| ~ spl0_135
| ~ spl0_319 ),
inference(avatar_split_clause,[],[f4321,f3584,f1359,f28204]) ).
fof(f28204,plain,
( spl0_820
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_lessequals(c_Power_Opower__class_Opower(X1,X3,X2),c_Power_Opower__class_Opower(X0,X3,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f4321,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_lessequals(c_Power_Opower__class_Opower(X1,X3,X2),c_Power_Opower__class_Opower(X0,X3,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_135
| ~ spl0_319 ),
inference(resolution,[],[f3585,f1360]) ).
fof(f28202,plain,
( spl0_819
| ~ spl0_136
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f4284,f3580,f1363,f28200]) ).
fof(f28200,plain,
( spl0_819
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,X2),c_Power_Opower__class_Opower(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f4284,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,X2),c_Power_Opower__class_Opower(X3,X0,X2),X2) )
| ~ spl0_136
| ~ spl0_318 ),
inference(resolution,[],[f3581,f1364]) ).
fof(f28198,plain,
( spl0_818
| ~ spl0_134
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f4283,f3580,f1355,f28196]) ).
fof(f28196,plain,
( spl0_818
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,X2),c_Power_Opower__class_Opower(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f4283,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,X2),c_Power_Opower__class_Opower(X3,X0,X2),X2) )
| ~ spl0_134
| ~ spl0_318 ),
inference(resolution,[],[f3581,f1356]) ).
fof(f28194,plain,
( spl0_817
| ~ spl0_143
| ~ spl0_317 ),
inference(avatar_split_clause,[],[f4278,f3576,f1391,f28192]) ).
fof(f28192,plain,
( spl0_817
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_lessequals(c_Power_Opower__class_Opower(X3,X1,X2),c_Power_Opower__class_Opower(X3,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f1391,plain,
( spl0_143
<=> ! [X4,X0,X2] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X2,X4,X0)
| c_lessequals(X4,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f4278,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_lessequals(c_Power_Opower__class_Opower(X3,X1,X2),c_Power_Opower__class_Opower(X3,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_143
| ~ spl0_317 ),
inference(resolution,[],[f3577,f1392]) ).
fof(f1392,plain,
( ! [X2,X0,X4] :
( c_lessequals(X4,X2,X0)
| c_lessequals(X2,X4,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f1391]) ).
fof(f28190,plain,
( spl0_816
| ~ spl0_143
| ~ spl0_316 ),
inference(avatar_split_clause,[],[f4264,f3572,f1391,f28188]) ).
fof(f28188,plain,
( spl0_816
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f3572,plain,
( spl0_316
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f4264,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_143
| ~ spl0_316 ),
inference(resolution,[],[f3573,f1392]) ).
fof(f3573,plain,
( ! [X3,X0,X1,X13] :
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0)
| c_lessequals(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_316 ),
inference(avatar_component_clause,[],[f3572]) ).
fof(f28186,plain,
( spl0_815
| ~ spl0_136
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f4230,f3568,f1363,f28184]) ).
fof(f28184,plain,
( spl0_815
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X3,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f4230,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X3,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) )
| ~ spl0_136
| ~ spl0_315 ),
inference(resolution,[],[f3569,f1364]) ).
fof(f28182,plain,
( spl0_814
| ~ spl0_134
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f4229,f3568,f1355,f28180]) ).
fof(f28180,plain,
( spl0_814
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X3,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f4229,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X3,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) )
| ~ spl0_134
| ~ spl0_315 ),
inference(resolution,[],[f3569,f1356]) ).
fof(f28178,plain,
( spl0_813
| ~ spl0_136
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f4204,f3527,f1363,f28176]) ).
fof(f28176,plain,
( spl0_813
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f4204,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) )
| ~ spl0_136
| ~ spl0_314 ),
inference(resolution,[],[f3528,f1364]) ).
fof(f28174,plain,
( spl0_812
| ~ spl0_449
| ~ spl0_669 ),
inference(avatar_split_clause,[],[f21533,f21402,f9464,f28172]) ).
fof(f21533,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X0,t_a),X2,t_a)
| ~ spl0_449
| ~ spl0_669 ),
inference(superposition,[],[f21403,f9465]) ).
fof(f28170,plain,
( spl0_811
| ~ spl0_134
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f4203,f3527,f1355,f28168]) ).
fof(f28168,plain,
( spl0_811
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f4203,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) )
| ~ spl0_134
| ~ spl0_314 ),
inference(resolution,[],[f3528,f1356]) ).
fof(f28166,plain,
( spl0_810
| ~ spl0_136
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f4178,f3523,f1363,f28164]) ).
fof(f28164,plain,
( spl0_810
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f4178,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2) )
| ~ spl0_136
| ~ spl0_313 ),
inference(resolution,[],[f3524,f1364]) ).
fof(f28162,plain,
( spl0_809
| ~ spl0_134
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f4177,f3523,f1355,f28160]) ).
fof(f28160,plain,
( spl0_809
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f4177,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2) )
| ~ spl0_134
| ~ spl0_313 ),
inference(resolution,[],[f3524,f1356]) ).
fof(f28158,plain,
( spl0_808
| ~ spl0_136
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f4152,f3519,f1363,f28156]) ).
fof(f28156,plain,
( spl0_808
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f4152,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) )
| ~ spl0_136
| ~ spl0_312 ),
inference(resolution,[],[f3520,f1364]) ).
fof(f28154,plain,
( spl0_807
| ~ spl0_134
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f4151,f3519,f1355,f28152]) ).
fof(f28152,plain,
( spl0_807
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f4151,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) )
| ~ spl0_134
| ~ spl0_312 ),
inference(resolution,[],[f3520,f1356]) ).
fof(f28150,plain,
( spl0_806
| ~ spl0_136
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f4126,f3515,f1363,f28148]) ).
fof(f28148,plain,
( spl0_806
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono1(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f4126,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono1(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) )
| ~ spl0_136
| ~ spl0_311 ),
inference(resolution,[],[f3516,f1364]) ).
fof(f28146,plain,
( spl0_805
| ~ spl0_134
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f4125,f3515,f1355,f28144]) ).
fof(f28144,plain,
( spl0_805
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono1(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f4125,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono1(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) )
| ~ spl0_134
| ~ spl0_311 ),
inference(resolution,[],[f3516,f1356]) ).
fof(f28142,plain,
( spl0_804
| ~ spl0_135
| ~ spl0_310 ),
inference(avatar_split_clause,[],[f4109,f3511,f1359,f28140]) ).
fof(f28140,plain,
( spl0_804
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f3511,plain,
( spl0_310
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f4109,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_135
| ~ spl0_310 ),
inference(resolution,[],[f3512,f1360]) ).
fof(f3512,plain,
( ! [X3,X0,X1,X13] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_310 ),
inference(avatar_component_clause,[],[f3511]) ).
fof(f28138,plain,
( spl0_803
| ~ spl0_135
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f4085,f3507,f1359,f28136]) ).
fof(f28136,plain,
( spl0_803
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X3,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f3507,plain,
( spl0_309
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f4085,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X3,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_135
| ~ spl0_309 ),
inference(resolution,[],[f3508,f1360]) ).
fof(f3508,plain,
( ! [X3,X0,X1,X13] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0)
| c_HOL_Oord__class_Oless(X3,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_309 ),
inference(avatar_component_clause,[],[f3507]) ).
fof(f28134,plain,
( spl0_802
| ~ spl0_135
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f4048,f3503,f1359,f28132]) ).
fof(f28132,plain,
( spl0_802
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f3503,plain,
( spl0_308
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f4048,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_135
| ~ spl0_308 ),
inference(resolution,[],[f3504,f1360]) ).
fof(f3504,plain,
( ! [X3,X0,X1,X13] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_308 ),
inference(avatar_component_clause,[],[f3503]) ).
fof(f28130,plain,
( spl0_801
| ~ spl0_361
| ~ spl0_459 ),
inference(avatar_split_clause,[],[f11604,f11244,f5201,f28128]) ).
fof(f28128,plain,
( spl0_801
<=> ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X1,X0,t_a) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oinverse__class_Oinverse(X0,t_a),t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f11604,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X1,X0,t_a) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oinverse__class_Oinverse(X0,t_a),t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_361
| ~ spl0_459 ),
inference(superposition,[],[f5202,f11245]) ).
fof(f28126,plain,
( spl0_800
| ~ spl0_135
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f4024,f3499,f1359,f28124]) ).
fof(f28124,plain,
( spl0_800
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f3499,plain,
( spl0_307
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f4024,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_135
| ~ spl0_307 ),
inference(resolution,[],[f3500,f1360]) ).
fof(f3500,plain,
( ! [X3,X0,X1,X13] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0)
| c_HOL_Oord__class_Oless(X3,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_307 ),
inference(avatar_component_clause,[],[f3499]) ).
fof(f28122,plain,
( spl0_799
| ~ spl0_142
| ~ spl0_306 ),
inference(avatar_split_clause,[],[f4002,f3495,f1387,f28120]) ).
fof(f28120,plain,
( spl0_799
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f4002,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) )
| ~ spl0_142
| ~ spl0_306 ),
inference(resolution,[],[f3496,f1388]) ).
fof(f28118,plain,
( spl0_798
| ~ spl0_141
| ~ spl0_306 ),
inference(avatar_split_clause,[],[f4001,f3495,f1383,f28116]) ).
fof(f28116,plain,
( spl0_798
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f4001,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) )
| ~ spl0_141
| ~ spl0_306 ),
inference(resolution,[],[f3496,f1384]) ).
fof(f28114,plain,
( spl0_797
| ~ spl0_140
| ~ spl0_306 ),
inference(avatar_split_clause,[],[f4000,f3495,f1379,f28112]) ).
fof(f28112,plain,
( spl0_797
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f4000,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_140
| ~ spl0_306 ),
inference(resolution,[],[f3496,f1380]) ).
fof(f28110,plain,
( spl0_796
| ~ spl0_138
| ~ spl0_306 ),
inference(avatar_split_clause,[],[f3999,f3495,f1371,f28108]) ).
fof(f28108,plain,
( spl0_796
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f3999,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) )
| ~ spl0_138
| ~ spl0_306 ),
inference(resolution,[],[f3496,f1372]) ).
fof(f28106,plain,
( spl0_795
| ~ spl0_137
| ~ spl0_306 ),
inference(avatar_split_clause,[],[f3998,f3495,f1367,f28104]) ).
fof(f28104,plain,
( spl0_795
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f3998,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) )
| ~ spl0_137
| ~ spl0_306 ),
inference(resolution,[],[f3496,f1368]) ).
fof(f28102,plain,
( spl0_794
| ~ spl0_142
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3972,f3491,f1387,f28100]) ).
fof(f28100,plain,
( spl0_794
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f3972,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2) )
| ~ spl0_142
| ~ spl0_305 ),
inference(resolution,[],[f3492,f1388]) ).
fof(f28098,plain,
( spl0_793
| ~ spl0_141
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3971,f3491,f1383,f28096]) ).
fof(f28096,plain,
( spl0_793
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f3971,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2) )
| ~ spl0_141
| ~ spl0_305 ),
inference(resolution,[],[f3492,f1384]) ).
fof(f28094,plain,
( spl0_792
| ~ spl0_140
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3970,f3491,f1379,f28092]) ).
fof(f28092,plain,
( spl0_792
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f3970,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_140
| ~ spl0_305 ),
inference(resolution,[],[f3492,f1380]) ).
fof(f28090,plain,
( spl0_791
| ~ spl0_138
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3969,f3491,f1371,f28088]) ).
fof(f28088,plain,
( spl0_791
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X3,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f3969,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X3,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) )
| ~ spl0_138
| ~ spl0_305 ),
inference(resolution,[],[f3492,f1372]) ).
fof(f27588,plain,
( spl0_790
| ~ spl0_137
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3968,f3491,f1367,f27586]) ).
fof(f27586,plain,
( spl0_790
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X3,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f3968,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X3,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) )
| ~ spl0_137
| ~ spl0_305 ),
inference(resolution,[],[f3492,f1368]) ).
fof(f27584,plain,
( spl0_789
| ~ spl0_142
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3943,f3459,f1387,f27582]) ).
fof(f27582,plain,
( spl0_789
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f3943,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2) )
| ~ spl0_142
| ~ spl0_304 ),
inference(resolution,[],[f3460,f1388]) ).
fof(f27580,plain,
( spl0_788
| ~ spl0_141
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3942,f3459,f1383,f27578]) ).
fof(f27578,plain,
( spl0_788
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f3942,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2) )
| ~ spl0_141
| ~ spl0_304 ),
inference(resolution,[],[f3460,f1384]) ).
fof(f27576,plain,
( spl0_787
| ~ spl0_140
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3941,f3459,f1379,f27574]) ).
fof(f27574,plain,
( spl0_787
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f3941,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_140
| ~ spl0_304 ),
inference(resolution,[],[f3460,f1380]) ).
fof(f27572,plain,
( spl0_786
| ~ spl0_138
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3940,f3459,f1371,f27570]) ).
fof(f27570,plain,
( spl0_786
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X3,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f3940,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X3,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) )
| ~ spl0_138
| ~ spl0_304 ),
inference(resolution,[],[f3460,f1372]) ).
fof(f27568,plain,
( spl0_785
| ~ spl0_137
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3939,f3459,f1367,f27566]) ).
fof(f27566,plain,
( spl0_785
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X3,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f3939,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X3,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) )
| ~ spl0_137
| ~ spl0_304 ),
inference(resolution,[],[f3460,f1368]) ).
fof(f27564,plain,
( spl0_784
| ~ spl0_142
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f3915,f3455,f1387,f27562]) ).
fof(f27562,plain,
( spl0_784
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X3,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f3915,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X3,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) )
| ~ spl0_142
| ~ spl0_303 ),
inference(resolution,[],[f3456,f1388]) ).
fof(f27560,plain,
( spl0_783
| ~ spl0_141
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f3914,f3455,f1383,f27558]) ).
fof(f27558,plain,
( spl0_783
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X3,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f3914,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X3,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) )
| ~ spl0_141
| ~ spl0_303 ),
inference(resolution,[],[f3456,f1384]) ).
fof(f27556,plain,
( spl0_782
| ~ spl0_140
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f3913,f3455,f1379,f27554]) ).
fof(f27554,plain,
( spl0_782
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X3,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f3913,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X3,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_140
| ~ spl0_303 ),
inference(resolution,[],[f3456,f1380]) ).
fof(f27552,plain,
( spl0_781
| ~ spl0_138
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f3912,f3455,f1371,f27550]) ).
fof(f27550,plain,
( spl0_781
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f3912,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2) )
| ~ spl0_138
| ~ spl0_303 ),
inference(resolution,[],[f3456,f1372]) ).
fof(f27547,plain,
( spl0_780
| ~ spl0_137
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f3911,f3455,f1367,f27545]) ).
fof(f27545,plain,
( spl0_780
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f3911,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2) )
| ~ spl0_137
| ~ spl0_303 ),
inference(resolution,[],[f3456,f1368]) ).
fof(f27543,plain,
( spl0_779
| ~ spl0_142
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3885,f3451,f1387,f27541]) ).
fof(f27541,plain,
( spl0_779
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f3885,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) )
| ~ spl0_142
| ~ spl0_302 ),
inference(resolution,[],[f3452,f1388]) ).
fof(f27539,plain,
( spl0_778
| ~ spl0_141
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3884,f3451,f1383,f27537]) ).
fof(f27537,plain,
( spl0_778
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f3884,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) )
| ~ spl0_141
| ~ spl0_302 ),
inference(resolution,[],[f3452,f1384]) ).
fof(f27535,plain,
( spl0_777
| ~ spl0_140
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3883,f3451,f1379,f27533]) ).
fof(f27533,plain,
( spl0_777
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f3883,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_140
| ~ spl0_302 ),
inference(resolution,[],[f3452,f1380]) ).
fof(f27531,plain,
( spl0_776
| ~ spl0_138
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3882,f3451,f1371,f27529]) ).
fof(f27529,plain,
( spl0_776
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f3882,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) )
| ~ spl0_138
| ~ spl0_302 ),
inference(resolution,[],[f3452,f1372]) ).
fof(f27527,plain,
( spl0_775
| ~ spl0_137
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3881,f3451,f1367,f27525]) ).
fof(f27525,plain,
( spl0_775
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f3881,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) )
| ~ spl0_137
| ~ spl0_302 ),
inference(resolution,[],[f3452,f1368]) ).
fof(f27523,plain,
( spl0_774
| ~ spl0_142
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3855,f3447,f1387,f27521]) ).
fof(f27521,plain,
( spl0_774
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f3855,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) )
| ~ spl0_142
| ~ spl0_301 ),
inference(resolution,[],[f3448,f1388]) ).
fof(f27519,plain,
( spl0_773
| ~ spl0_141
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3854,f3447,f1383,f27517]) ).
fof(f27517,plain,
( spl0_773
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f3854,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) )
| ~ spl0_141
| ~ spl0_301 ),
inference(resolution,[],[f3448,f1384]) ).
fof(f27515,plain,
( spl0_772
| ~ spl0_140
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3853,f3447,f1379,f27513]) ).
fof(f27513,plain,
( spl0_772
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f3853,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_140
| ~ spl0_301 ),
inference(resolution,[],[f3448,f1380]) ).
fof(f27511,plain,
( spl0_771
| ~ spl0_138
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3852,f3447,f1371,f27509]) ).
fof(f27509,plain,
( spl0_771
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f3852,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) )
| ~ spl0_138
| ~ spl0_301 ),
inference(resolution,[],[f3448,f1372]) ).
fof(f27506,plain,
( spl0_770
| ~ spl0_137
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3851,f3447,f1367,f27504]) ).
fof(f27504,plain,
( spl0_770
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f3851,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) )
| ~ spl0_137
| ~ spl0_301 ),
inference(resolution,[],[f3448,f1368]) ).
fof(f27502,plain,
( spl0_769
| ~ spl0_142
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3827,f3443,f1387,f27500]) ).
fof(f27500,plain,
( spl0_769
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f3827,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) )
| ~ spl0_142
| ~ spl0_300 ),
inference(resolution,[],[f3444,f1388]) ).
fof(f27498,plain,
( spl0_768
| ~ spl0_141
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3826,f3443,f1383,f27496]) ).
fof(f27496,plain,
( spl0_768
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f3826,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) )
| ~ spl0_141
| ~ spl0_300 ),
inference(resolution,[],[f3444,f1384]) ).
fof(f27494,plain,
( spl0_767
| ~ spl0_140
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3825,f3443,f1379,f27492]) ).
fof(f27492,plain,
( spl0_767
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f3825,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_140
| ~ spl0_300 ),
inference(resolution,[],[f3444,f1380]) ).
fof(f27490,plain,
( spl0_766
| ~ spl0_138
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3824,f3443,f1371,f27488]) ).
fof(f27488,plain,
( spl0_766
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f3824,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) )
| ~ spl0_138
| ~ spl0_300 ),
inference(resolution,[],[f3444,f1372]) ).
fof(f27486,plain,
( spl0_765
| ~ spl0_137
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3823,f3443,f1367,f27484]) ).
fof(f27484,plain,
( spl0_765
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f3823,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) )
| ~ spl0_137
| ~ spl0_300 ),
inference(resolution,[],[f3444,f1368]) ).
fof(f27482,plain,
( spl0_764
| ~ spl0_135
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f3801,f3439,f1359,f27480]) ).
fof(f27480,plain,
( spl0_764
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f3439,plain,
( spl0_299
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f3801,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_135
| ~ spl0_299 ),
inference(resolution,[],[f3440,f1360]) ).
fof(f3440,plain,
( ! [X3,X0,X1,X13] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_299 ),
inference(avatar_component_clause,[],[f3439]) ).
fof(f27478,plain,
( spl0_763
| ~ spl0_135
| ~ spl0_298 ),
inference(avatar_split_clause,[],[f3787,f3435,f1359,f27476]) ).
fof(f27476,plain,
( spl0_763
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f3435,plain,
( spl0_298
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f3787,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_135
| ~ spl0_298 ),
inference(resolution,[],[f3436,f1360]) ).
fof(f3436,plain,
( ! [X3,X0,X1,X13] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0)
| c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_298 ),
inference(avatar_component_clause,[],[f3435]) ).
fof(f27474,plain,
( spl0_762
| ~ spl0_136
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f3762,f3431,f1363,f27472]) ).
fof(f27472,plain,
( spl0_762
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f3762,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) )
| ~ spl0_136
| ~ spl0_297 ),
inference(resolution,[],[f3432,f1364]) ).
fof(f27470,plain,
( spl0_761
| ~ spl0_134
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f3761,f3431,f1355,f27468]) ).
fof(f27468,plain,
( spl0_761
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f3761,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X0,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) )
| ~ spl0_134
| ~ spl0_297 ),
inference(resolution,[],[f3432,f1356]) ).
fof(f27466,plain,
( spl0_760
| ~ spl0_283
| ~ spl0_738 ),
inference(avatar_split_clause,[],[f27372,f26974,f3010,f27464]) ).
fof(f27464,plain,
( spl0_760
<=> ! [X0] :
( c_HOL_Oone__class_Oone(t_a) != X0
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(t_a),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f27372,plain,
( ! [X0] :
( c_HOL_Oone__class_Oone(t_a) != X0
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(t_a),t_a) )
| ~ spl0_283
| ~ spl0_738 ),
inference(superposition,[],[f26975,f3011]) ).
fof(f27462,plain,
( spl0_759
| ~ spl0_143
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f3749,f3427,f1391,f27460]) ).
fof(f27460,plain,
( spl0_759
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f3427,plain,
( spl0_296
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f3749,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_143
| ~ spl0_296 ),
inference(resolution,[],[f3428,f1392]) ).
fof(f3428,plain,
( ! [X3,X0,X1,X13] :
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0)
| c_lessequals(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_296 ),
inference(avatar_component_clause,[],[f3427]) ).
fof(f27458,plain,
( spl0_758
| ~ spl0_136
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f3720,f3423,f1363,f27456]) ).
fof(f27456,plain,
( spl0_758
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f3720,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) )
| ~ spl0_136
| ~ spl0_295 ),
inference(resolution,[],[f3424,f1364]) ).
fof(f27454,plain,
( spl0_757
| ~ spl0_134
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f3719,f3423,f1355,f27452]) ).
fof(f27452,plain,
( spl0_757
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f3719,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2) )
| ~ spl0_134
| ~ spl0_295 ),
inference(resolution,[],[f3424,f1356]) ).
fof(f27450,plain,
( spl0_756
| ~ spl0_143
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f3709,f3415,f1391,f27448]) ).
fof(f27448,plain,
( spl0_756
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f3415,plain,
( spl0_293
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f3709,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_143
| ~ spl0_293 ),
inference(resolution,[],[f3416,f1392]) ).
fof(f3416,plain,
( ! [X3,X0,X1,X13] :
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0)
| c_lessequals(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0) )
| ~ spl0_293 ),
inference(avatar_component_clause,[],[f3415]) ).
fof(f27446,plain,
( spl0_755
| ~ spl0_143
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3696,f3411,f1391,f27444]) ).
fof(f27444,plain,
( spl0_755
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f3411,plain,
( spl0_292
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f3696,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_143
| ~ spl0_292 ),
inference(resolution,[],[f3412,f1392]) ).
fof(f3412,plain,
( ! [X3,X0,X1,X13] :
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0)
| c_lessequals(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0) )
| ~ spl0_292 ),
inference(avatar_component_clause,[],[f3411]) ).
fof(f27442,plain,
( spl0_754
| ~ spl0_135
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f3682,f3407,f1359,f27440]) ).
fof(f27440,plain,
( spl0_754
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f3407,plain,
( spl0_291
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f3682,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_135
| ~ spl0_291 ),
inference(resolution,[],[f3408,f1360]) ).
fof(f3408,plain,
( ! [X3,X0,X1,X13] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ class_Ring__and__Field_Oordered__semiring(X0) )
| ~ spl0_291 ),
inference(avatar_component_clause,[],[f3407]) ).
fof(f27438,plain,
( spl0_753
| ~ spl0_135
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f3669,f3403,f1359,f27436]) ).
fof(f27436,plain,
( spl0_753
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f3403,plain,
( spl0_290
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f3669,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_135
| ~ spl0_290 ),
inference(resolution,[],[f3404,f1360]) ).
fof(f3404,plain,
( ! [X3,X0,X1,X13] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ class_Ring__and__Field_Oordered__semiring(X0) )
| ~ spl0_290 ),
inference(avatar_component_clause,[],[f3403]) ).
fof(f27434,plain,
( spl0_752
| ~ spl0_135
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3656,f3399,f1359,f27432]) ).
fof(f27432,plain,
( spl0_752
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f3656,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_135
| ~ spl0_289 ),
inference(resolution,[],[f3400,f1360]) ).
fof(f27430,plain,
( spl0_751
| ~ spl0_135
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3643,f3395,f1359,f27428]) ).
fof(f27428,plain,
( spl0_751
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f3643,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_135
| ~ spl0_288 ),
inference(resolution,[],[f3396,f1360]) ).
fof(f27426,plain,
( spl0_750
| ~ spl0_185
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2322,f2273,f1923,f27424]) ).
fof(f27424,plain,
( spl0_750
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oone__class_Oone(X1) = c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f1923,plain,
( spl0_185
<=> ! [X2,X0] :
( ~ class_Int_Onumber__ring(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f2322,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oone__class_Oone(X1) = c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X1),c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1) )
| ~ spl0_185
| ~ spl0_209 ),
inference(resolution,[],[f2274,f1924]) ).
fof(f1924,plain,
( ! [X2,X0] :
( ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X2,X0) )
| ~ spl0_185 ),
inference(avatar_component_clause,[],[f1923]) ).
fof(f27422,plain,
( spl0_749
| ~ spl0_285
| ~ spl0_738 ),
inference(avatar_split_clause,[],[f27364,f26974,f3088,f27420]) ).
fof(f27420,plain,
( spl0_749
<=> ! [X0] :
( c_HOL_Oone__class_Oone(t_a) != X0
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),X0,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f27364,plain,
( ! [X0] :
( c_HOL_Oone__class_Oone(t_a) != X0
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),X0,t_a) )
| ~ spl0_285
| ~ spl0_738 ),
inference(superposition,[],[f26975,f3089]) ).
fof(f27418,plain,
( spl0_748
| ~ spl0_149
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2214,f1986,f1497,f27416]) ).
fof(f27416,plain,
( spl0_748
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) = c_HOL_Ominus__class_Ominus(X2,X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f2214,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) = c_HOL_Ominus__class_Ominus(X2,X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),tc_nat) )
| ~ spl0_149
| ~ spl0_199 ),
inference(resolution,[],[f1987,f1498]) ).
fof(f27414,plain,
( spl0_747
| ~ spl0_157
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2212,f1986,f1530,f27412]) ).
fof(f27412,plain,
( spl0_747
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) = c_HOL_Ominus__class_Ominus(X2,X0,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f2212,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) = c_HOL_Ominus__class_Ominus(X2,X0,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) )
| ~ spl0_157
| ~ spl0_199 ),
inference(resolution,[],[f1987,f1531]) ).
fof(f27410,plain,
( spl0_746
| ~ spl0_149
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2190,f1982,f1497,f27408]) ).
fof(f27408,plain,
( spl0_746
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X2,tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f2190,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X2,tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) )
| ~ spl0_149
| ~ spl0_198 ),
inference(resolution,[],[f1983,f1498]) ).
fof(f27406,plain,
( spl0_745
| ~ spl0_157
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2188,f1982,f1530,f27404]) ).
fof(f27404,plain,
( spl0_745
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X2,tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f2188,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X2,tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat) )
| ~ spl0_157
| ~ spl0_198 ),
inference(resolution,[],[f1983,f1531]) ).
fof(f27402,plain,
( spl0_744
| ~ spl0_181
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2167,f1978,f1771,f27400]) ).
fof(f27400,plain,
( spl0_744
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_HOL_Ominus__class_Ominus(X0,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f2167,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_HOL_Ominus__class_Ominus(X0,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2)
| ~ class_Orderings_Oorder(X2) )
| ~ spl0_181
| ~ spl0_197 ),
inference(resolution,[],[f1979,f1772]) ).
fof(f27398,plain,
( spl0_743
| ~ spl0_175
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2166,f1978,f1745,f27396]) ).
fof(f27396,plain,
( spl0_743
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_HOL_Ominus__class_Ominus(X0,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f2166,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_HOL_Ominus__class_Ominus(X0,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) )
| ~ spl0_175
| ~ spl0_197 ),
inference(resolution,[],[f1979,f1746]) ).
fof(f27394,plain,
( spl0_742
| ~ spl0_174
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2165,f1978,f1741,f27392]) ).
fof(f27392,plain,
( spl0_742
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_HOL_Ominus__class_Ominus(X0,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f2165,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_HOL_Ominus__class_Ominus(X0,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) )
| ~ spl0_174
| ~ spl0_197 ),
inference(resolution,[],[f1979,f1742]) ).
fof(f27390,plain,
( spl0_741
| ~ spl0_172
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f2035,f1927,f1733,f27388]) ).
fof(f27388,plain,
( spl0_741
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f1733,plain,
( spl0_172
<=> ! [X9,X0,X2] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f2035,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_172
| ~ spl0_186 ),
inference(resolution,[],[f1928,f1734]) ).
fof(f1734,plain,
( ! [X2,X0,X9] :
( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X9,X0),X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_172 ),
inference(avatar_component_clause,[],[f1733]) ).
fof(f27386,plain,
( spl0_740
| ~ spl0_176
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f2011,f1919,f1749,f27384]) ).
fof(f27384,plain,
( spl0_740
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2)
| c_HOL_Ominus__class_Ominus(X0,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f1749,plain,
( spl0_176
<=> ! [X4,X0,X2] :
( ~ class_Orderings_Olinorder(X0)
| X2 = X4
| c_HOL_Oord__class_Oless(X4,X2,X0)
| c_HOL_Oord__class_Oless(X2,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f1919,plain,
( spl0_184
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f2011,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2)
| c_HOL_Ominus__class_Ominus(X0,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_176
| ~ spl0_184 ),
inference(resolution,[],[f1920,f1750]) ).
fof(f1750,plain,
( ! [X2,X0,X4] :
( c_HOL_Oord__class_Oless(X4,X2,X0)
| c_HOL_Oord__class_Oless(X2,X4,X0)
| X2 = X4
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f1749]) ).
fof(f1920,plain,
( ! [X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
| ~ spl0_184 ),
inference(avatar_component_clause,[],[f1919]) ).
fof(f27382,plain,
( spl0_739
| ~ spl0_177
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f2009,f1919,f1753,f27380]) ).
fof(f27380,plain,
( spl0_739
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2)
| c_HOL_Ominus__class_Ominus(X0,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f2009,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2)
| c_HOL_Ominus__class_Ominus(X0,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) )
| ~ spl0_177
| ~ spl0_184 ),
inference(resolution,[],[f1920,f1754]) ).
fof(f26976,plain,
( spl0_738
| ~ spl0_286
| ~ spl0_643
| ~ spl0_735 ),
inference(avatar_split_clause,[],[f23652,f22784,f18506,f3208,f26974]) ).
fof(f3208,plain,
( spl0_286
<=> c_HOL_Oone__class_Oone(t_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f23652,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Otimes__class_Otimes(X0,X1,t_a)
| c_HOL_Oone__class_Oone(t_a) != c_HOL_Otimes__class_Otimes(X1,X0,t_a) )
| ~ spl0_286
| ~ spl0_643
| ~ spl0_735 ),
inference(forward_demodulation,[],[f23515,f3210]) ).
fof(f3210,plain,
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a)
| ~ spl0_286 ),
inference(avatar_component_clause,[],[f3208]) ).
fof(f23515,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != c_HOL_Otimes__class_Otimes(X1,X0,t_a)
| c_HOL_Otimes__class_Otimes(X0,X1,t_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a) )
| ~ spl0_643
| ~ spl0_735 ),
inference(superposition,[],[f18507,f22785]) ).
fof(f24907,plain,
( spl0_737
| ~ spl0_283
| ~ spl0_735 ),
inference(avatar_split_clause,[],[f23644,f22784,f3010,f24905]) ).
fof(f23644,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X1,X0,t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,t_a),c_HOL_Oone__class_Oone(t_a),t_a)
| ~ spl0_283
| ~ spl0_735 ),
inference(forward_demodulation,[],[f23504,f3011]) ).
fof(f23504,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,t_a),c_HOL_Oone__class_Oone(t_a),t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_HOL_Otimes__class_Otimes(X1,X0,t_a),t_a)
| ~ spl0_735 ),
inference(superposition,[],[f22785,f22785]) ).
fof(f24349,plain,
( spl0_736
| ~ spl0_283
| ~ spl0_712
| ~ spl0_735 ),
inference(avatar_split_clause,[],[f23640,f22784,f21753,f3010,f24347]) ).
fof(f24347,plain,
( spl0_736
<=> ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X0,t_a),X0,t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f23640,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X0,t_a),X0,t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_283
| ~ spl0_712
| ~ spl0_735 ),
inference(forward_demodulation,[],[f23497,f3011]) ).
fof(f23497,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),X1,t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X0,t_a),X0,t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_712
| ~ spl0_735 ),
inference(superposition,[],[f22785,f21754]) ).
fof(f22786,plain,
( spl0_735
| ~ spl0_283
| ~ spl0_680 ),
inference(avatar_split_clause,[],[f21992,f21446,f3010,f22784]) ).
fof(f21992,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),c_HOL_Otimes__class_Otimes(X1,X0,t_a),t_a)
| ~ spl0_283
| ~ spl0_680 ),
inference(superposition,[],[f21447,f3011]) ).
fof(f22185,plain,
( spl0_734
| ~ spl0_78
| ~ spl0_92
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f4927,f4855,f1136,f1073,f22183]) ).
fof(f22183,plain,
( spl0_734
<=> ! [X2,X0,X1] :
( c_Power_Opower__class_Opower(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),X0)
| ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f1073,plain,
( spl0_78
<=> ! [X9] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f1136,plain,
( spl0_92
<=> ! [X19] : c_HOL_Ominus__class_Ominus(X19,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X19 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f4927,plain,
( ! [X2,X0,X1] :
( c_Power_Opower__class_Opower(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),X0)
| ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1 )
| ~ spl0_78
| ~ spl0_92
| ~ spl0_348 ),
inference(forward_demodulation,[],[f4883,f1137]) ).
fof(f1137,plain,
( ! [X19] : c_HOL_Ominus__class_Ominus(X19,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X19
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f1136]) ).
fof(f4883,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),X0) )
| ~ spl0_78
| ~ spl0_348 ),
inference(resolution,[],[f4856,f1074]) ).
fof(f1074,plain,
( ! [X9] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f1073]) ).
fof(f22181,plain,
( spl0_733
| ~ spl0_59
| ~ spl0_91
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f4926,f4855,f1132,f980,f22179]) ).
fof(f980,plain,
( spl0_59
<=> ! [X9] : c_lessequals(X9,X9,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f1132,plain,
( spl0_91
<=> ! [X19] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X19,X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f4926,plain,
( ! [X2,X0,X1] :
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,X2,X0),X0)
| ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1 )
| ~ spl0_59
| ~ spl0_91
| ~ spl0_348 ),
inference(forward_demodulation,[],[f4882,f1133]) ).
fof(f1133,plain,
( ! [X19] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X19,X19,tc_nat)
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f1132]) ).
fof(f4882,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(X2,X2,tc_nat),X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) )
| ~ spl0_59
| ~ spl0_348 ),
inference(resolution,[],[f4856,f981]) ).
fof(f981,plain,
( ! [X9] : c_lessequals(X9,X9,tc_nat)
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f980]) ).
fof(f21981,plain,
( spl0_732
| ~ spl0_102
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f4565,f4441,f1180,f21979]) ).
fof(f21979,plain,
( spl0_732
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(X2,X1,tc_nat)
| ~ c_lessequals(X0,X2,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f4441,plain,
( spl0_331
<=> ! [X9,X23,X19] :
( ~ c_lessequals(X23,X19,tc_nat)
| ~ c_lessequals(X23,X9,tc_nat)
| c_lessequals(X19,X9,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X19,X23,tc_nat),c_HOL_Ominus__class_Ominus(X9,X23,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f4565,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(X2,X1,tc_nat)
| ~ c_lessequals(X0,X2,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),tc_nat) )
| ~ spl0_102
| ~ spl0_331 ),
inference(resolution,[],[f4442,f1181]) ).
fof(f4442,plain,
( ! [X19,X9,X23] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X19,X23,tc_nat),c_HOL_Ominus__class_Ominus(X9,X23,tc_nat),tc_nat)
| ~ c_lessequals(X23,X9,tc_nat)
| c_lessequals(X19,X9,tc_nat)
| ~ c_lessequals(X23,X19,tc_nat) )
| ~ spl0_331 ),
inference(avatar_component_clause,[],[f4441]) ).
fof(f21977,plain,
( spl0_731
| ~ spl0_313
| ~ spl0_316 ),
inference(avatar_split_clause,[],[f4258,f3572,f3523,f21975]) ).
fof(f21975,plain,
( spl0_731
<=> ! [X2,X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X2,X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Omult__mono(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f4258,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X2,X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Omult__mono(X1) )
| ~ spl0_313
| ~ spl0_316 ),
inference(resolution,[],[f3573,f3524]) ).
fof(f21973,plain,
( spl0_730
| ~ spl0_315
| ~ spl0_316 ),
inference(avatar_split_clause,[],[f4257,f3572,f3568,f21971]) ).
fof(f21971,plain,
( spl0_730
<=> ! [X2,X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X2,X2,X1)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f4257,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X2,X2,X1)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1) )
| ~ spl0_315
| ~ spl0_316 ),
inference(resolution,[],[f3573,f3569]) ).
fof(f21969,plain,
( spl0_729
| ~ spl0_311
| ~ spl0_316 ),
inference(avatar_split_clause,[],[f4254,f3572,f3515,f21967]) ).
fof(f21967,plain,
( spl0_729
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(X1,X0,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f4254,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(X1,X0,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono1(X2) )
| ~ spl0_311
| ~ spl0_316 ),
inference(resolution,[],[f3573,f3516]) ).
fof(f21965,plain,
( spl0_728
| ~ spl0_312
| ~ spl0_316 ),
inference(avatar_split_clause,[],[f4253,f3572,f3519,f21963]) ).
fof(f21963,plain,
( spl0_728
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(X1,X0,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f4253,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(X1,X0,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Omult__mono(X2) )
| ~ spl0_312
| ~ spl0_316 ),
inference(resolution,[],[f3573,f3520]) ).
fof(f21961,plain,
( spl0_727
| ~ spl0_296
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f4227,f3568,f3427,f21959]) ).
fof(f21959,plain,
( spl0_727
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X0,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| c_lessequals(X2,X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f4227,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X0,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| c_lessequals(X2,X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) )
| ~ spl0_296
| ~ spl0_315 ),
inference(resolution,[],[f3569,f3428]) ).
fof(f21957,plain,
( spl0_726
| ~ spl0_293
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f4202,f3527,f3415,f21955]) ).
fof(f21955,plain,
( spl0_726
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| c_lessequals(X1,X0,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f4202,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| c_lessequals(X1,X0,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) )
| ~ spl0_293
| ~ spl0_314 ),
inference(resolution,[],[f3528,f3416]) ).
fof(f21953,plain,
( spl0_725
| ~ spl0_296
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f4201,f3527,f3427,f21951]) ).
fof(f21951,plain,
( spl0_725
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| c_lessequals(X1,X0,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f4201,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| c_lessequals(X1,X0,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) )
| ~ spl0_296
| ~ spl0_314 ),
inference(resolution,[],[f3528,f3428]) ).
fof(f21949,plain,
( spl0_724
| ~ spl0_292
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f4200,f3527,f3411,f21947]) ).
fof(f21947,plain,
( spl0_724
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X0,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| c_lessequals(X2,X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f4200,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X0,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| c_lessequals(X2,X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) )
| ~ spl0_292
| ~ spl0_314 ),
inference(resolution,[],[f3528,f3412]) ).
fof(f21945,plain,
( spl0_723
| ~ spl0_296
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f4175,f3523,f3427,f21943]) ).
fof(f21943,plain,
( spl0_723
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X0,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Omult__mono(X1)
| c_lessequals(X2,X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f4175,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X0,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Omult__mono(X1)
| c_lessequals(X2,X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) )
| ~ spl0_296
| ~ spl0_313 ),
inference(resolution,[],[f3524,f3428]) ).
fof(f21795,plain,
( spl0_722
| ~ spl0_292
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f4148,f3519,f3411,f21793]) ).
fof(f21793,plain,
( spl0_722
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X0,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Omult__mono(X1)
| c_lessequals(X2,X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f4148,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X0,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Omult__mono(X1)
| c_lessequals(X2,X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) )
| ~ spl0_292
| ~ spl0_312 ),
inference(resolution,[],[f3520,f3412]) ).
fof(f21791,plain,
( spl0_721
| ~ spl0_292
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f4122,f3515,f3411,f21789]) ).
fof(f21789,plain,
( spl0_721
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X0,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Omult__mono1(X1)
| c_lessequals(X2,X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f4122,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X0,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Omult__mono1(X1)
| c_lessequals(X2,X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) )
| ~ spl0_292
| ~ spl0_311 ),
inference(resolution,[],[f3516,f3412]) ).
fof(f21787,plain,
( spl0_720
| ~ spl0_290
| ~ spl0_306 ),
inference(avatar_split_clause,[],[f3990,f3495,f3403,f21785]) ).
fof(f21785,plain,
( spl0_720
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semiring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f3990,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semiring(X1) )
| ~ spl0_290
| ~ spl0_306 ),
inference(resolution,[],[f3496,f3404]) ).
fof(f21783,plain,
( spl0_719
| ~ spl0_289
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3813,f3443,f3399,f21781]) ).
fof(f21781,plain,
( spl0_719
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oord__class_Oless(X1,X0,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f3813,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oord__class_Oless(X1,X0,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) )
| ~ spl0_289
| ~ spl0_300 ),
inference(resolution,[],[f3444,f3400]) ).
fof(f21779,plain,
( spl0_718
| ~ spl0_291
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3812,f3443,f3407,f21777]) ).
fof(f21777,plain,
( spl0_718
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oord__class_Oless(X1,X0,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f3812,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oord__class_Oless(X1,X0,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring(X2) )
| ~ spl0_291
| ~ spl0_300 ),
inference(resolution,[],[f3444,f3408]) ).
fof(f21775,plain,
( spl0_717
| ~ spl0_292
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f3758,f3431,f3411,f21773]) ).
fof(f21773,plain,
( spl0_717
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_lessequals(X2,X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f3758,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_lessequals(X2,X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) )
| ~ spl0_292
| ~ spl0_297 ),
inference(resolution,[],[f3432,f3412]) ).
fof(f21771,plain,
( spl0_716
| ~ spl0_292
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f3717,f3423,f3411,f21769]) ).
fof(f21769,plain,
( spl0_716
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_lessequals(X2,X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f3717,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_lessequals(X2,X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) )
| ~ spl0_292
| ~ spl0_295 ),
inference(resolution,[],[f3424,f3412]) ).
fof(f21767,plain,
( spl0_715
| ~ spl0_142
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3367,f2994,f1387,f21765]) ).
fof(f21765,plain,
( spl0_715
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X1),c_HOL_Oone__class_Oone(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f3367,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X1),c_HOL_Oone__class_Oone(X1),X1) )
| ~ spl0_142
| ~ spl0_279 ),
inference(resolution,[],[f2995,f1388]) ).
fof(f21763,plain,
( spl0_714
| ~ spl0_141
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3366,f2994,f1383,f21761]) ).
fof(f21761,plain,
( spl0_714
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X1),c_HOL_Oone__class_Oone(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f3366,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X1),c_HOL_Oone__class_Oone(X1),X1) )
| ~ spl0_141
| ~ spl0_279 ),
inference(resolution,[],[f2995,f1384]) ).
fof(f21759,plain,
( spl0_713
| ~ spl0_140
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3365,f2994,f1379,f21757]) ).
fof(f21757,plain,
( spl0_713
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f3365,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Orderings_Opreorder(X1) )
| ~ spl0_140
| ~ spl0_279 ),
inference(resolution,[],[f2995,f1380]) ).
fof(f21755,plain,
( spl0_712
| ~ spl0_283
| ~ spl0_484
| ~ spl0_527
| ~ spl0_669 ),
inference(avatar_split_clause,[],[f21689,f21402,f13797,f12230,f3010,f21753]) ).
fof(f21689,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Odivide(X1,X0,t_a),t_a) = X1
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_283
| ~ spl0_484
| ~ spl0_527
| ~ spl0_669 ),
inference(forward_demodulation,[],[f21688,f3011]) ).
fof(f21688,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),X1,t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Odivide(X1,X0,t_a),t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_484
| ~ spl0_527
| ~ spl0_669 ),
inference(forward_demodulation,[],[f21538,f12231]) ).
fof(f21538,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),X1,t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,t_a),X1,t_a),t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ~ spl0_527
| ~ spl0_669 ),
inference(superposition,[],[f21403,f13798]) ).
fof(f21751,plain,
( spl0_711
| ~ spl0_138
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3364,f2994,f1371,f21749]) ).
fof(f21749,plain,
( spl0_711
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f3364,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X0,X1),X1) )
| ~ spl0_138
| ~ spl0_279 ),
inference(resolution,[],[f2995,f1372]) ).
fof(f21747,plain,
( spl0_710
| ~ spl0_137
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3363,f2994,f1367,f21745]) ).
fof(f21745,plain,
( spl0_710
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f3363,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X0,X1),X1) )
| ~ spl0_137
| ~ spl0_279 ),
inference(resolution,[],[f2995,f1368]) ).
fof(f21743,plain,
( spl0_709
| ~ spl0_142
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f3359,f2990,f1387,f21741]) ).
fof(f21741,plain,
( spl0_709
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X0),X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f3359,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X0),X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) )
| ~ spl0_142
| ~ spl0_278 ),
inference(resolution,[],[f2991,f1388]) ).
fof(f21739,plain,
( spl0_708
| ~ spl0_141
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f3358,f2990,f1383,f21737]) ).
fof(f21737,plain,
( spl0_708
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X0),X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f3358,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X0),X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) )
| ~ spl0_141
| ~ spl0_278 ),
inference(resolution,[],[f2991,f1384]) ).
fof(f21735,plain,
( spl0_707
| ~ spl0_140
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f3357,f2990,f1379,f21733]) ).
fof(f21733,plain,
( spl0_707
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X0),X0),c_Power_Opower__class_Opower(X1,X2,X0),X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f3357,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X0),X0),c_Power_Opower__class_Opower(X1,X2,X0),X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_140
| ~ spl0_278 ),
inference(resolution,[],[f2991,f1380]) ).
fof(f21731,plain,
( spl0_706
| ~ spl0_138
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f3356,f2990,f1371,f21729]) ).
fof(f21729,plain,
( spl0_706
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f3356,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X0),X0),X0) )
| ~ spl0_138
| ~ spl0_278 ),
inference(resolution,[],[f2991,f1372]) ).
fof(f21727,plain,
( spl0_705
| ~ spl0_137
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f3355,f2990,f1367,f21725]) ).
fof(f21725,plain,
( spl0_705
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f3355,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X0),X0),X0) )
| ~ spl0_137
| ~ spl0_278 ),
inference(resolution,[],[f2991,f1368]) ).
fof(f21723,plain,
( spl0_704
| ~ spl0_142
| ~ spl0_277 ),
inference(avatar_split_clause,[],[f3351,f2986,f1387,f21721]) ).
fof(f21721,plain,
( spl0_704
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f3351,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0) )
| ~ spl0_142
| ~ spl0_277 ),
inference(resolution,[],[f2987,f1388]) ).
fof(f21719,plain,
( spl0_703
| ~ spl0_141
| ~ spl0_277 ),
inference(avatar_split_clause,[],[f3350,f2986,f1383,f21717]) ).
fof(f21717,plain,
( spl0_703
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f3350,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0) )
| ~ spl0_141
| ~ spl0_277 ),
inference(resolution,[],[f2987,f1384]) ).
fof(f21715,plain,
( spl0_702
| ~ spl0_140
| ~ spl0_277 ),
inference(avatar_split_clause,[],[f3349,f2986,f1379,f21713]) ).
fof(f21713,plain,
( spl0_702
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f3349,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_140
| ~ spl0_277 ),
inference(resolution,[],[f2987,f1380]) ).
fof(f21532,plain,
( spl0_701
| ~ spl0_138
| ~ spl0_277 ),
inference(avatar_split_clause,[],[f3348,f2986,f1371,f21530]) ).
fof(f21530,plain,
( spl0_701
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f3348,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) )
| ~ spl0_138
| ~ spl0_277 ),
inference(resolution,[],[f2987,f1372]) ).
fof(f21528,plain,
( spl0_700
| ~ spl0_137
| ~ spl0_277 ),
inference(avatar_split_clause,[],[f3347,f2986,f1367,f21526]) ).
fof(f21526,plain,
( spl0_700
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f3347,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) )
| ~ spl0_137
| ~ spl0_277 ),
inference(resolution,[],[f2987,f1368]) ).
fof(f21524,plain,
( spl0_699
| ~ spl0_136
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f3328,f2982,f1363,f21522]) ).
fof(f21522,plain,
( spl0_699
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f3328,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) )
| ~ spl0_136
| ~ spl0_276 ),
inference(resolution,[],[f2983,f1364]) ).
fof(f21520,plain,
( spl0_698
| ~ spl0_134
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f3327,f2982,f1355,f21518]) ).
fof(f21518,plain,
( spl0_698
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f3327,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) )
| ~ spl0_134
| ~ spl0_276 ),
inference(resolution,[],[f2983,f1356]) ).
fof(f21516,plain,
( spl0_697
| ~ spl0_136
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f3306,f2978,f1363,f21514]) ).
fof(f21514,plain,
( spl0_697
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f3306,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X0,X1),X1) )
| ~ spl0_136
| ~ spl0_275 ),
inference(resolution,[],[f2979,f1364]) ).
fof(f21512,plain,
( spl0_696
| ~ spl0_134
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f3305,f2978,f1355,f21510]) ).
fof(f21510,plain,
( spl0_696
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f3305,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X0,X1),X1) )
| ~ spl0_134
| ~ spl0_275 ),
inference(resolution,[],[f2979,f1356]) ).
fof(f21508,plain,
( spl0_695
| ~ spl0_136
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3282,f2974,f1363,f21506]) ).
fof(f21506,plain,
( spl0_695
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f3282,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) )
| ~ spl0_136
| ~ spl0_274 ),
inference(resolution,[],[f2975,f1364]) ).
fof(f21504,plain,
( spl0_694
| ~ spl0_134
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3281,f2974,f1355,f21502]) ).
fof(f21502,plain,
( spl0_694
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f3281,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) )
| ~ spl0_134
| ~ spl0_274 ),
inference(resolution,[],[f2975,f1356]) ).
fof(f21500,plain,
( spl0_693
| ~ spl0_136
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f3258,f2970,f1363,f21498]) ).
fof(f21498,plain,
( spl0_693
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f3258,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X0,X1),X1) )
| ~ spl0_136
| ~ spl0_273 ),
inference(resolution,[],[f2971,f1364]) ).
fof(f21496,plain,
( spl0_692
| ~ spl0_134
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f3257,f2970,f1355,f21494]) ).
fof(f21494,plain,
( spl0_692
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f3257,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X0,X1),X1) )
| ~ spl0_134
| ~ spl0_273 ),
inference(resolution,[],[f2971,f1356]) ).
fof(f21492,plain,
( spl0_691
| ~ spl0_93
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f2588,f2546,f1140,f21490]) ).
fof(f1140,plain,
( spl0_93
<=> class_Ring__and__Field_Ocomm__semiring__1(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f2546,plain,
( spl0_227
<=> ! [X18,X0,X17,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X15,c_HOL_Otimes__class_Otimes(X17,X18,X0),X0) = c_HOL_Otimes__class_Otimes(X17,c_HOL_Otimes__class_Otimes(X15,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f2588,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,t_a),t_a) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X0,X2,t_a),t_a)
| ~ spl0_93
| ~ spl0_227 ),
inference(resolution,[],[f2547,f1142]) ).
fof(f1142,plain,
( class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f1140]) ).
fof(f2547,plain,
( ! [X0,X18,X17,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X15,c_HOL_Otimes__class_Otimes(X17,X18,X0),X0) = c_HOL_Otimes__class_Otimes(X17,c_HOL_Otimes__class_Otimes(X15,X18,X0),X0) )
| ~ spl0_227 ),
inference(avatar_component_clause,[],[f2546]) ).
fof(f21488,plain,
( spl0_690
| ~ spl0_136
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f3190,f2946,f1363,f21486]) ).
fof(f21486,plain,
( spl0_690
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f3190,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_136
| ~ spl0_267 ),
inference(resolution,[],[f2947,f1364]) ).
fof(f21484,plain,
( spl0_689
| ~ spl0_134
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f3189,f2946,f1355,f21482]) ).
fof(f21482,plain,
( spl0_689
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f3189,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_134
| ~ spl0_267 ),
inference(resolution,[],[f2947,f1356]) ).
fof(f21480,plain,
( spl0_688
| ~ spl0_136
| ~ spl0_266 ),
inference(avatar_split_clause,[],[f3172,f2942,f1363,f21478]) ).
fof(f21478,plain,
( spl0_688
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f3172,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_136
| ~ spl0_266 ),
inference(resolution,[],[f2943,f1364]) ).
fof(f21476,plain,
( spl0_687
| ~ spl0_134
| ~ spl0_266 ),
inference(avatar_split_clause,[],[f3171,f2942,f1355,f21474]) ).
fof(f21474,plain,
( spl0_687
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f3171,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_134
| ~ spl0_266 ),
inference(resolution,[],[f2943,f1356]) ).
fof(f21472,plain,
( spl0_686
| ~ spl0_136
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f3154,f2938,f1363,f21470]) ).
fof(f21470,plain,
( spl0_686
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f3154,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_136
| ~ spl0_265 ),
inference(resolution,[],[f2939,f1364]) ).
fof(f21468,plain,
( spl0_685
| ~ spl0_134
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f3153,f2938,f1355,f21466]) ).
fof(f21466,plain,
( spl0_685
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f3153,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_134
| ~ spl0_265 ),
inference(resolution,[],[f2939,f1356]) ).
fof(f21464,plain,
( spl0_684
| ~ spl0_136
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f3136,f2934,f1363,f21462]) ).
fof(f21462,plain,
( spl0_684
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f3136,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_136
| ~ spl0_264 ),
inference(resolution,[],[f2935,f1364]) ).
fof(f21460,plain,
( spl0_683
| ~ spl0_134
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f3135,f2934,f1355,f21458]) ).
fof(f21458,plain,
( spl0_683
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f3135,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_134
| ~ spl0_264 ),
inference(resolution,[],[f2935,f1356]) ).
fof(f21456,plain,
( spl0_682
| ~ spl0_136
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f3118,f2930,f1363,f21454]) ).
fof(f21454,plain,
( spl0_682
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f3118,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_136
| ~ spl0_263 ),
inference(resolution,[],[f2931,f1364]) ).
fof(f21452,plain,
( spl0_681
| ~ spl0_134
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f3117,f2930,f1355,f21450]) ).
fof(f21450,plain,
( spl0_681
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f3117,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_134
| ~ spl0_263 ),
inference(resolution,[],[f2931,f1356]) ).
fof(f21448,plain,
( spl0_680
| ~ spl0_93
| ~ spl0_100
| ~ spl0_224
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f2580,f2538,f2534,f1171,f1140,f21446]) ).
fof(f1171,plain,
( spl0_100
<=> class_OrderedGroup_Oab__semigroup__mult(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f2534,plain,
( spl0_224
<=> ! [X13,X0,X3,X1] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X3,X0),X13,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f2538,plain,
( spl0_225
<=> ! [X17,X0,X16,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X15,X16,X0),X17,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X15,X17,X0),X16,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f2580,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,t_a),X2,t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,X1,t_a),t_a)
| ~ spl0_93
| ~ spl0_100
| ~ spl0_224
| ~ spl0_225 ),
inference(forward_demodulation,[],[f2577,f2574]) ).
fof(f2574,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,t_a),X2,t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,t_a),t_a)
| ~ spl0_100
| ~ spl0_224 ),
inference(resolution,[],[f2535,f1173]) ).
fof(f1173,plain,
( class_OrderedGroup_Oab__semigroup__mult(t_a)
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f1171]) ).
fof(f2535,plain,
( ! [X3,X0,X1,X13] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X3,X0),X13,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) )
| ~ spl0_224 ),
inference(avatar_component_clause,[],[f2534]) ).
fof(f2577,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,t_a),X2,t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X2,t_a),X1,t_a)
| ~ spl0_93
| ~ spl0_225 ),
inference(resolution,[],[f2539,f1142]) ).
fof(f2539,plain,
( ! [X0,X16,X17,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X15,X16,X0),X17,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X15,X17,X0),X16,X0) )
| ~ spl0_225 ),
inference(avatar_component_clause,[],[f2538]) ).
fof(f21444,plain,
( spl0_679
| ~ spl0_142
| ~ spl0_258 ),
inference(avatar_split_clause,[],[f3098,f2909,f1387,f21442]) ).
fof(f21442,plain,
( spl0_679
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f3098,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X0,X1),X1) )
| ~ spl0_142
| ~ spl0_258 ),
inference(resolution,[],[f2910,f1388]) ).
fof(f21440,plain,
( spl0_678
| ~ spl0_141
| ~ spl0_258 ),
inference(avatar_split_clause,[],[f3097,f2909,f1383,f21438]) ).
fof(f21438,plain,
( spl0_678
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f3097,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X0,X1),X1) )
| ~ spl0_141
| ~ spl0_258 ),
inference(resolution,[],[f2910,f1384]) ).
fof(f21436,plain,
( spl0_677
| ~ spl0_140
| ~ spl0_258 ),
inference(avatar_split_clause,[],[f3096,f2909,f1379,f21434]) ).
fof(f21434,plain,
( spl0_677
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f3096,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X0,X1),X1)
| ~ class_Orderings_Opreorder(X1) )
| ~ spl0_140
| ~ spl0_258 ),
inference(resolution,[],[f2910,f1380]) ).
fof(f21432,plain,
( spl0_676
| ~ spl0_138
| ~ spl0_258 ),
inference(avatar_split_clause,[],[f3095,f2909,f1371,f21430]) ).
fof(f21430,plain,
( spl0_676
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X0,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f3095,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X0,X1),c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_138
| ~ spl0_258 ),
inference(resolution,[],[f2910,f1372]) ).
fof(f21428,plain,
( spl0_675
| ~ spl0_137
| ~ spl0_258 ),
inference(avatar_split_clause,[],[f3094,f2909,f1367,f21426]) ).
fof(f21426,plain,
( spl0_675
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X0,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f3094,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X0,X1),c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_137
| ~ spl0_258 ),
inference(resolution,[],[f2910,f1368]) ).
fof(f21424,plain,
( spl0_674
| ~ spl0_142
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f3084,f2905,f1387,f21422]) ).
fof(f21422,plain,
( spl0_674
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f3084,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) )
| ~ spl0_142
| ~ spl0_257 ),
inference(resolution,[],[f2906,f1388]) ).
fof(f21420,plain,
( spl0_673
| ~ spl0_141
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f3083,f2905,f1383,f21418]) ).
fof(f21418,plain,
( spl0_673
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f3083,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) )
| ~ spl0_141
| ~ spl0_257 ),
inference(resolution,[],[f2906,f1384]) ).
fof(f21416,plain,
( spl0_672
| ~ spl0_140
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f3082,f2905,f1379,f21414]) ).
fof(f21414,plain,
( spl0_672
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f3082,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1)
| ~ class_Orderings_Opreorder(X1) )
| ~ spl0_140
| ~ spl0_257 ),
inference(resolution,[],[f2906,f1380]) ).
fof(f21412,plain,
( spl0_671
| ~ spl0_138
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f3081,f2905,f1371,f21410]) ).
fof(f21410,plain,
( spl0_671
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f3081,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_138
| ~ spl0_257 ),
inference(resolution,[],[f2906,f1372]) ).
fof(f21408,plain,
( spl0_670
| ~ spl0_137
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f3080,f2905,f1367,f21406]) ).
fof(f21406,plain,
( spl0_670
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f3080,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_137
| ~ spl0_257 ),
inference(resolution,[],[f2906,f1368]) ).
fof(f21404,plain,
( spl0_669
| ~ spl0_100
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2574,f2534,f1171,f21402]) ).
fof(f21400,plain,
( spl0_668
| ~ spl0_135
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f3073,f2901,f1359,f21398]) ).
fof(f21398,plain,
( spl0_668
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f2901,plain,
( spl0_256
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f3073,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_135
| ~ spl0_256 ),
inference(resolution,[],[f2902,f1360]) ).
fof(f2902,plain,
( ! [X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0) )
| ~ spl0_256 ),
inference(avatar_component_clause,[],[f2901]) ).
fof(f21396,plain,
( spl0_667
| ~ spl0_135
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f3061,f2897,f1359,f21394]) ).
fof(f21394,plain,
( spl0_667
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f2897,plain,
( spl0_255
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f3061,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_135
| ~ spl0_255 ),
inference(resolution,[],[f2898,f1360]) ).
fof(f2898,plain,
( ! [X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0) )
| ~ spl0_255 ),
inference(avatar_component_clause,[],[f2897]) ).
fof(f21392,plain,
( spl0_666
| ~ spl0_142
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f3050,f2893,f1387,f21390]) ).
fof(f21390,plain,
( spl0_666
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f3050,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_142
| ~ spl0_254 ),
inference(resolution,[],[f2894,f1388]) ).
fof(f21388,plain,
( spl0_665
| ~ spl0_141
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f3049,f2893,f1383,f21386]) ).
fof(f21386,plain,
( spl0_665
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f3049,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_141
| ~ spl0_254 ),
inference(resolution,[],[f2894,f1384]) ).
fof(f21384,plain,
( spl0_664
| ~ spl0_140
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f3048,f2893,f1379,f21382]) ).
fof(f21382,plain,
( spl0_664
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f3048,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_140
| ~ spl0_254 ),
inference(resolution,[],[f2894,f1380]) ).
fof(f21380,plain,
( spl0_663
| ~ spl0_138
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f3047,f2893,f1371,f21378]) ).
fof(f21378,plain,
( spl0_663
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f3047,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) )
| ~ spl0_138
| ~ spl0_254 ),
inference(resolution,[],[f2894,f1372]) ).
fof(f21376,plain,
( spl0_662
| ~ spl0_137
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f3046,f2893,f1367,f21374]) ).
fof(f21374,plain,
( spl0_662
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f3046,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) )
| ~ spl0_137
| ~ spl0_254 ),
inference(resolution,[],[f2894,f1368]) ).
fof(f21372,plain,
( spl0_661
| ~ spl0_142
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3042,f2889,f1387,f21370]) ).
fof(f21370,plain,
( spl0_661
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f3042,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_142
| ~ spl0_253 ),
inference(resolution,[],[f2890,f1388]) ).
fof(f21368,plain,
( spl0_660
| ~ spl0_141
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3041,f2889,f1383,f21366]) ).
fof(f21366,plain,
( spl0_660
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f3041,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_141
| ~ spl0_253 ),
inference(resolution,[],[f2890,f1384]) ).
fof(f21364,plain,
( spl0_659
| ~ spl0_140
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3040,f2889,f1379,f21362]) ).
fof(f21362,plain,
( spl0_659
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f3040,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1) )
| ~ spl0_140
| ~ spl0_253 ),
inference(resolution,[],[f2890,f1380]) ).
fof(f21349,plain,
( spl0_658
| ~ spl0_138
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3039,f2889,f1371,f21347]) ).
fof(f21347,plain,
( spl0_658
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f3039,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) )
| ~ spl0_138
| ~ spl0_253 ),
inference(resolution,[],[f2890,f1372]) ).
fof(f21345,plain,
( spl0_657
| ~ spl0_137
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f3038,f2889,f1367,f21343]) ).
fof(f21343,plain,
( spl0_657
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f3038,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X2,X1),X1) )
| ~ spl0_137
| ~ spl0_253 ),
inference(resolution,[],[f2890,f1368]) ).
fof(f21341,plain,
( spl0_656
| ~ spl0_135
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f3034,f2885,f1359,f21339]) ).
fof(f21339,plain,
( spl0_656
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| c_HOL_Oord__class_Oless(X1,X0,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f2885,plain,
( spl0_252
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f3034,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| c_HOL_Oord__class_Oless(X1,X0,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X0,X3,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_135
| ~ spl0_252 ),
inference(resolution,[],[f2886,f1360]) ).
fof(f2886,plain,
( ! [X3,X0,X1,X13] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_252 ),
inference(avatar_component_clause,[],[f2885]) ).
fof(f21337,plain,
( spl0_655
| ~ spl0_135
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3027,f2877,f1359,f21335]) ).
fof(f21335,plain,
( spl0_655
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| c_HOL_Oord__class_Oless(X1,X0,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f3027,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| c_HOL_Oord__class_Oless(X1,X0,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X3,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_135
| ~ spl0_250 ),
inference(resolution,[],[f2878,f1360]) ).
fof(f21303,plain,
( ~ spl0_8
| spl0_654
| ~ spl0_149
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2351,f2281,f1497,f21301,f726]) ).
fof(f21301,plain,
( spl0_654
<=> ! [X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Power_Opower__class_Opower(X0,X1,tc_nat),tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f2351,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Power_Opower__class_Opower(X0,X1,tc_nat),tc_nat) )
| ~ spl0_149
| ~ spl0_211 ),
inference(resolution,[],[f2282,f1498]) ).
fof(f21289,plain,
( ~ spl0_8
| spl0_653
| ~ spl0_157
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2349,f2281,f1530,f21287,f726]) ).
fof(f21287,plain,
( spl0_653
<=> ! [X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X0,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f2349,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,X1,tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X0,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
| ~ spl0_157
| ~ spl0_211 ),
inference(resolution,[],[f2282,f1531]) ).
fof(f21285,plain,
( spl0_652
| ~ spl0_177
| ~ spl0_207 ),
inference(avatar_split_clause,[],[f2313,f2265,f1753,f21283]) ).
fof(f21283,plain,
( spl0_652
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X0,X2,X1),X1)
| c_HOL_Ozero__class_Ozero(X1) = c_Power_Opower__class_Opower(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f2265,plain,
( spl0_207
<=> ! [X2,X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f2313,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X0,X2,X1),X1)
| c_HOL_Ozero__class_Ozero(X1) = c_Power_Opower__class_Opower(X0,X2,X1) )
| ~ spl0_177
| ~ spl0_207 ),
inference(duplicate_literal_removal,[],[f2305]) ).
fof(f2305,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X0,X2,X1),X1)
| c_HOL_Ozero__class_Ozero(X1) = c_Power_Opower__class_Opower(X0,X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_177
| ~ spl0_207 ),
inference(resolution,[],[f2266,f1754]) ).
fof(f2266,plain,
( ! [X2,X0,X9] :
( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_207 ),
inference(avatar_component_clause,[],[f2265]) ).
fof(f21281,plain,
( spl0_651
| ~ spl0_172
| ~ spl0_181 ),
inference(avatar_split_clause,[],[f1908,f1771,f1733,f21279]) ).
fof(f21279,plain,
( spl0_651
<=> ! [X2,X0,X1] :
( c_Power_Opower__class_Opower(X0,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_Power_Opower__class_Opower(X0,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f1908,plain,
( ! [X2,X0,X1] :
( c_Power_Opower__class_Opower(X0,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_Power_Opower__class_Opower(X0,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X2) )
| ~ spl0_172
| ~ spl0_181 ),
inference(resolution,[],[f1772,f1734]) ).
fof(f20124,plain,
( spl0_650
| ~ spl0_484
| ~ spl0_606 ),
inference(avatar_split_clause,[],[f18134,f18083,f12230,f20122]) ).
fof(f20122,plain,
( spl0_650
<=> ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != c_HOL_Oinverse__class_Odivide(X1,X0,t_a)
| c_HOL_Oinverse__class_Oinverse(X0,t_a) = c_HOL_Oinverse__class_Oinverse(X1,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f18134,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != c_HOL_Oinverse__class_Odivide(X1,X0,t_a)
| c_HOL_Oinverse__class_Oinverse(X0,t_a) = c_HOL_Oinverse__class_Oinverse(X1,t_a) )
| ~ spl0_484
| ~ spl0_606 ),
inference(superposition,[],[f18084,f12231]) ).
fof(f19424,plain,
( spl0_649
| ~ spl0_361
| ~ spl0_606 ),
inference(avatar_split_clause,[],[f18130,f18083,f5201,f19422]) ).
fof(f19422,plain,
( spl0_649
<=> ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != c_HOL_Oinverse__class_Odivide(X0,X1,t_a)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,t_a),t_a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f18130,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != c_HOL_Oinverse__class_Odivide(X0,X1,t_a)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,t_a),t_a) = X0 )
| ~ spl0_361
| ~ spl0_606 ),
inference(superposition,[],[f18084,f5202]) ).
fof(f18564,plain,
( spl0_648
| ~ spl0_34
| ~ spl0_35
| ~ spl0_224
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f4600,f4586,f2534,f861,f856,f18562]) ).
fof(f18562,plain,
( spl0_648
<=> ! [X0,X3,X2,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),c_HOL_Otimes__class_Otimes(X2,X3,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f856,plain,
( spl0_34
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f861,plain,
( spl0_35
<=> class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f4586,plain,
( spl0_332
<=> ! [X18,X0,X16,X17,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X15,X16,X0),c_HOL_Otimes__class_Otimes(X17,X18,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X15,X17,X0),c_HOL_Otimes__class_Otimes(X16,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f4600,plain,
( ! [X2,X3,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),c_HOL_Otimes__class_Otimes(X2,X3,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint)
| ~ spl0_34
| ~ spl0_35
| ~ spl0_224
| ~ spl0_332 ),
inference(forward_demodulation,[],[f4597,f2573]) ).
fof(f2573,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),X2,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Int_Oint),tc_Int_Oint)
| ~ spl0_35
| ~ spl0_224 ),
inference(resolution,[],[f2535,f863]) ).
fof(f863,plain,
( class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f861]) ).
fof(f4597,plain,
( ! [X2,X3,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),c_HOL_Otimes__class_Otimes(X2,X3,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X2,tc_Int_Oint),c_HOL_Otimes__class_Otimes(X1,X3,tc_Int_Oint),tc_Int_Oint)
| ~ spl0_34
| ~ spl0_332 ),
inference(resolution,[],[f4587,f858]) ).
fof(f858,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint)
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f856]) ).
fof(f4587,plain,
( ! [X0,X18,X16,X17,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X15,X16,X0),c_HOL_Otimes__class_Otimes(X17,X18,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X15,X17,X0),c_HOL_Otimes__class_Otimes(X16,X18,X0),X0) )
| ~ spl0_332 ),
inference(avatar_component_clause,[],[f4586]) ).
fof(f18560,plain,
( spl0_647
| ~ spl0_9
| ~ spl0_10
| ~ spl0_224
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f4599,f4586,f2534,f736,f731,f18558]) ).
fof(f18558,plain,
( spl0_647
<=> ! [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_647])]) ).
fof(f731,plain,
( spl0_9
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f736,plain,
( spl0_10
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f4599,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_9
| ~ spl0_10
| ~ spl0_224
| ~ spl0_332 ),
inference(forward_demodulation,[],[f4596,f2572]) ).
fof(f2572,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_10
| ~ spl0_224 ),
inference(resolution,[],[f2535,f738]) ).
fof(f738,plain,
( class_OrderedGroup_Oab__semigroup__mult(tc_nat)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f736]) ).
fof(f4596,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_9
| ~ spl0_332 ),
inference(resolution,[],[f4587,f733]) ).
fof(f733,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f731]) ).
fof(f18556,plain,
( spl0_646
| ~ spl0_305
| ~ spl0_325 ),
inference(avatar_split_clause,[],[f4463,f4417,f3491,f18554]) ).
fof(f18554,plain,
( spl0_646
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f4463,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) )
| ~ spl0_305
| ~ spl0_325 ),
inference(duplicate_literal_removal,[],[f4448]) ).
fof(f4448,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) )
| ~ spl0_305
| ~ spl0_325 ),
inference(resolution,[],[f4418,f3492]) ).
fof(f18552,plain,
( spl0_645
| ~ spl0_303
| ~ spl0_325 ),
inference(avatar_split_clause,[],[f4462,f4417,f3455,f18550]) ).
fof(f18550,plain,
( spl0_645
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f4462,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_303
| ~ spl0_325 ),
inference(duplicate_literal_removal,[],[f4450]) ).
fof(f4450,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) )
| ~ spl0_303
| ~ spl0_325 ),
inference(resolution,[],[f4418,f3456]) ).
fof(f18512,plain,
( ~ spl0_8
| spl0_644
| ~ spl0_97
| ~ spl0_322 ),
inference(avatar_split_clause,[],[f4368,f3596,f1159,f18510,f726]) ).
fof(f18510,plain,
( spl0_644
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X2,X0,tc_nat),c_Power_Opower__class_Opower(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f4368,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X2,X0,tc_nat),c_Power_Opower__class_Opower(X2,X1,tc_nat),tc_nat) )
| ~ spl0_97
| ~ spl0_322 ),
inference(resolution,[],[f3597,f1160]) ).
fof(f18508,plain,
( spl0_643
| ~ spl0_449
| ~ spl0_606 ),
inference(avatar_split_clause,[],[f18126,f18083,f9464,f18506]) ).
fof(f18126,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != c_HOL_Otimes__class_Otimes(X1,X0,t_a)
| c_HOL_Oinverse__class_Oinverse(X1,t_a) = X0 )
| ~ spl0_449
| ~ spl0_606 ),
inference(superposition,[],[f18084,f9465]) ).
fof(f18468,plain,
( ~ spl0_8
| spl0_642
| ~ spl0_102
| ~ spl0_317 ),
inference(avatar_split_clause,[],[f4276,f3576,f1180,f18466,f726]) ).
fof(f18466,plain,
( spl0_642
<=> ! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X2,X1,tc_nat),c_Power_Opower__class_Opower(X2,X0,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f4276,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X2,X1,tc_nat),c_Power_Opower__class_Opower(X2,X0,tc_nat),tc_nat) )
| ~ spl0_102
| ~ spl0_317 ),
inference(resolution,[],[f3577,f1181]) ).
fof(f18410,plain,
( ~ spl0_4
| spl0_641
| ~ spl0_97
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3935,f3459,f1159,f18408,f706]) ).
fof(f18408,plain,
( spl0_641
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f3935,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) )
| ~ spl0_97
| ~ spl0_304 ),
inference(resolution,[],[f3460,f1160]) ).
fof(f18347,plain,
( ~ spl0_4
| spl0_640
| ~ spl0_97
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3847,f3447,f1159,f18345,f706]) ).
fof(f18345,plain,
( spl0_640
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X0,tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f3847,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X0,tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) )
| ~ spl0_97
| ~ spl0_301 ),
inference(resolution,[],[f3448,f1160]) ).
fof(f18283,plain,
( ~ spl0_4
| spl0_639
| ~ spl0_102
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f3707,f3415,f1180,f18281,f706]) ).
fof(f18281,plain,
( spl0_639
<=> ! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X2,X0,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f3707,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X2,X0,tc_nat),tc_nat) )
| ~ spl0_102
| ~ spl0_293 ),
inference(resolution,[],[f3416,f1181]) ).
fof(f18225,plain,
( ~ spl0_4
| spl0_638
| ~ spl0_102
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3694,f3411,f1180,f18223,f706]) ).
fof(f18223,plain,
( spl0_638
<=> ! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f3694,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat) )
| ~ spl0_102
| ~ spl0_292 ),
inference(resolution,[],[f3412,f1181]) ).
fof(f18220,plain,
( spl0_637
| ~ spl0_143
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2865,f2817,f1391,f18218]) ).
fof(f18218,plain,
( spl0_637
<=> ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = X1
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f2817,plain,
( spl0_247
<=> ! [X2,X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f2865,plain,
( ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = X1
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_143
| ~ spl0_247 ),
inference(resolution,[],[f2818,f1392]) ).
fof(f2818,plain,
( ! [X2,X0,X9] :
( ~ c_lessequals(c_Power_Opower__class_Opower(X2,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_247 ),
inference(avatar_component_clause,[],[f2817]) ).
fof(f18216,plain,
( spl0_636
| ~ spl0_136
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f2822,f2793,f1363,f18214]) ).
fof(f18214,plain,
( spl0_636
<=> ! [X0,X3,X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X3),c_Power_Opower__class_Opower(X1,X0,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f2822,plain,
( ! [X2,X3,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X3),c_Power_Opower__class_Opower(X1,X0,X3),X3) )
| ~ spl0_136
| ~ spl0_241 ),
inference(resolution,[],[f2794,f1364]) ).
fof(f18212,plain,
( spl0_635
| ~ spl0_134
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f2821,f2793,f1355,f18210]) ).
fof(f18210,plain,
( spl0_635
<=> ! [X0,X3,X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X3),c_Power_Opower__class_Opower(X1,X0,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f2821,plain,
( ! [X2,X3,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X3),c_Power_Opower__class_Opower(X1,X0,X3),X3) )
| ~ spl0_134
| ~ spl0_241 ),
inference(resolution,[],[f2794,f1356]) ).
fof(f18208,plain,
( spl0_634
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2410,f2297,f18206]) ).
fof(f18206,plain,
( spl0_634
<=> ! [X0,X3,X2,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X3,tc_nat),X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f2410,plain,
( ! [X2,X3,X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X3,tc_nat),X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),X3,tc_nat)
| ~ spl0_215 ),
inference(superposition,[],[f2298,f2298]) ).
fof(f18204,plain,
( spl0_633
| ~ spl0_195
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2400,f2293,f1970,f18202]) ).
fof(f18202,plain,
( spl0_633
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(X2,c_Power_Opower__class_Opower(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f2400,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(X2,c_Power_Opower__class_Opower(X1,X3,X0),X0) )
| ~ spl0_195
| ~ spl0_214 ),
inference(resolution,[],[f2294,f1971]) ).
fof(f18200,plain,
( spl0_632
| ~ spl0_194
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2399,f2293,f1966,f18198]) ).
fof(f18198,plain,
( spl0_632
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f2399,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0) )
| ~ spl0_194
| ~ spl0_214 ),
inference(resolution,[],[f2294,f1967]) ).
fof(f18196,plain,
( spl0_631
| ~ spl0_190
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2398,f2293,f1950,f18194]) ).
fof(f18194,plain,
( spl0_631
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f2398,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) )
| ~ spl0_190
| ~ spl0_214 ),
inference(resolution,[],[f2294,f1951]) ).
fof(f18192,plain,
( spl0_630
| ~ spl0_189
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2397,f2293,f1946,f18190]) ).
fof(f18190,plain,
( spl0_630
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f2397,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X1,X3,X0),X0) )
| ~ spl0_189
| ~ spl0_214 ),
inference(resolution,[],[f2294,f1947]) ).
fof(f18188,plain,
( spl0_629
| ~ spl0_188
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2396,f2293,f1942,f18186]) ).
fof(f18186,plain,
( spl0_629
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f2396,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X1,X3,X0),X0) )
| ~ spl0_188
| ~ spl0_214 ),
inference(resolution,[],[f2294,f1943]) ).
fof(f18184,plain,
( spl0_628
| ~ spl0_187
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2395,f2293,f1938,f18182]) ).
fof(f18182,plain,
( spl0_628
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f2395,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) )
| ~ spl0_187
| ~ spl0_214 ),
inference(resolution,[],[f2294,f1939]) ).
fof(f18180,plain,
( spl0_627
| ~ spl0_285
| ~ spl0_606 ),
inference(avatar_split_clause,[],[f18129,f18083,f3088,f18178]) ).
fof(f18178,plain,
( spl0_627
<=> ! [X0] :
( c_HOL_Oone__class_Oone(t_a) != X0
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f18129,plain,
( ! [X0] :
( c_HOL_Oone__class_Oone(t_a) != X0
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a) = X0 )
| ~ spl0_285
| ~ spl0_606 ),
inference(superposition,[],[f18084,f3089]) ).
fof(f18176,plain,
( spl0_626
| ~ spl0_195
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2382,f2289,f1970,f18174]) ).
fof(f18174,plain,
( spl0_626
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(X2,c_Power_Opower__class_Opower(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f2382,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(X2,c_Power_Opower__class_Opower(X1,X3,X0),X0) )
| ~ spl0_195
| ~ spl0_213 ),
inference(resolution,[],[f2290,f1971]) ).
fof(f18172,plain,
( spl0_625
| ~ spl0_194
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2381,f2289,f1966,f18170]) ).
fof(f18170,plain,
( spl0_625
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f2381,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0) )
| ~ spl0_194
| ~ spl0_213 ),
inference(resolution,[],[f2290,f1967]) ).
fof(f18168,plain,
( spl0_624
| ~ spl0_190
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2380,f2289,f1950,f18166]) ).
fof(f18166,plain,
( spl0_624
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f2380,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) )
| ~ spl0_190
| ~ spl0_213 ),
inference(resolution,[],[f2290,f1951]) ).
fof(f18164,plain,
( spl0_623
| ~ spl0_189
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2379,f2289,f1946,f18162]) ).
fof(f18162,plain,
( spl0_623
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f2379,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X1,X3,X0),X0) )
| ~ spl0_189
| ~ spl0_213 ),
inference(resolution,[],[f2290,f1947]) ).
fof(f18160,plain,
( spl0_622
| ~ spl0_188
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2378,f2289,f1942,f18158]) ).
fof(f18158,plain,
( spl0_622
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f2378,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X1,X3,X0),X0) )
| ~ spl0_188
| ~ spl0_213 ),
inference(resolution,[],[f2290,f1943]) ).
fof(f18156,plain,
( spl0_621
| ~ spl0_187
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2377,f2289,f1938,f18154]) ).
fof(f18154,plain,
( spl0_621
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f2377,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) )
| ~ spl0_187
| ~ spl0_213 ),
inference(resolution,[],[f2290,f1939]) ).
fof(f18152,plain,
( spl0_620
| ~ spl0_195
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2363,f2285,f1970,f18150]) ).
fof(f18150,plain,
( spl0_620
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(X2,c_Power_Opower__class_Opower(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f2363,plain,
( ! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(X2,c_Power_Opower__class_Opower(X3,X1,X0),X0) )
| ~ spl0_195
| ~ spl0_212 ),
inference(resolution,[],[f2286,f1971]) ).
fof(f18148,plain,
( spl0_619
| ~ spl0_194
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2362,f2285,f1966,f18146]) ).
fof(f18146,plain,
( spl0_619
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X1,X0),X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f2362,plain,
( ! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X1,X0),X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0) )
| ~ spl0_194
| ~ spl0_212 ),
inference(resolution,[],[f2286,f1967]) ).
fof(f18144,plain,
( spl0_618
| ~ spl0_190
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2361,f2285,f1950,f18142]) ).
fof(f18142,plain,
( spl0_618
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X1,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f2361,plain,
( ! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X1,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) )
| ~ spl0_190
| ~ spl0_212 ),
inference(resolution,[],[f2286,f1951]) ).
fof(f18140,plain,
( spl0_617
| ~ spl0_189
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2360,f2285,f1946,f18138]) ).
fof(f18138,plain,
( spl0_617
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f2360,plain,
( ! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X3,X1,X0),X0) )
| ~ spl0_189
| ~ spl0_212 ),
inference(resolution,[],[f2286,f1947]) ).
fof(f18125,plain,
( spl0_616
| ~ spl0_188
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2359,f2285,f1942,f18123]) ).
fof(f18123,plain,
( spl0_616
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f2359,plain,
( ! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X3,X1,X0),X0) )
| ~ spl0_188
| ~ spl0_212 ),
inference(resolution,[],[f2286,f1943]) ).
fof(f18121,plain,
( spl0_615
| ~ spl0_187
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2358,f2285,f1938,f18119]) ).
fof(f18119,plain,
( spl0_615
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X1,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f2358,plain,
( ! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X1,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) )
| ~ spl0_187
| ~ spl0_212 ),
inference(resolution,[],[f2286,f1939]) ).
fof(f18117,plain,
( spl0_614
| ~ spl0_195
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2346,f2281,f1970,f18115]) ).
fof(f18115,plain,
( spl0_614
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(X2,c_Power_Opower__class_Opower(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f2346,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(X2,c_Power_Opower__class_Opower(X1,X3,X0),X0) )
| ~ spl0_195
| ~ spl0_211 ),
inference(resolution,[],[f2282,f1971]) ).
fof(f18113,plain,
( spl0_613
| ~ spl0_194
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2345,f2281,f1966,f18111]) ).
fof(f18111,plain,
( spl0_613
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f2345,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),X3,X0) )
| ~ spl0_194
| ~ spl0_211 ),
inference(resolution,[],[f2282,f1967]) ).
fof(f18109,plain,
( spl0_612
| ~ spl0_190
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2344,f2281,f1950,f18107]) ).
fof(f18107,plain,
( spl0_612
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f2344,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0) )
| ~ spl0_190
| ~ spl0_211 ),
inference(resolution,[],[f2282,f1951]) ).
fof(f18105,plain,
( spl0_611
| ~ spl0_189
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2343,f2281,f1946,f18103]) ).
fof(f18103,plain,
( spl0_611
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X0),X0)
| c_HOL_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f2343,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X0),X0)
| c_HOL_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X1,X3,X0),X0) )
| ~ spl0_189
| ~ spl0_211 ),
inference(resolution,[],[f2282,f1947]) ).
fof(f18101,plain,
( spl0_610
| ~ spl0_188
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2342,f2281,f1942,f18099]) ).
fof(f18099,plain,
( spl0_610
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X0),X0)
| c_HOL_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f2342,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X0),X0)
| c_HOL_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X1,X3,X0),X0) )
| ~ spl0_188
| ~ spl0_211 ),
inference(resolution,[],[f2282,f1943]) ).
fof(f18097,plain,
( spl0_609
| ~ spl0_187
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2341,f2281,f1938,f18095]) ).
fof(f18095,plain,
( spl0_609
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f2341,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0) )
| ~ spl0_187
| ~ spl0_211 ),
inference(resolution,[],[f2282,f1939]) ).
fof(f18093,plain,
( spl0_608
| ~ spl0_193
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f2321,f2269,f1962,f18091]) ).
fof(f18091,plain,
( spl0_608
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f2269,plain,
( spl0_208
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f2321,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0) )
| ~ spl0_193
| ~ spl0_208 ),
inference(resolution,[],[f2270,f1963]) ).
fof(f2270,plain,
( ! [X0,X1,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_208 ),
inference(avatar_component_clause,[],[f2269]) ).
fof(f18089,plain,
( spl0_607
| ~ spl0_192
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f2320,f2269,f1958,f18087]) ).
fof(f18087,plain,
( spl0_607
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f2320,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X1,X3,X0),X0) )
| ~ spl0_192
| ~ spl0_208 ),
inference(resolution,[],[f2270,f1959]) ).
fof(f18085,plain,
( ~ spl0_114
| spl0_606
| ~ spl0_182
| ~ spl0_449 ),
inference(avatar_split_clause,[],[f10044,f9464,f1911,f18083,f1240]) ).
fof(f1911,plain,
( spl0_182
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oinverse__class_Oinverse(X1,X0) = X3
| c_HOL_Otimes__class_Otimes(X1,X3,X0) != c_HOL_Oone__class_Oone(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f10044,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) != c_HOL_Otimes__class_Otimes(X1,X0,t_a)
| c_HOL_Oinverse__class_Oinverse(X0,t_a) = X1
| ~ class_Ring__and__Field_Odivision__ring(t_a) )
| ~ spl0_182
| ~ spl0_449 ),
inference(superposition,[],[f1912,f9465]) ).
fof(f1912,plain,
( ! [X3,X0,X1] :
( c_HOL_Otimes__class_Otimes(X1,X3,X0) != c_HOL_Oone__class_Oone(X0)
| c_HOL_Oinverse__class_Oinverse(X1,X0) = X3
| ~ class_Ring__and__Field_Odivision__ring(X0) )
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f1911]) ).
fof(f17168,plain,
( spl0_605
| ~ spl0_169
| ~ spl0_122
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2520,f2484,f1305,f1716,f17166]) ).
fof(f17166,plain,
( spl0_605
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Ozero__class_Ozero(t_a) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(t_a),X0,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f1716,plain,
( spl0_169
<=> class_Power_Opower(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f1305,plain,
( spl0_122
<=> class_Ring__and__Field_Osemiring__0(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f2484,plain,
( spl0_219
<=> ! [X9,X0] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X9
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f2520,plain,
( ! [X0] :
( ~ class_Power_Opower(t_a)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Ozero__class_Ozero(t_a) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(t_a),X0,t_a) )
| ~ spl0_122
| ~ spl0_219 ),
inference(resolution,[],[f2485,f1307]) ).
fof(f1307,plain,
( class_Ring__and__Field_Osemiring__0(t_a)
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f1305]) ).
fof(f2485,plain,
( ! [X0,X9] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X9
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X9,X0) )
| ~ spl0_219 ),
inference(avatar_component_clause,[],[f2484]) ).
fof(f16352,plain,
( spl0_604
| ~ spl0_91
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f4574,f4441,f1132,f16350]) ).
fof(f16350,plain,
( spl0_604
<=> ! [X0,X1] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_lessequals(X0,X0,tc_nat)
| c_lessequals(X1,X0,tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f4574,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_lessequals(X0,X0,tc_nat)
| c_lessequals(X1,X0,tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) )
| ~ spl0_91
| ~ spl0_331 ),
inference(superposition,[],[f4442,f1133]) ).
fof(f16348,plain,
( spl0_603
| ~ spl0_288
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3863,f3447,f3395,f16346]) ).
fof(f16346,plain,
( spl0_603
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f3863,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1) )
| ~ spl0_288
| ~ spl0_301 ),
inference(duplicate_literal_removal,[],[f3844]) ).
fof(f3844,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) )
| ~ spl0_288
| ~ spl0_301 ),
inference(resolution,[],[f3448,f3396]) ).
fof(f16344,plain,
( spl0_602
| ~ spl0_299
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3837,f3443,f3439,f16342]) ).
fof(f16342,plain,
( spl0_602
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oord__class_Oless(X1,X0,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f3837,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oord__class_Oless(X1,X0,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2) )
| ~ spl0_299
| ~ spl0_300 ),
inference(duplicate_literal_removal,[],[f3810]) ).
fof(f3810,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oord__class_Oless(X1,X0,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) )
| ~ spl0_299
| ~ spl0_300 ),
inference(resolution,[],[f3444,f3440]) ).
fof(f16340,plain,
( spl0_601
| ~ spl0_296
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f3782,f3431,f3427,f16338]) ).
fof(f16338,plain,
( spl0_601
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_lessequals(X1,X0,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f3782,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_lessequals(X1,X0,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2) )
| ~ spl0_296
| ~ spl0_297 ),
inference(duplicate_literal_removal,[],[f3759]) ).
fof(f3759,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_lessequals(X1,X0,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) )
| ~ spl0_296
| ~ spl0_297 ),
inference(resolution,[],[f3432,f3428]) ).
fof(f16336,plain,
( spl0_600
| ~ spl0_361
| ~ spl0_484 ),
inference(avatar_split_clause,[],[f12550,f12230,f5201,f16334]) ).
fof(f16334,plain,
( spl0_600
<=> ! [X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Oinverse(X1,t_a),X0,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Oinverse(X0,t_a),X1,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f12550,plain,
( ! [X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Oinverse(X1,t_a),X0,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Oinverse(X0,t_a),X1,t_a)
| ~ spl0_361
| ~ spl0_484 ),
inference(superposition,[],[f12231,f5202]) ).
fof(f16332,plain,
( spl0_599
| ~ spl0_103
| ~ spl0_284 ),
inference(avatar_split_clause,[],[f3382,f3014,f1184,f16330]) ).
fof(f16330,plain,
( spl0_599
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X1,X0,tc_nat)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f1184,plain,
( spl0_103
<=> ! [X9] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f3382,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X1,X0,tc_nat)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
| ~ spl0_103
| ~ spl0_284 ),
inference(superposition,[],[f3015,f1185]) ).
fof(f1185,plain,
( ! [X9] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f1184]) ).
fof(f16298,plain,
( ~ spl0_8
| spl0_598
| ~ spl0_97
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3362,f2994,f1159,f16296,f726]) ).
fof(f16296,plain,
( spl0_598
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
| c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_Power_Opower__class_Opower(X1,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f3362,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_Power_Opower__class_Opower(X1,X0,tc_nat),tc_nat) )
| ~ spl0_97
| ~ spl0_279 ),
inference(resolution,[],[f2995,f1160]) ).
fof(f16257,plain,
( ~ spl0_8
| spl0_597
| ~ spl0_97
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f3354,f2990,f1159,f16255,f726]) ).
fof(f16255,plain,
( spl0_597
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X1,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f3354,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X1,tc_nat),tc_nat),tc_nat) )
| ~ spl0_97
| ~ spl0_278 ),
inference(resolution,[],[f2991,f1160]) ).
fof(f16216,plain,
( ~ spl0_8
| spl0_596
| ~ spl0_97
| ~ spl0_277 ),
inference(avatar_split_clause,[],[f3346,f2986,f1159,f16214,f726]) ).
fof(f16214,plain,
( spl0_596
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f3346,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) )
| ~ spl0_97
| ~ spl0_277 ),
inference(resolution,[],[f2987,f1160]) ).
fof(f16212,plain,
( spl0_595
| ~ spl0_142
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f2762,f2652,f1387,f16210]) ).
fof(f16210,plain,
( spl0_595
<=> ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f2762,plain,
( ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X1),c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_142
| ~ spl0_239 ),
inference(resolution,[],[f2653,f1388]) ).
fof(f16208,plain,
( spl0_594
| ~ spl0_141
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f2761,f2652,f1383,f16206]) ).
fof(f16206,plain,
( spl0_594
<=> ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f2761,plain,
( ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X1),c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_141
| ~ spl0_239 ),
inference(resolution,[],[f2653,f1384]) ).
fof(f16204,plain,
( spl0_593
| ~ spl0_140
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f2760,f2652,f1379,f16202]) ).
fof(f16202,plain,
( spl0_593
<=> ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f2760,plain,
( ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X0,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1) )
| ~ spl0_140
| ~ spl0_239 ),
inference(resolution,[],[f2653,f1380]) ).
fof(f16177,plain,
( spl0_592
| ~ spl0_138
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f2759,f2652,f1371,f16175]) ).
fof(f16175,plain,
( spl0_592
<=> ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f2759,plain,
( ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X0,X1),X1) )
| ~ spl0_138
| ~ spl0_239 ),
inference(resolution,[],[f2653,f1372]) ).
fof(f16173,plain,
( spl0_591
| ~ spl0_137
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f2758,f2652,f1367,f16171]) ).
fof(f16171,plain,
( spl0_591
<=> ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f2758,plain,
( ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X0,X1),X1) )
| ~ spl0_137
| ~ spl0_239 ),
inference(resolution,[],[f2653,f1368]) ).
fof(f16169,plain,
( spl0_590
| ~ spl0_142
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f2751,f2648,f1387,f16167]) ).
fof(f16167,plain,
( spl0_590
<=> ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X1,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f2751,plain,
( ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X1,X0,X2),X2) )
| ~ spl0_142
| ~ spl0_238 ),
inference(resolution,[],[f2649,f1388]) ).
fof(f16165,plain,
( spl0_589
| ~ spl0_141
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f2750,f2648,f1383,f16163]) ).
fof(f16163,plain,
( spl0_589
<=> ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X1,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f2750,plain,
( ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X1,X0,X2),X2) )
| ~ spl0_141
| ~ spl0_238 ),
inference(resolution,[],[f2649,f1384]) ).
fof(f16161,plain,
( spl0_588
| ~ spl0_140
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f2749,f2648,f1379,f16159]) ).
fof(f16159,plain,
( spl0_588
<=> ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X1,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f2749,plain,
( ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X1,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_140
| ~ spl0_238 ),
inference(resolution,[],[f2649,f1380]) ).
fof(f16157,plain,
( spl0_587
| ~ spl0_138
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f2748,f2648,f1371,f16155]) ).
fof(f16155,plain,
( spl0_587
<=> ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(c_Power_Opower__class_Opower(X1,X0,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f2748,plain,
( ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(c_Power_Opower__class_Opower(X1,X0,X2),c_HOL_Ozero__class_Ozero(X2),X2) )
| ~ spl0_138
| ~ spl0_238 ),
inference(resolution,[],[f2649,f1372]) ).
fof(f16153,plain,
( spl0_586
| ~ spl0_137
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f2747,f2648,f1367,f16151]) ).
fof(f16151,plain,
( spl0_586
<=> ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_Power_Opower__class_Opower(X1,X0,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f2747,plain,
( ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_Power_Opower__class_Opower(X1,X0,X2),c_HOL_Ozero__class_Ozero(X2),X2) )
| ~ spl0_137
| ~ spl0_238 ),
inference(resolution,[],[f2649,f1368]) ).
fof(f16149,plain,
( spl0_585
| ~ spl0_143
| ~ spl0_237 ),
inference(avatar_split_clause,[],[f2740,f2644,f1391,f16147]) ).
fof(f16147,plain,
( spl0_585
<=> ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X1,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f2644,plain,
( spl0_237
<=> ! [X9,X0,X2] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f2740,plain,
( ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X1,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_143
| ~ spl0_237 ),
inference(resolution,[],[f2645,f1392]) ).
fof(f2645,plain,
( ! [X2,X0,X9] :
( ~ c_lessequals(c_Power_Opower__class_Opower(X2,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_237 ),
inference(avatar_component_clause,[],[f2644]) ).
fof(f16114,plain,
( ~ spl0_18
| spl0_584
| ~ spl0_140
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2711,f2636,f1379,f16112,f776]) ).
fof(f16112,plain,
( spl0_584
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat)
| ~ c_lessequals(X2,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f2711,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_lessequals(X2,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat)
| ~ class_Orderings_Opreorder(tc_nat) )
| ~ spl0_140
| ~ spl0_235 ),
inference(resolution,[],[f2637,f1380]) ).
fof(f16080,plain,
( ~ spl0_18
| spl0_583
| ~ spl0_140
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2688,f2632,f1379,f16078,f776]) ).
fof(f16078,plain,
( spl0_583
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f2688,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| ~ class_Orderings_Opreorder(tc_nat) )
| ~ spl0_140
| ~ spl0_234 ),
inference(resolution,[],[f2633,f1380]) ).
fof(f16076,plain,
( spl0_582
| ~ spl0_142
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2664,f2624,f1387,f16074]) ).
fof(f16074,plain,
( spl0_582
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X0),X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f2664,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X0),X0),c_HOL_Oone__class_Oone(X0),X0) )
| ~ spl0_142
| ~ spl0_232 ),
inference(resolution,[],[f2625,f1388]) ).
fof(f16072,plain,
( spl0_581
| ~ spl0_141
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2663,f2624,f1383,f16070]) ).
fof(f16070,plain,
( spl0_581
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X0),X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f2663,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X0),X0),c_HOL_Oone__class_Oone(X0),X0) )
| ~ spl0_141
| ~ spl0_232 ),
inference(resolution,[],[f2625,f1384]) ).
fof(f16068,plain,
( spl0_580
| ~ spl0_140
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2662,f2624,f1379,f16066]) ).
fof(f16066,plain,
( spl0_580
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X0),X0),c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f2662,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X0),X0),c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_140
| ~ spl0_232 ),
inference(resolution,[],[f2625,f1380]) ).
fof(f16064,plain,
( spl0_579
| ~ spl0_138
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2661,f2624,f1371,f16062]) ).
fof(f16062,plain,
( spl0_579
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f2661,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X0),X0),X0) )
| ~ spl0_138
| ~ spl0_232 ),
inference(resolution,[],[f2625,f1372]) ).
fof(f16060,plain,
( spl0_578
| ~ spl0_137
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2660,f2624,f1367,f16058]) ).
fof(f16058,plain,
( spl0_578
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f2660,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X0),X0),X0) )
| ~ spl0_137
| ~ spl0_232 ),
inference(resolution,[],[f2625,f1368]) ).
fof(f16056,plain,
( spl0_577
| ~ spl0_199
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2430,f2297,f1986,f16054]) ).
fof(f16054,plain,
( spl0_577
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X3,tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f2430,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X3,tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) )
| ~ spl0_199
| ~ spl0_215 ),
inference(superposition,[],[f1987,f2298]) ).
fof(f16052,plain,
( spl0_576
| ~ spl0_199
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2429,f2297,f1986,f16050]) ).
fof(f16050,plain,
( spl0_576
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X3,tc_nat),tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f2429,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X3,tc_nat),tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) )
| ~ spl0_199
| ~ spl0_215 ),
inference(superposition,[],[f1987,f2298]) ).
fof(f16048,plain,
( spl0_575
| ~ spl0_198
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2428,f2297,f1982,f16046]) ).
fof(f16046,plain,
( spl0_575
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),tc_nat)
| ~ c_lessequals(X3,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f2428,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),tc_nat)
| ~ c_lessequals(X3,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) )
| ~ spl0_198
| ~ spl0_215 ),
inference(superposition,[],[f1983,f2298]) ).
fof(f16044,plain,
( spl0_574
| ~ spl0_363
| ~ spl0_449 ),
inference(avatar_split_clause,[],[f10043,f9464,f5479,f16042]) ).
fof(f10043,plain,
( ! [X0,X1] :
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X0,t_a),X1,t_a) = X0
| c_HOL_Ozero__class_Ozero(t_a) = X1 )
| ~ spl0_363
| ~ spl0_449 ),
inference(superposition,[],[f5480,f9465]) ).
fof(f16040,plain,
( spl0_573
| ~ spl0_198
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2427,f2297,f1982,f16038]) ).
fof(f16038,plain,
( spl0_573
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f2427,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X3,tc_nat) )
| ~ spl0_198
| ~ spl0_215 ),
inference(superposition,[],[f1983,f2298]) ).
fof(f16004,plain,
( ~ spl0_18
| spl0_572
| ~ spl0_195
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2226,f1986,f1970,f16002,f776]) ).
fof(f16002,plain,
( spl0_572
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(X2,c_HOL_Ominus__class_Ominus(X3,X0,tc_nat),tc_nat)
| ~ c_lessequals(X2,c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f2226,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X2,c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| c_lessequals(X2,c_HOL_Ominus__class_Ominus(X3,X0,tc_nat),tc_nat) )
| ~ spl0_195
| ~ spl0_199 ),
inference(resolution,[],[f1987,f1971]) ).
fof(f15973,plain,
( ~ spl0_18
| spl0_571
| ~ spl0_188
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2222,f1986,f1942,f15971,f776]) ).
fof(f15971,plain,
( spl0_571
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X3,X0,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f2222,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X3,X0,tc_nat),tc_nat) )
| ~ spl0_188
| ~ spl0_199 ),
inference(resolution,[],[f1987,f1943]) ).
fof(f15940,plain,
( ~ spl0_18
| spl0_570
| ~ spl0_187
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2221,f1986,f1938,f15938,f776]) ).
fof(f15938,plain,
( spl0_570
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f2221,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat) )
| ~ spl0_187
| ~ spl0_199 ),
inference(resolution,[],[f1987,f1939]) ).
fof(f15903,plain,
( ~ spl0_18
| spl0_569
| ~ spl0_195
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2202,f1982,f1970,f15901,f776]) ).
fof(f15901,plain,
( spl0_569
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(X2,c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),tc_nat)
| ~ c_lessequals(X2,c_HOL_Ominus__class_Ominus(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f2202,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X2,c_HOL_Ominus__class_Ominus(X0,X3,tc_nat),tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| c_lessequals(X2,c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),tc_nat) )
| ~ spl0_195
| ~ spl0_198 ),
inference(resolution,[],[f1983,f1971]) ).
fof(f15871,plain,
( ~ spl0_568
| spl0_81
| ~ spl0_350
| ~ spl0_360 ),
inference(avatar_split_clause,[],[f6502,f5190,f4959,f1088,f15868]) ).
fof(f1088,plain,
( spl0_81
<=> c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_x,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f6502,plain,
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_x,t_a) != c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a)
| spl0_81
| ~ spl0_350
| ~ spl0_360 ),
inference(forward_demodulation,[],[f6444,f5191]) ).
fof(f6444,plain,
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_x,t_a) != c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a)
| spl0_81
| ~ spl0_350 ),
inference(superposition,[],[f1090,f4960]) ).
fof(f1090,plain,
( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_x,t_a)
| spl0_81 ),
inference(avatar_component_clause,[],[f1088]) ).
fof(f15866,plain,
( ~ spl0_18
| spl0_567
| ~ spl0_188
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2198,f1982,f1942,f15864,f776]) ).
fof(f15864,plain,
( spl0_567
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f2198,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X0,X3,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),tc_nat) )
| ~ spl0_188
| ~ spl0_198 ),
inference(resolution,[],[f1983,f1943]) ).
fof(f15833,plain,
( ~ spl0_18
| spl0_566
| ~ spl0_187
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2197,f1982,f1938,f15831,f776]) ).
fof(f15831,plain,
( spl0_566
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f2197,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X3,tc_nat) )
| ~ spl0_187
| ~ spl0_198 ),
inference(resolution,[],[f1983,f1939]) ).
fof(f15829,plain,
( spl0_565
| ~ spl0_195
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2174,f1978,f1970,f15827]) ).
fof(f15827,plain,
( spl0_565
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(X3,c_HOL_Ominus__class_Ominus(X0,X1,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f2174,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(X3,c_HOL_Ominus__class_Ominus(X0,X1,X2),X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2) )
| ~ spl0_195
| ~ spl0_197 ),
inference(resolution,[],[f1979,f1971]) ).
fof(f15825,plain,
( spl0_564
| ~ spl0_194
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2173,f1978,f1966,f15823]) ).
fof(f15823,plain,
( spl0_564
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f2173,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,X2),X3,X2) )
| ~ spl0_194
| ~ spl0_197 ),
inference(resolution,[],[f1979,f1967]) ).
fof(f15821,plain,
( spl0_563
| ~ spl0_190
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2172,f1978,f1950,f15819]) ).
fof(f15819,plain,
( spl0_563
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f2172,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,X2),X3,X2) )
| ~ spl0_190
| ~ spl0_197 ),
inference(resolution,[],[f1979,f1951]) ).
fof(f15817,plain,
( spl0_562
| ~ spl0_189
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2171,f1978,f1946,f15815]) ).
fof(f15815,plain,
( spl0_562
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ominus__class_Ominus(X0,X1,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f2171,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ominus__class_Ominus(X0,X1,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2) )
| ~ spl0_189
| ~ spl0_197 ),
inference(resolution,[],[f1979,f1947]) ).
fof(f15813,plain,
( spl0_561
| ~ spl0_188
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2170,f1978,f1942,f15811]) ).
fof(f15811,plain,
( spl0_561
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ominus__class_Ominus(X0,X1,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f2170,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ominus__class_Ominus(X0,X1,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2) )
| ~ spl0_188
| ~ spl0_197 ),
inference(resolution,[],[f1979,f1943]) ).
fof(f15809,plain,
( spl0_560
| ~ spl0_187
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2169,f1978,f1938,f15807]) ).
fof(f15807,plain,
( spl0_560
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f2169,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,X2),X3,X2) )
| ~ spl0_187
| ~ spl0_197 ),
inference(resolution,[],[f1979,f1939]) ).
fof(f15805,plain,
( spl0_559
| ~ spl0_183
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f2124,f1962,f1915,f15803]) ).
fof(f15803,plain,
( spl0_559
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f1915,plain,
( spl0_183
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f2124,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
| ~ spl0_183
| ~ spl0_193 ),
inference(resolution,[],[f1963,f1916]) ).
fof(f1916,plain,
( ! [X3,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
| ~ spl0_183 ),
inference(avatar_component_clause,[],[f1915]) ).
fof(f15793,plain,
( spl0_558
| ~ spl0_183
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f2110,f1958,f1915,f15791]) ).
fof(f15791,plain,
( spl0_558
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X1,X2,X3),X3)
| ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f2110,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X1,X2,X3),X3)
| ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) )
| ~ spl0_183
| ~ spl0_192 ),
inference(resolution,[],[f1959,f1916]) ).
fof(f15789,plain,
( spl0_557
| ~ spl0_160
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f2022,f1923,f1636,f15787]) ).
fof(f15787,plain,
( spl0_557
<=> ! [X2,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f1636,plain,
( spl0_160
<=> ! [X2,X4] :
( ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X2,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f2022,plain,
( ! [X2,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) )
| ~ spl0_160
| ~ spl0_185 ),
inference(resolution,[],[f1924,f1637]) ).
fof(f1637,plain,
( ! [X2,X4] :
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X2,X4,tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) )
| ~ spl0_160 ),
inference(avatar_component_clause,[],[f1636]) ).
fof(f15785,plain,
( spl0_556
| ~ spl0_161
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f2021,f1923,f1640,f15783]) ).
fof(f15783,plain,
( spl0_556
<=> ! [X2,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X0)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f1640,plain,
( spl0_161
<=> ! [X2,X4] :
( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X2,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f2021,plain,
( ! [X2,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X0)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) )
| ~ spl0_161
| ~ spl0_185 ),
inference(resolution,[],[f1924,f1641]) ).
fof(f1641,plain,
( ! [X2,X4] :
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X2,X4,tc_nat),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) )
| ~ spl0_161 ),
inference(avatar_component_clause,[],[f1640]) ).
fof(f15781,plain,
( spl0_555
| ~ spl0_173
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f1877,f1753,f1737,f15779]) ).
fof(f15779,plain,
( spl0_555
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X0,X1,X2),X2)
| c_Power_Opower__class_Opower(X0,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f1737,plain,
( spl0_173
<=> ! [X9,X0,X2] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f1877,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X0,X1,X2),X2)
| c_Power_Opower__class_Opower(X0,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) )
| ~ spl0_173
| ~ spl0_177 ),
inference(duplicate_literal_removal,[],[f1859]) ).
fof(f1859,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X0,X1,X2),X2)
| c_Power_Opower__class_Opower(X0,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X2) )
| ~ spl0_173
| ~ spl0_177 ),
inference(resolution,[],[f1754,f1738]) ).
fof(f1738,plain,
( ! [X2,X0,X9] :
( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_173 ),
inference(avatar_component_clause,[],[f1737]) ).
fof(f14939,plain,
( ~ spl0_3
| spl0_554
| ~ spl0_116
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f3326,f2982,f1249,f14937,f701]) ).
fof(f701,plain,
( spl0_3
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f14937,plain,
( spl0_554
<=> ! [X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f1249,plain,
( spl0_116
<=> ! [X9] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X9
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f3326,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) )
| ~ spl0_116
| ~ spl0_276 ),
inference(resolution,[],[f2983,f1250]) ).
fof(f1250,plain,
( ! [X9] :
( ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X9 )
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f1249]) ).
fof(f14935,plain,
( ~ spl0_551
| spl0_552
| spl0_553
| ~ spl0_256
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f3561,f3010,f2901,f14933,f14929,f14925]) ).
fof(f14925,plain,
( spl0_551
<=> class_Ring__and__Field_Oordered__semiring__strict(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f14929,plain,
( spl0_552
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f14933,plain,
( spl0_553
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(t_a),X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f3561,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(t_a),X0,t_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(t_a),c_HOL_Oone__class_Oone(t_a),t_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(t_a) )
| ~ spl0_256
| ~ spl0_283 ),
inference(duplicate_literal_removal,[],[f3542]) ).
fof(f3542,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(t_a),X0,t_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(t_a),X0,t_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(t_a),c_HOL_Oone__class_Oone(t_a),t_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(t_a) )
| ~ spl0_256
| ~ spl0_283 ),
inference(superposition,[],[f2902,f3011]) ).
fof(f14889,plain,
( ~ spl0_3
| spl0_550
| ~ spl0_116
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f3304,f2978,f1249,f14886,f701]) ).
fof(f14886,plain,
( spl0_550
<=> ! [X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f3304,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) )
| ~ spl0_116
| ~ spl0_275 ),
inference(resolution,[],[f2979,f1250]) ).
fof(f14888,plain,
( ~ spl0_549
| spl0_550
| ~ spl0_116
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f3256,f2970,f1249,f14886,f14882]) ).
fof(f14882,plain,
( spl0_549
<=> class_Ring__and__Field_Oordered__ring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f3256,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) )
| ~ spl0_116
| ~ spl0_273 ),
inference(resolution,[],[f2971,f1250]) ).
fof(f14853,plain,
( ~ spl0_4
| spl0_548
| ~ spl0_115
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f3067,f2901,f1245,f14851,f706]) ).
fof(f14851,plain,
( spl0_548
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f1245,plain,
( spl0_115
<=> ! [X9] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X9
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f3067,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) )
| ~ spl0_115
| ~ spl0_256 ),
inference(resolution,[],[f2902,f1246]) ).
fof(f1246,plain,
( ! [X9] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X9 )
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f1245]) ).
fof(f14821,plain,
( ~ spl0_4
| spl0_547
| ~ spl0_115
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f3055,f2897,f1245,f14819,f706]) ).
fof(f14819,plain,
( spl0_547
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f3055,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) )
| ~ spl0_115
| ~ spl0_255 ),
inference(resolution,[],[f2898,f1246]) ).
fof(f14792,plain,
( ~ spl0_8
| spl0_546
| ~ spl0_164
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2348,f2281,f1652,f14790,f726]) ).
fof(f14790,plain,
( spl0_546
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X0,X1,tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f2348,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X0,X1,tc_nat),X2,tc_nat)
| c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat) )
| ~ spl0_164
| ~ spl0_211 ),
inference(resolution,[],[f2282,f1653]) ).
fof(f14640,plain,
( spl0_545
| ~ spl0_172
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2149,f1970,f1733,f14638]) ).
fof(f14638,plain,
( spl0_545
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X0,c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f2149,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X0,c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_172
| ~ spl0_195 ),
inference(resolution,[],[f1971,f1734]) ).
fof(f14636,plain,
( spl0_544
| ~ spl0_172
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f2136,f1966,f1733,f14634]) ).
fof(f14634,plain,
( spl0_544
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(c_Power_Opower__class_Opower(X0,X1,X2),X3,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f2136,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(c_Power_Opower__class_Opower(X0,X1,X2),X3,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X2) )
| ~ spl0_172
| ~ spl0_194 ),
inference(resolution,[],[f1967,f1734]) ).
fof(f14632,plain,
( spl0_543
| ~ spl0_176
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f2118,f1962,f1749,f14630]) ).
fof(f14630,plain,
( spl0_543
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(X3,X1,X2)
| c_HOL_Oord__class_Oless(X0,X3,X2)
| X0 = X3
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f2118,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(X3,X1,X2)
| c_HOL_Oord__class_Oless(X0,X3,X2)
| X0 = X3
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_176
| ~ spl0_193 ),
inference(resolution,[],[f1963,f1750]) ).
fof(f14628,plain,
( spl0_542
| ~ spl0_177
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f2116,f1962,f1753,f14626]) ).
fof(f14626,plain,
( spl0_542
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(X3,X1,X2)
| c_HOL_Oord__class_Oless(X0,X3,X2)
| X0 = X3
| ~ class_Ring__and__Field_Oordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f2116,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(X3,X1,X2)
| c_HOL_Oord__class_Oless(X0,X3,X2)
| X0 = X3
| ~ class_Ring__and__Field_Oordered__idom(X2) )
| ~ spl0_177
| ~ spl0_193 ),
inference(resolution,[],[f1963,f1754]) ).
fof(f14624,plain,
( spl0_541
| ~ spl0_176
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f2104,f1958,f1749,f14622]) ).
fof(f14622,plain,
( spl0_541
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X0,X3,X2)
| c_HOL_Oord__class_Oless(X3,X1,X2)
| X1 = X3
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f2104,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X0,X3,X2)
| c_HOL_Oord__class_Oless(X3,X1,X2)
| X1 = X3
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_176
| ~ spl0_192 ),
inference(resolution,[],[f1959,f1750]) ).
fof(f14620,plain,
( spl0_540
| ~ spl0_177
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f2102,f1958,f1753,f14618]) ).
fof(f14618,plain,
( spl0_540
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X0,X3,X2)
| c_HOL_Oord__class_Oless(X3,X1,X2)
| X1 = X3
| ~ class_Ring__and__Field_Oordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f2102,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X0,X3,X2)
| c_HOL_Oord__class_Oless(X3,X1,X2)
| X1 = X3
| ~ class_Ring__and__Field_Oordered__idom(X2) )
| ~ spl0_177
| ~ spl0_192 ),
inference(resolution,[],[f1959,f1754]) ).
fof(f14616,plain,
( spl0_539
| ~ spl0_172
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f2092,f1950,f1733,f14614]) ).
fof(f14614,plain,
( spl0_539
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f2092,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_172
| ~ spl0_190 ),
inference(resolution,[],[f1951,f1734]) ).
fof(f14612,plain,
( spl0_538
| ~ spl0_172
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f2079,f1946,f1733,f14610]) ).
fof(f14610,plain,
( spl0_538
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X2,X3,X0),X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f2079,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X2,X3,X0),X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_172
| ~ spl0_189 ),
inference(resolution,[],[f1947,f1734]) ).
fof(f14608,plain,
( spl0_537
| ~ spl0_172
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f2066,f1942,f1733,f14606]) ).
fof(f14606,plain,
( spl0_537
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X2,X3,X0),X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f2066,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X2,X3,X0),X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_172
| ~ spl0_188 ),
inference(resolution,[],[f1943,f1734]) ).
fof(f14604,plain,
( spl0_536
| ~ spl0_172
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f2053,f1938,f1733,f14602]) ).
fof(f14602,plain,
( spl0_536
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f2053,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_172
| ~ spl0_187 ),
inference(resolution,[],[f1939,f1734]) ).
fof(f14464,plain,
( spl0_535
| ~ spl0_129
| ~ spl0_181 ),
inference(avatar_split_clause,[],[f1906,f1771,f1334,f14462]) ).
fof(f14462,plain,
( spl0_535
<=> ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X0,X0,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,X0,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Oorder(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f1334,plain,
( spl0_129
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1906,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X0,X0,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,X0,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Oorder(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) )
| ~ spl0_129
| ~ spl0_181 ),
inference(resolution,[],[f1772,f1335]) ).
fof(f1335,plain,
( ! [X0,X1] :
( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X1,X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_129 ),
inference(avatar_component_clause,[],[f1334]) ).
fof(f14460,plain,
( spl0_534
| ~ spl0_128
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f1857,f1753,f1330,f14458]) ).
fof(f14458,plain,
( spl0_534
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X0,X1),X1)
| c_HOL_Otimes__class_Otimes(X0,X0,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f1330,plain,
( spl0_128
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f1857,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X0,X1),X1)
| c_HOL_Otimes__class_Otimes(X0,X0,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) )
| ~ spl0_128
| ~ spl0_177 ),
inference(resolution,[],[f1754,f1331]) ).
fof(f1331,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_128 ),
inference(avatar_component_clause,[],[f1330]) ).
fof(f14456,plain,
( spl0_533
| ~ spl0_129
| ~ spl0_175 ),
inference(avatar_split_clause,[],[f1807,f1745,f1334,f14454]) ).
fof(f14454,plain,
( spl0_533
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,X1,X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X1,X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f1807,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,X1,X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X1,X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_129
| ~ spl0_175 ),
inference(resolution,[],[f1746,f1335]) ).
fof(f14452,plain,
( spl0_532
| ~ spl0_129
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f1794,f1741,f1334,f14450]) ).
fof(f14450,plain,
( spl0_532
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,X1,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X1,X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f1794,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,X1,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X1,X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_129
| ~ spl0_174 ),
inference(resolution,[],[f1742,f1335]) ).
fof(f14014,plain,
( spl0_531
| ~ spl0_114
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f2302,f2253,f1240,f14012]) ).
fof(f2253,plain,
( spl0_204
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f2302,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(t_a) = X0
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,t_a),X0,t_a) )
| ~ spl0_114
| ~ spl0_204 ),
inference(resolution,[],[f2254,f1242]) ).
fof(f2254,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),X1,X0) )
| ~ spl0_204 ),
inference(avatar_component_clause,[],[f2253]) ).
fof(f13822,plain,
( spl0_530
| ~ spl0_91
| ~ spl0_284 ),
inference(avatar_split_clause,[],[f3380,f3014,f1132,f13820]) ).
fof(f13820,plain,
( spl0_530
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X1,X0,tc_nat)
| ~ c_lessequals(X0,X0,tc_nat)
| ~ c_lessequals(X0,X1,tc_nat)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f3380,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X1,X0,tc_nat)
| ~ c_lessequals(X0,X0,tc_nat)
| ~ c_lessequals(X0,X1,tc_nat)
| X0 = X1 )
| ~ spl0_91
| ~ spl0_284 ),
inference(superposition,[],[f3015,f1133]) ).
fof(f13807,plain,
( ~ spl0_4
| spl0_529
| ~ spl0_98
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f3056,f2897,f1163,f13805,f706]) ).
fof(f13805,plain,
( spl0_529
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f1163,plain,
( spl0_98
<=> ! [X9] :
( c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f3056,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) )
| ~ spl0_98
| ~ spl0_255 ),
inference(resolution,[],[f2898,f1164]) ).
fof(f1164,plain,
( ! [X9] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) )
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f1163]) ).
fof(f13803,plain,
( spl0_528
| ~ spl0_36
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3018,f2869,f866,f13801]) ).
fof(f13801,plain,
( spl0_528
<=> ! [X2,X0,X1] : c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),X2,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X2,tc_Int_Oint),c_Power_Opower__class_Opower(X1,X2,tc_Int_Oint),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f866,plain,
( spl0_36
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f2869,plain,
( spl0_248
<=> ! [X3,X0,X9,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X3,X0),X9,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X3,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f3018,plain,
( ! [X2,X0,X1] : c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),X2,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X2,tc_Int_Oint),c_Power_Opower__class_Opower(X1,X2,tc_Int_Oint),tc_Int_Oint)
| ~ spl0_36
| ~ spl0_248 ),
inference(resolution,[],[f2870,f868]) ).
fof(f868,plain,
( class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f866]) ).
fof(f2870,plain,
( ! [X3,X0,X1,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X3,X0),X9,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X3,X9,X0),X0) )
| ~ spl0_248 ),
inference(avatar_component_clause,[],[f2869]) ).
fof(f13799,plain,
( spl0_527
| ~ spl0_114
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2301,f2249,f1240,f13797]) ).
fof(f2249,plain,
( spl0_203
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f2301,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(t_a) = X0
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X0,t_a),t_a) )
| ~ spl0_114
| ~ spl0_203 ),
inference(resolution,[],[f2250,f1242]) ).
fof(f2250,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X1,X0),X0) )
| ~ spl0_203 ),
inference(avatar_component_clause,[],[f2249]) ).
fof(f13795,plain,
( spl0_526
| ~ spl0_11
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3017,f2869,f741,f13793]) ).
fof(f13793,plain,
( spl0_526
<=> ! [X2,X0,X1] : c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X2,tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f741,plain,
( spl0_11
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f3017,plain,
( ! [X2,X0,X1] : c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X2,tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat)
| ~ spl0_11
| ~ spl0_248 ),
inference(resolution,[],[f2870,f743]) ).
fof(f743,plain,
( class_OrderedGroup_Ocomm__monoid__mult(tc_nat)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f741]) ).
fof(f13791,plain,
( spl0_525
| ~ spl0_97
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2705,f2636,f1159,f13789]) ).
fof(f13789,plain,
( spl0_525
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_lessequals(X2,X0,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f2705,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_lessequals(X2,X0,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) )
| ~ spl0_97
| ~ spl0_235 ),
inference(resolution,[],[f2637,f1160]) ).
fof(f13787,plain,
( spl0_524
| ~ spl0_97
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2682,f2632,f1159,f13785]) ).
fof(f13785,plain,
( spl0_524
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f2682,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) )
| ~ spl0_97
| ~ spl0_234 ),
inference(resolution,[],[f2633,f1160]) ).
fof(f13747,plain,
( ~ spl0_8
| spl0_523
| ~ spl0_97
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2659,f2624,f1159,f13745,f726]) ).
fof(f13745,plain,
( spl0_523
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X1,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f2659,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X1,tc_nat),tc_nat),tc_nat) )
| ~ spl0_97
| ~ spl0_232 ),
inference(resolution,[],[f2625,f1160]) ).
fof(f13743,plain,
( spl0_522
| ~ spl0_163
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2426,f2297,f1648,f13741]) ).
fof(f13741,plain,
( spl0_522
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f1648,plain,
( spl0_163
<=> ! [X9,X19] :
( ~ c_HOL_Oord__class_Oless(X19,X9,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X9,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f2426,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) )
| ~ spl0_163
| ~ spl0_215 ),
inference(superposition,[],[f1649,f2298]) ).
fof(f1649,plain,
( ! [X19,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X9,X19,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X19,X9,tc_nat) )
| ~ spl0_163 ),
inference(avatar_component_clause,[],[f1648]) ).
fof(f13739,plain,
( spl0_521
| ~ spl0_162
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2425,f2297,f1644,f13737]) ).
fof(f13737,plain,
( spl0_521
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f1644,plain,
( spl0_162
<=> ! [X9,X19] :
( c_HOL_Oord__class_Oless(X19,X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X9,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f2425,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) )
| ~ spl0_162
| ~ spl0_215 ),
inference(superposition,[],[f1645,f2298]) ).
fof(f1645,plain,
( ! [X19,X9] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X9,X19,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X19,X9,tc_nat) )
| ~ spl0_162 ),
inference(avatar_component_clause,[],[f1644]) ).
fof(f13735,plain,
( spl0_520
| ~ spl0_161
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2424,f2297,f1640,f13733]) ).
fof(f13733,plain,
( spl0_520
<=> ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f2424,plain,
( ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) )
| ~ spl0_161
| ~ spl0_215 ),
inference(superposition,[],[f1641,f2298]) ).
fof(f13731,plain,
( spl0_519
| ~ spl0_160
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2423,f2297,f1636,f13729]) ).
fof(f13729,plain,
( spl0_519
<=> ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f2423,plain,
( ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) )
| ~ spl0_160
| ~ spl0_215 ),
inference(superposition,[],[f1637,f2298]) ).
fof(f13702,plain,
( ~ spl0_8
| spl0_518
| ~ spl0_156
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2350,f2281,f1526,f13700,f726]) ).
fof(f13700,plain,
( spl0_518
<=> ! [X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),c_Power_Opower__class_Opower(X0,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f2350,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),c_Power_Opower__class_Opower(X0,X1,tc_nat),tc_nat) )
| ~ spl0_156
| ~ spl0_211 ),
inference(resolution,[],[f2282,f1527]) ).
fof(f13698,plain,
( spl0_517
| ~ spl0_164
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2211,f1986,f1652,f13696]) ).
fof(f13696,plain,
( spl0_517
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),X3,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f2211,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),X3,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat) )
| ~ spl0_164
| ~ spl0_199 ),
inference(resolution,[],[f1987,f1653]) ).
fof(f13694,plain,
( spl0_516
| ~ spl0_164
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2187,f1982,f1652,f13692]) ).
fof(f13692,plain,
( spl0_516
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f2187,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X3,tc_nat) )
| ~ spl0_164
| ~ spl0_198 ),
inference(resolution,[],[f1983,f1653]) ).
fof(f13690,plain,
( spl0_515
| ~ spl0_139
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f2023,f1923,f1375,f13688]) ).
fof(f13688,plain,
( spl0_515
<=> ! [X2,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f1375,plain,
( spl0_139
<=> ! [X4,X2] :
( ~ c_HOL_Oord__class_Oless(X2,X4,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X2,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f2023,plain,
( ! [X2,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
| ~ spl0_139
| ~ spl0_185 ),
inference(resolution,[],[f1924,f1376]) ).
fof(f1376,plain,
( ! [X2,X4] :
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X2,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_nat) )
| ~ spl0_139 ),
inference(avatar_component_clause,[],[f1375]) ).
fof(f13191,plain,
( ~ spl0_512
| spl0_513
| spl0_514
| ~ spl0_183
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f4064,f3371,f1915,f13188,f13185,f13181]) ).
fof(f13181,plain,
( spl0_512
<=> class_OrderedGroup_Opordered__ab__group__add(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f13185,plain,
( spl0_513
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(X0,X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f13188,plain,
( spl0_514
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(t_a),c_HOL_Ozero__class_Ozero(t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f3371,plain,
( spl0_287
<=> ! [X0] : c_HOL_Ozero__class_Ozero(t_a) = c_HOL_Ominus__class_Ominus(X0,X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f4064,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(t_a),c_HOL_Ozero__class_Ozero(t_a),t_a)
| ~ c_HOL_Oord__class_Oless(X0,X0,t_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_a) )
| ~ spl0_183
| ~ spl0_287 ),
inference(superposition,[],[f1916,f3372]) ).
fof(f3372,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(t_a) = c_HOL_Ominus__class_Ominus(X0,X0,t_a)
| ~ spl0_287 ),
inference(avatar_component_clause,[],[f3371]) ).
fof(f12918,plain,
( spl0_510
| spl0_511
| ~ spl0_208
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2669,f2628,f2269,f12916,f12913]) ).
fof(f12913,plain,
( spl0_510
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f12916,plain,
( spl0_511
<=> ! [X0] :
( ~ c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f2628,plain,
( spl0_233
<=> ! [X9,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X9
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f2669,plain,
( ! [X0,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) )
| ~ spl0_208
| ~ spl0_233 ),
inference(resolution,[],[f2629,f2270]) ).
fof(f2629,plain,
( ! [X0,X9] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X9,X0),X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X9
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_233 ),
inference(avatar_component_clause,[],[f2628]) ).
fof(f12911,plain,
( spl0_509
| ~ spl0_155
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2422,f2297,f1522,f12909]) ).
fof(f12909,plain,
( spl0_509
<=> ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f1522,plain,
( spl0_155
<=> ! [X9,X19] :
( c_lessequals(X19,X9,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X19,X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f2422,plain,
( ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat) )
| ~ spl0_155
| ~ spl0_215 ),
inference(superposition,[],[f1523,f2298]) ).
fof(f1523,plain,
( ! [X19,X9] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X19,X9,tc_nat)
| c_lessequals(X19,X9,tc_nat) )
| ~ spl0_155 ),
inference(avatar_component_clause,[],[f1522]) ).
fof(f12907,plain,
( spl0_508
| ~ spl0_148
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2421,f2297,f1493,f12905]) ).
fof(f12905,plain,
( spl0_508
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f1493,plain,
( spl0_148
<=> ! [X22,X9,X23] :
( ~ c_HOL_Oord__class_Oless(X22,X23,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X22,X9,tc_nat),X23,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f2421,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X3,tc_nat) )
| ~ spl0_148
| ~ spl0_215 ),
inference(superposition,[],[f1494,f2298]) ).
fof(f1494,plain,
( ! [X9,X22,X23] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X22,X9,tc_nat),X23,tc_nat)
| ~ c_HOL_Oord__class_Oless(X22,X23,tc_nat) )
| ~ spl0_148 ),
inference(avatar_component_clause,[],[f1493]) ).
fof(f12903,plain,
( spl0_507
| ~ spl0_136
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2390,f2293,f1363,f12901]) ).
fof(f12901,plain,
( spl0_507
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f2390,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_136
| ~ spl0_214 ),
inference(resolution,[],[f2294,f1364]) ).
fof(f12899,plain,
( spl0_506
| ~ spl0_134
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2389,f2293,f1355,f12897]) ).
fof(f12897,plain,
( spl0_506
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f2389,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_134
| ~ spl0_214 ),
inference(resolution,[],[f2294,f1356]) ).
fof(f12894,plain,
( spl0_505
| ~ spl0_136
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2372,f2289,f1363,f12892]) ).
fof(f12892,plain,
( spl0_505
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f2372,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_136
| ~ spl0_213 ),
inference(resolution,[],[f2290,f1364]) ).
fof(f12890,plain,
( spl0_504
| ~ spl0_134
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2371,f2289,f1355,f12888]) ).
fof(f12888,plain,
( spl0_504
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f2371,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_134
| ~ spl0_213 ),
inference(resolution,[],[f2290,f1356]) ).
fof(f12886,plain,
( spl0_503
| ~ spl0_136
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2353,f2285,f1363,f12884]) ).
fof(f12884,plain,
( spl0_503
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f2353,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_136
| ~ spl0_212 ),
inference(resolution,[],[f2286,f1364]) ).
fof(f12882,plain,
( spl0_502
| ~ spl0_134
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2352,f2285,f1355,f12880]) ).
fof(f12880,plain,
( spl0_502
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f2352,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_134
| ~ spl0_212 ),
inference(resolution,[],[f2286,f1356]) ).
fof(f12878,plain,
( spl0_501
| ~ spl0_136
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2336,f2281,f1363,f12876]) ).
fof(f12876,plain,
( spl0_501
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f2336,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0) )
| ~ spl0_136
| ~ spl0_211 ),
inference(resolution,[],[f2282,f1364]) ).
fof(f12874,plain,
( spl0_500
| ~ spl0_134
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2335,f2281,f1355,f12872]) ).
fof(f12872,plain,
( spl0_500
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f2335,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0) )
| ~ spl0_134
| ~ spl0_211 ),
inference(resolution,[],[f2282,f1356]) ).
fof(f12870,plain,
( spl0_499
| ~ spl0_142
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f2319,f2269,f1387,f12868]) ).
fof(f12868,plain,
( spl0_499
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f2319,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_142
| ~ spl0_208 ),
inference(resolution,[],[f2270,f1388]) ).
fof(f12866,plain,
( spl0_498
| ~ spl0_141
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f2318,f2269,f1383,f12864]) ).
fof(f12864,plain,
( spl0_498
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f2318,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_141
| ~ spl0_208 ),
inference(resolution,[],[f2270,f1384]) ).
fof(f12862,plain,
( spl0_497
| ~ spl0_140
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f2317,f2269,f1379,f12860]) ).
fof(f12860,plain,
( spl0_497
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f2317,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_140
| ~ spl0_208 ),
inference(resolution,[],[f2270,f1380]) ).
fof(f12858,plain,
( spl0_496
| ~ spl0_138
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f2316,f2269,f1371,f12856]) ).
fof(f12856,plain,
( spl0_496
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f2316,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) )
| ~ spl0_138
| ~ spl0_208 ),
inference(resolution,[],[f2270,f1372]) ).
fof(f12854,plain,
( ~ spl0_114
| spl0_495
| ~ spl0_182
| ~ spl0_285 ),
inference(avatar_split_clause,[],[f3609,f3088,f1911,f12852,f1240]) ).
fof(f12852,plain,
( spl0_495
<=> ! [X0] :
( c_HOL_Oone__class_Oone(t_a) != X0
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Oinverse__class_Oinverse(X0,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f3609,plain,
( ! [X0] :
( c_HOL_Oone__class_Oone(t_a) != X0
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Oinverse__class_Oinverse(X0,t_a)
| ~ class_Ring__and__Field_Odivision__ring(t_a) )
| ~ spl0_182
| ~ spl0_285 ),
inference(superposition,[],[f1912,f3089]) ).
fof(f12850,plain,
( spl0_494
| ~ spl0_137
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f2315,f2269,f1367,f12848]) ).
fof(f12848,plain,
( spl0_494
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f2315,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) )
| ~ spl0_137
| ~ spl0_208 ),
inference(resolution,[],[f2270,f1368]) ).
fof(f12846,plain,
( spl0_493
| ~ spl0_135
| ~ spl0_207 ),
inference(avatar_split_clause,[],[f2309,f2265,f1359,f12844]) ).
fof(f12844,plain,
( spl0_493
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X0,X2,X1),X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f2309,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X0,X2,X1),X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_135
| ~ spl0_207 ),
inference(resolution,[],[f2266,f1360]) ).
fof(f12842,plain,
( spl0_492
| ~ spl0_156
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2213,f1986,f1526,f12840]) ).
fof(f12840,plain,
( spl0_492
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f2213,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),tc_nat) )
| ~ spl0_156
| ~ spl0_199 ),
inference(resolution,[],[f1987,f1527]) ).
fof(f12838,plain,
( spl0_491
| ~ spl0_156
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2189,f1982,f1526,f12836]) ).
fof(f12836,plain,
( spl0_491
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f2189,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) )
| ~ spl0_156
| ~ spl0_198 ),
inference(resolution,[],[f1983,f1527]) ).
fof(f12778,plain,
( ~ spl0_20
| spl0_490
| ~ spl0_148
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f2123,f1962,f1493,f12776,f786]) ).
fof(f12776,plain,
( spl0_490
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f2123,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ class_Orderings_Oorder(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat) )
| ~ spl0_148
| ~ spl0_193 ),
inference(resolution,[],[f1963,f1494]) ).
fof(f12724,plain,
( ~ spl0_20
| spl0_489
| ~ spl0_152
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f2121,f1962,f1509,f12722,f786]) ).
fof(f12722,plain,
( spl0_489
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| X0 = X2
| c_HOL_Oord__class_Oless(X0,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f2121,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ class_Orderings_Oorder(tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,X2,tc_nat)
| X0 = X2 )
| ~ spl0_152
| ~ spl0_193 ),
inference(resolution,[],[f1963,f1510]) ).
fof(f12720,plain,
( spl0_488
| ~ spl0_151
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f2115,f1962,f1505,f12718]) ).
fof(f12718,plain,
( spl0_488
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),X1),X2,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f1505,plain,
( spl0_151
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f2115,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),X1),X2,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_151
| ~ spl0_193 ),
inference(resolution,[],[f1963,f1506]) ).
fof(f1506,plain,
( ! [X2,X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_151 ),
inference(avatar_component_clause,[],[f1505]) ).
fof(f12543,plain,
( ~ spl0_18
| spl0_487
| ~ spl0_148
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f2109,f1958,f1493,f12541,f776]) ).
fof(f12541,plain,
( spl0_487
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| c_HOL_Oord__class_Oless(X0,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f2109,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| c_HOL_Oord__class_Oless(X0,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) )
| ~ spl0_148
| ~ spl0_192 ),
inference(resolution,[],[f1959,f1494]) ).
fof(f12489,plain,
( ~ spl0_18
| spl0_486
| ~ spl0_152
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f2107,f1958,f1509,f12487,f776]) ).
fof(f12487,plain,
( spl0_486
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f2107,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| c_HOL_Oord__class_Oless(X0,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X1 = X2 )
| ~ spl0_152
| ~ spl0_192 ),
inference(resolution,[],[f1959,f1510]) ).
fof(f12485,plain,
( spl0_485
| ~ spl0_151
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f2101,f1958,f1505,f12483]) ).
fof(f12483,plain,
( spl0_485
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_HOL_Oord__class_Oless(X0,c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f2101,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_HOL_Oord__class_Oless(X0,c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_151
| ~ spl0_192 ),
inference(resolution,[],[f1959,f1506]) ).
fof(f12232,plain,
( spl0_484
| ~ spl0_361
| ~ spl0_449 ),
inference(avatar_split_clause,[],[f10033,f9464,f5201,f12230]) ).
fof(f10033,plain,
( ! [X0,X1] : c_HOL_Oinverse__class_Odivide(X0,X1,t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,t_a),X0,t_a)
| ~ spl0_361
| ~ spl0_449 ),
inference(superposition,[],[f9465,f5202]) ).
fof(f11400,plain,
( ~ spl0_482
| spl0_483
| ~ spl0_98
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2671,f2628,f1163,f11398,f11394]) ).
fof(f11394,plain,
( spl0_482
<=> class_Ring__and__Field_Oordered__idom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f11398,plain,
( spl0_483
<=> ! [X0] :
( ~ c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f2671,plain,
( ! [X0] :
( ~ c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_Ring__and__Field_Oordered__idom(tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),tc_nat) )
| ~ spl0_98
| ~ spl0_233 ),
inference(resolution,[],[f2629,f1164]) ).
fof(f11392,plain,
( spl0_481
| ~ spl0_139
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2420,f2297,f1375,f11390]) ).
fof(f11390,plain,
( spl0_481
<=> ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f2420,plain,
( ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat) )
| ~ spl0_139
| ~ spl0_215 ),
inference(superposition,[],[f1376,f2298]) ).
fof(f11360,plain,
( ~ spl0_19
| spl0_480
| ~ spl0_134
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2215,f1986,f1355,f11358,f781]) ).
fof(f781,plain,
( spl0_19
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f11358,plain,
( spl0_480
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f2215,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) )
| ~ spl0_134
| ~ spl0_199 ),
inference(resolution,[],[f1987,f1356]) ).
fof(f11326,plain,
( ~ spl0_19
| spl0_479
| ~ spl0_134
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2191,f1982,f1355,f11324,f781]) ).
fof(f11324,plain,
( spl0_479
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f2191,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat) )
| ~ spl0_134
| ~ spl0_198 ),
inference(resolution,[],[f1983,f1356]) ).
fof(f11322,plain,
( spl0_478
| ~ spl0_136
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2164,f1978,f1363,f11320]) ).
fof(f11320,plain,
( spl0_478
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f2164,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2) )
| ~ spl0_136
| ~ spl0_197 ),
inference(resolution,[],[f1979,f1364]) ).
fof(f11318,plain,
( spl0_477
| ~ spl0_134
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2163,f1978,f1355,f11316]) ).
fof(f11316,plain,
( spl0_477
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f2163,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2) )
| ~ spl0_134
| ~ spl0_197 ),
inference(resolution,[],[f1979,f1356]) ).
fof(f11314,plain,
( spl0_476
| ~ spl0_143
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f2154,f1974,f1391,f11312]) ).
fof(f11312,plain,
( spl0_476
<=> ! [X2,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f1974,plain,
( spl0_196
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f2154,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_143
| ~ spl0_196 ),
inference(resolution,[],[f1975,f1392]) ).
fof(f1975,plain,
( ! [X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,X3,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
| ~ spl0_196 ),
inference(avatar_component_clause,[],[f1974]) ).
fof(f11310,plain,
( spl0_475
| ~ spl0_129
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2147,f1970,f1334,f11308]) ).
fof(f11308,plain,
( spl0_475
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X0,c_HOL_Otimes__class_Otimes(X2,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f2147,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X0,c_HOL_Otimes__class_Otimes(X2,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) )
| ~ spl0_129
| ~ spl0_195 ),
inference(resolution,[],[f1971,f1335]) ).
fof(f11306,plain,
( spl0_474
| ~ spl0_143
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2145,f1970,f1391,f11304]) ).
fof(f11304,plain,
( spl0_474
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X0,X3,X2)
| c_lessequals(X3,X1,X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f2145,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X0,X3,X2)
| c_lessequals(X3,X1,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_143
| ~ spl0_195 ),
inference(resolution,[],[f1971,f1392]) ).
fof(f11302,plain,
( spl0_473
| ~ spl0_129
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f2134,f1966,f1334,f11300]) ).
fof(f11300,plain,
( spl0_473
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,X0,X1),X2,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f2134,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,X0,X1),X2,X1)
| ~ class_Orderings_Oorder(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) )
| ~ spl0_129
| ~ spl0_194 ),
inference(resolution,[],[f1967,f1335]) ).
fof(f11298,plain,
( spl0_472
| ~ spl0_143
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f2132,f1966,f1391,f11296]) ).
fof(f11296,plain,
( spl0_472
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(X3,X1,X2)
| c_lessequals(X0,X3,X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f2132,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(X3,X1,X2)
| c_lessequals(X0,X3,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_143
| ~ spl0_194 ),
inference(resolution,[],[f1967,f1392]) ).
fof(f11294,plain,
( ~ spl0_1
| spl0_470
| ~ spl0_471
| ~ spl0_216
| ~ spl0_329 ),
inference(avatar_split_clause,[],[f4595,f4433,f2472,f11291,f11288,f691]) ).
fof(f11288,plain,
( spl0_470
<=> ! [X0] : c_HOL_Oone__class_Oone(t_a) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f11291,plain,
( spl0_471
<=> c_HOL_Ozero__class_Ozero(t_a) = c_HOL_Oone__class_Oone(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f4595,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(t_a) != c_HOL_Oone__class_Oone(t_a)
| c_HOL_Oone__class_Oone(t_a) = X0
| ~ class_Ring__and__Field_Ofield(t_a) )
| ~ spl0_216
| ~ spl0_329 ),
inference(inner_rewriting,[],[f4594]) ).
fof(f4594,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(t_a) != c_HOL_Oone__class_Oone(t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0
| ~ class_Ring__and__Field_Ofield(t_a) )
| ~ spl0_216
| ~ spl0_329 ),
inference(duplicate_literal_removal,[],[f4593]) ).
fof(f4593,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(t_a) != c_HOL_Oone__class_Oone(t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X0
| c_HOL_Ozero__class_Ozero(t_a) = X0
| ~ class_Ring__and__Field_Ofield(t_a) )
| ~ spl0_216
| ~ spl0_329 ),
inference(superposition,[],[f2473,f4434]) ).
fof(f11286,plain,
( spl0_469
| ~ spl0_129
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f2090,f1950,f1334,f11284]) ).
fof(f11284,plain,
( spl0_469
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f2090,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_129
| ~ spl0_190 ),
inference(resolution,[],[f1951,f1335]) ).
fof(f11282,plain,
( spl0_468
| ~ spl0_143
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f2088,f1950,f1391,f11280]) ).
fof(f11280,plain,
( spl0_468
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X3,X2,X0)
| c_lessequals(X1,X3,X0)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f2088,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X3,X2,X0)
| c_lessequals(X1,X3,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_143
| ~ spl0_190 ),
inference(resolution,[],[f1951,f1392]) ).
fof(f11278,plain,
( spl0_467
| ~ spl0_129
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f2077,f1946,f1334,f11276]) ).
fof(f11276,plain,
( spl0_467
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X2,X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f2077,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X2,X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_129
| ~ spl0_189 ),
inference(resolution,[],[f1947,f1335]) ).
fof(f11274,plain,
( spl0_466
| ~ spl0_143
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f2075,f1946,f1391,f11272]) ).
fof(f11272,plain,
( spl0_466
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| c_lessequals(X3,X2,X0)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f2075,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| c_lessequals(X3,X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_143
| ~ spl0_189 ),
inference(resolution,[],[f1947,f1392]) ).
fof(f11270,plain,
( spl0_465
| ~ spl0_129
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f2064,f1942,f1334,f11268]) ).
fof(f11268,plain,
( spl0_465
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X2,X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f2064,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X2,X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_129
| ~ spl0_188 ),
inference(resolution,[],[f1943,f1335]) ).
fof(f11266,plain,
( spl0_464
| ~ spl0_143
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f2062,f1942,f1391,f11264]) ).
fof(f11264,plain,
( spl0_464
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| c_lessequals(X3,X2,X0)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f2062,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| c_lessequals(X3,X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_143
| ~ spl0_188 ),
inference(resolution,[],[f1943,f1392]) ).
fof(f11262,plain,
( spl0_463
| ~ spl0_129
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f2051,f1938,f1334,f11260]) ).
fof(f11260,plain,
( spl0_463
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f2051,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_129
| ~ spl0_187 ),
inference(resolution,[],[f1939,f1335]) ).
fof(f11258,plain,
( spl0_462
| ~ spl0_143
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f2049,f1938,f1391,f11256]) ).
fof(f11256,plain,
( spl0_462
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X3,X2,X0)
| c_lessequals(X1,X3,X0)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f2049,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X3,X2,X0)
| c_lessequals(X1,X3,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_143
| ~ spl0_187 ),
inference(resolution,[],[f1939,f1392]) ).
fof(f11254,plain,
( spl0_461
| ~ spl0_135
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f2013,f1919,f1359,f11252]) ).
fof(f11252,plain,
( spl0_461
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f2013,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_135
| ~ spl0_184 ),
inference(resolution,[],[f1920,f1360]) ).
fof(f11250,plain,
( spl0_460
| ~ spl0_137
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2003,f1915,f1367,f11248]) ).
fof(f11248,plain,
( spl0_460
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f2003,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) )
| ~ spl0_137
| ~ spl0_183 ),
inference(resolution,[],[f1916,f1368]) ).
fof(f11246,plain,
( spl0_459
| ~ spl0_114
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f2159,f1757,f1240,f11244]) ).
fof(f1757,plain,
( spl0_178
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f2159,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(t_a) = X0
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X0,t_a),t_a) = X0 )
| ~ spl0_114
| ~ spl0_178 ),
inference(resolution,[],[f1242,f1758]) ).
fof(f1758,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = X1 )
| ~ spl0_178 ),
inference(avatar_component_clause,[],[f1757]) ).
fof(f11242,plain,
( spl0_458
| ~ spl0_138
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2002,f1915,f1371,f11240]) ).
fof(f11240,plain,
( spl0_458
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f2002,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) )
| ~ spl0_138
| ~ spl0_183 ),
inference(resolution,[],[f1916,f1372]) ).
fof(f11238,plain,
( spl0_457
| ~ spl0_140
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2001,f1915,f1379,f11236]) ).
fof(f11236,plain,
( spl0_457
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f2001,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_140
| ~ spl0_183 ),
inference(resolution,[],[f1916,f1380]) ).
fof(f11234,plain,
( spl0_456
| ~ spl0_141
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2000,f1915,f1383,f11232]) ).
fof(f11232,plain,
( spl0_456
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f2000,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2) )
| ~ spl0_141
| ~ spl0_183 ),
inference(resolution,[],[f1916,f1384]) ).
fof(f11230,plain,
( spl0_455
| ~ spl0_142
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f1999,f1915,f1387,f11228]) ).
fof(f11228,plain,
( spl0_455
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f1999,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2) )
| ~ spl0_142
| ~ spl0_183 ),
inference(resolution,[],[f1916,f1388]) ).
fof(f9486,plain,
( spl0_454
| ~ spl0_252
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3892,f3451,f2885,f9484]) ).
fof(f9484,plain,
( spl0_454
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f3892,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1) )
| ~ spl0_252
| ~ spl0_302 ),
inference(duplicate_literal_removal,[],[f3875]) ).
fof(f3875,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1)
| c_HOL_Oord__class_Oless(X2,X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) )
| ~ spl0_252
| ~ spl0_302 ),
inference(resolution,[],[f3452,f2886]) ).
fof(f9482,plain,
( spl0_453
| ~ spl0_252
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3834,f3443,f2885,f9480]) ).
fof(f9480,plain,
( spl0_453
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f3834,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1) )
| ~ spl0_252
| ~ spl0_300 ),
inference(duplicate_literal_removal,[],[f3817]) ).
fof(f3817,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1)
| c_HOL_Oord__class_Oless(X2,X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) )
| ~ spl0_252
| ~ spl0_300 ),
inference(resolution,[],[f3444,f2886]) ).
fof(f9478,plain,
( spl0_452
| ~ spl0_34
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f2587,f2546,f856,f9476]) ).
fof(f9476,plain,
( spl0_452
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X0,X2,tc_Int_Oint),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f2587,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X0,X2,tc_Int_Oint),tc_Int_Oint)
| ~ spl0_34
| ~ spl0_227 ),
inference(resolution,[],[f2547,f858]) ).
fof(f9474,plain,
( spl0_451
| ~ spl0_9
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f2586,f2546,f731,f9472]) ).
fof(f9472,plain,
( spl0_451
<=> ! [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_451])]) ).
fof(f2586,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_9
| ~ spl0_227 ),
inference(resolution,[],[f2547,f733]) ).
fof(f9470,plain,
( spl0_450
| ~ spl0_34
| ~ spl0_35
| ~ spl0_224
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f2579,f2538,f2534,f861,f856,f9468]) ).
fof(f9468,plain,
( spl0_450
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),X2,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,X1,tc_Int_Oint),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f2579,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),X2,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,X1,tc_Int_Oint),tc_Int_Oint)
| ~ spl0_34
| ~ spl0_35
| ~ spl0_224
| ~ spl0_225 ),
inference(forward_demodulation,[],[f2576,f2573]) ).
fof(f2576,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),X2,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X2,tc_Int_Oint),X1,tc_Int_Oint)
| ~ spl0_34
| ~ spl0_225 ),
inference(resolution,[],[f2539,f858]) ).
fof(f9466,plain,
( spl0_449
| ~ spl0_93
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1936,f1489,f1140,f9464]) ).
fof(f1489,plain,
( spl0_147
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,X3,X0) = c_HOL_Otimes__class_Otimes(X3,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f1936,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,t_a) = c_HOL_Otimes__class_Otimes(X1,X0,t_a)
| ~ spl0_93
| ~ spl0_147 ),
inference(resolution,[],[f1142,f1490]) ).
fof(f1490,plain,
( ! [X3,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,X3,X0) = c_HOL_Otimes__class_Otimes(X3,X1,X0) )
| ~ spl0_147 ),
inference(avatar_component_clause,[],[f1489]) ).
fof(f9462,plain,
( spl0_448
| ~ spl0_9
| ~ spl0_10
| ~ spl0_224
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f2578,f2538,f2534,f736,f731,f9460]) ).
fof(f9460,plain,
( spl0_448
<=> ! [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_448])]) ).
fof(f2578,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_9
| ~ spl0_10
| ~ spl0_224
| ~ spl0_225 ),
inference(forward_demodulation,[],[f2575,f2572]) ).
fof(f2575,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_9
| ~ spl0_225 ),
inference(resolution,[],[f2539,f733]) ).
fof(f9458,plain,
( spl0_447
| ~ spl0_35
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2573,f2534,f861,f9456]) ).
fof(f9456,plain,
( spl0_447
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint),X2,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Int_Oint),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f9454,plain,
( spl0_446
| ~ spl0_10
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2572,f2534,f736,f9452]) ).
fof(f9452,plain,
( spl0_446
<=> ! [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_446])]) ).
fof(f9450,plain,
( spl0_445
| ~ spl0_94
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f1880,f1763,f1145,f9448]) ).
fof(f9448,plain,
( spl0_445
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f1880,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),tc_nat)
| ~ spl0_94
| ~ spl0_179 ),
inference(resolution,[],[f1764,f1146]) ).
fof(f9446,plain,
( spl0_444
| ~ spl0_137
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f1855,f1753,f1367,f9444]) ).
fof(f9444,plain,
( spl0_444
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X1,X0,X2)
| X0 = X1
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f1855,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X1,X0,X2)
| X0 = X1
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Orderings_Oorder(X2)
| c_lessequals(X0,X1,X2) )
| ~ spl0_137
| ~ spl0_177 ),
inference(resolution,[],[f1754,f1368]) ).
fof(f9442,plain,
( spl0_443
| ~ spl0_138
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f1854,f1753,f1371,f9440]) ).
fof(f9440,plain,
( spl0_443
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X1,X0,X2)
| X0 = X1
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f1854,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X1,X0,X2)
| X0 = X1
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Orderings_Opreorder(X2)
| c_lessequals(X0,X1,X2) )
| ~ spl0_138
| ~ spl0_177 ),
inference(resolution,[],[f1754,f1372]) ).
fof(f9310,plain,
( spl0_442
| ~ spl0_128
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f3077,f2905,f1330,f9308]) ).
fof(f9308,plain,
( spl0_442
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f3077,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) )
| ~ spl0_128
| ~ spl0_257 ),
inference(resolution,[],[f2906,f1331]) ).
fof(f9238,plain,
( spl0_441
| ~ spl0_54
| ~ spl0_40
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2519,f2484,f886,f956,f9236]) ).
fof(f9236,plain,
( spl0_441
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f956,plain,
( spl0_54
<=> class_Power_Opower(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f886,plain,
( spl0_40
<=> class_Ring__and__Field_Osemiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f2519,plain,
( ! [X0] :
( ~ class_Power_Opower(tc_Int_Oint)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint) )
| ~ spl0_40
| ~ spl0_219 ),
inference(resolution,[],[f2485,f888]) ).
fof(f888,plain,
( class_Ring__and__Field_Osemiring__0(tc_Int_Oint)
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f886]) ).
fof(f9166,plain,
( spl0_440
| ~ spl0_21
| ~ spl0_13
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2518,f2484,f751,f791,f9164]) ).
fof(f9164,plain,
( spl0_440
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f791,plain,
( spl0_21
<=> class_Power_Opower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f751,plain,
( spl0_13
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f2518,plain,
( ! [X0] :
( ~ class_Power_Opower(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
| ~ spl0_13
| ~ spl0_219 ),
inference(resolution,[],[f2485,f753]) ).
fof(f753,plain,
( class_Ring__and__Field_Osemiring__0(tc_nat)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f751]) ).
fof(f9162,plain,
( spl0_439
| ~ spl0_95
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2148,f1970,f1151,f9160]) ).
fof(f9160,plain,
( spl0_439
<=> ! [X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f1151,plain,
( spl0_95
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f2148,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) )
| ~ spl0_95
| ~ spl0_195 ),
inference(resolution,[],[f1971,f1152]) ).
fof(f1152,plain,
( ! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f1151]) ).
fof(f9158,plain,
( spl0_438
| ~ spl0_95
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f2135,f1966,f1151,f9156]) ).
fof(f9156,plain,
( spl0_438
<=> ! [X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f2135,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_95
| ~ spl0_194 ),
inference(resolution,[],[f1967,f1152]) ).
fof(f9154,plain,
( ~ spl0_437
| spl0_422
| ~ spl0_143
| spl0_392 ),
inference(avatar_split_clause,[],[f8162,f7308,f1391,f8623,f9151]) ).
fof(f9151,plain,
( spl0_437
<=> class_Orderings_Olinorder(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f8623,plain,
( spl0_422
<=> c_lessequals(c_HOL_Oone__class_Oone(t_a),c_HOL_Ozero__class_Ozero(t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f7308,plain,
( spl0_392
<=> c_lessequals(c_HOL_Ozero__class_Ozero(t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f8162,plain,
( c_lessequals(c_HOL_Oone__class_Oone(t_a),c_HOL_Ozero__class_Ozero(t_a),t_a)
| ~ class_Orderings_Olinorder(t_a)
| ~ spl0_143
| spl0_392 ),
inference(resolution,[],[f7309,f1392]) ).
fof(f7309,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(t_a),c_HOL_Oone__class_Oone(t_a),t_a)
| spl0_392 ),
inference(avatar_component_clause,[],[f7308]) ).
fof(f9149,plain,
( spl0_436
| ~ spl0_95
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f2091,f1950,f1151,f9147]) ).
fof(f9147,plain,
( spl0_436
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f2091,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_95
| ~ spl0_190 ),
inference(resolution,[],[f1951,f1152]) ).
fof(f9145,plain,
( spl0_435
| ~ spl0_95
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f2078,f1946,f1151,f9143]) ).
fof(f9143,plain,
( spl0_435
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f2078,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_95
| ~ spl0_189 ),
inference(resolution,[],[f1947,f1152]) ).
fof(f9141,plain,
( spl0_434
| ~ spl0_95
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f2065,f1942,f1151,f9139]) ).
fof(f9139,plain,
( spl0_434
<=> ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f2065,plain,
( ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_95
| ~ spl0_188 ),
inference(resolution,[],[f1943,f1152]) ).
fof(f9091,plain,
( spl0_433
| ~ spl0_18
| ~ spl0_102
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f2060,f1942,f1180,f776,f9089]) ).
fof(f9089,plain,
( spl0_433
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f2060,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) )
| ~ spl0_102
| ~ spl0_188 ),
inference(resolution,[],[f1943,f1181]) ).
fof(f9087,plain,
( spl0_432
| ~ spl0_95
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f2052,f1938,f1151,f9085]) ).
fof(f9085,plain,
( spl0_432
<=> ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f2052,plain,
( ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_95
| ~ spl0_187 ),
inference(resolution,[],[f1939,f1152]) ).
fof(f9037,plain,
( spl0_431
| ~ spl0_18
| ~ spl0_102
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f2047,f1938,f1180,f776,f9035]) ).
fof(f9035,plain,
( spl0_431
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(X0,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f2047,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_lessequals(X0,X2,tc_nat) )
| ~ spl0_102
| ~ spl0_187 ),
inference(resolution,[],[f1939,f1181]) ).
fof(f8705,plain,
( spl0_430
| ~ spl0_94
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2419,f2297,f1145,f8703]) ).
fof(f8703,plain,
( spl0_430
<=> ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f2419,plain,
( ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ spl0_94
| ~ spl0_215 ),
inference(superposition,[],[f1146,f2298]) ).
fof(f8701,plain,
( spl0_429
| ~ spl0_139
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2329,f2277,f1375,f8699]) ).
fof(f8699,plain,
( spl0_429
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f2329,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
| ~ spl0_139
| ~ spl0_210 ),
inference(resolution,[],[f2278,f1376]) ).
fof(f8697,plain,
( spl0_428
| ~ spl0_53
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f2304,f2261,f951,f8695]) ).
fof(f8695,plain,
( spl0_428
<=> ! [X0] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint) = c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint),X0,tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f951,plain,
( spl0_53
<=> class_Int_Onumber__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f2261,plain,
( spl0_206
<=> ! [X2,X0] :
( ~ class_Int_Onumber__ring(X0)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0) = c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f2304,plain,
( ! [X0] :
( c_Parity_Oeven__odd__class_Oeven(X0,tc_nat)
| c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint) = c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint),X0,tc_Int_Oint) )
| ~ spl0_53
| ~ spl0_206 ),
inference(resolution,[],[f2262,f953]) ).
fof(f953,plain,
( class_Int_Onumber__ring(tc_Int_Oint)
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f951]) ).
fof(f2262,plain,
( ! [X2,X0] :
( ~ class_Int_Onumber__ring(X0)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0) = c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X2,X0) )
| ~ spl0_206 ),
inference(avatar_component_clause,[],[f2261]) ).
fof(f8668,plain,
( ~ spl0_18
| spl0_427
| ~ spl0_94
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2140,f1970,f1145,f8666,f776]) ).
fof(f8666,plain,
( spl0_427
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f2140,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| c_lessequals(X0,X1,tc_nat) )
| ~ spl0_94
| ~ spl0_195 ),
inference(resolution,[],[f1971,f1146]) ).
fof(f8642,plain,
( spl0_426
| ~ spl0_18
| ~ spl0_94
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f2057,f1942,f1145,f776,f8640]) ).
fof(f8640,plain,
( spl0_426
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f2057,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
| ~ spl0_94
| ~ spl0_188 ),
inference(resolution,[],[f1943,f1146]) ).
fof(f8638,plain,
( spl0_425
| ~ spl0_102
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f1883,f1763,f1180,f8636]) ).
fof(f8636,plain,
( spl0_425
<=> ! [X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) = X1
| c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f1883,plain,
( ! [X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) = X1
| c_lessequals(X0,X1,tc_nat) )
| ~ spl0_102
| ~ spl0_179 ),
inference(resolution,[],[f1764,f1181]) ).
fof(f8634,plain,
( spl0_424
| ~ spl0_94
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1625,f1530,f1145,f8632]) ).
fof(f8632,plain,
( spl0_424
<=> ! [X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = X0
| ~ c_lessequals(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f1625,plain,
( ! [X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = X0
| ~ c_lessequals(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) )
| ~ spl0_94
| ~ spl0_157 ),
inference(resolution,[],[f1531,f1146]) ).
fof(f8630,plain,
( spl0_423
| ~ spl0_143
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f1605,f1513,f1391,f8628]) ).
fof(f8628,plain,
( spl0_423
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),X0)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f1513,plain,
( spl0_153
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f1605,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_143
| ~ spl0_153 ),
inference(resolution,[],[f1514,f1392]) ).
fof(f1514,plain,
( ! [X2,X0] :
( ~ c_lessequals(c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_153 ),
inference(avatar_component_clause,[],[f1513]) ).
fof(f8626,plain,
( ~ spl0_421
| ~ spl0_422
| ~ spl0_153
| ~ spl0_350 ),
inference(avatar_split_clause,[],[f6446,f4959,f1513,f8623,f8619]) ).
fof(f8619,plain,
( spl0_421
<=> class_Ring__and__Field_Oordered__idom(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f6446,plain,
( ~ c_lessequals(c_HOL_Oone__class_Oone(t_a),c_HOL_Ozero__class_Ozero(t_a),t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a)
| ~ spl0_153
| ~ spl0_350 ),
inference(superposition,[],[f1514,f4960]) ).
fof(f8617,plain,
( spl0_420
| ~ spl0_137
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1570,f1505,f1367,f8615]) ).
fof(f8615,plain,
( spl0_420
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f1570,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),X0) )
| ~ spl0_137
| ~ spl0_151 ),
inference(resolution,[],[f1506,f1368]) ).
fof(f8613,plain,
( spl0_419
| ~ spl0_138
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1569,f1505,f1371,f8611]) ).
fof(f8611,plain,
( spl0_419
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f1569,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),X0) )
| ~ spl0_138
| ~ spl0_151 ),
inference(resolution,[],[f1506,f1372]) ).
fof(f8609,plain,
( spl0_418
| ~ spl0_140
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1568,f1505,f1379,f8607]) ).
fof(f8607,plain,
( spl0_418
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f1568,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_140
| ~ spl0_151 ),
inference(resolution,[],[f1506,f1380]) ).
fof(f8605,plain,
( spl0_417
| ~ spl0_141
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1567,f1505,f1383,f8603]) ).
fof(f8603,plain,
( spl0_417
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f1567,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_141
| ~ spl0_151 ),
inference(resolution,[],[f1506,f1384]) ).
fof(f8601,plain,
( spl0_416
| ~ spl0_142
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1566,f1505,f1387,f8599]) ).
fof(f8599,plain,
( spl0_416
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f1566,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_142
| ~ spl0_151 ),
inference(resolution,[],[f1506,f1388]) ).
fof(f8597,plain,
( spl0_415
| ~ spl0_94
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f1555,f1497,f1145,f8595]) ).
fof(f8595,plain,
( spl0_415
<=> ! [X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = X0
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f1555,plain,
( ! [X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = X0
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat) )
| ~ spl0_94
| ~ spl0_149 ),
inference(resolution,[],[f1498,f1146]) ).
fof(f8571,plain,
( ~ spl0_20
| spl0_414
| ~ spl0_142
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1545,f1493,f1387,f8569,f786]) ).
fof(f8569,plain,
( spl0_414
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f1545,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ class_Orderings_Oorder(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat) )
| ~ spl0_142
| ~ spl0_148 ),
inference(resolution,[],[f1494,f1388]) ).
fof(f8380,plain,
( spl0_413
| ~ spl0_129
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f3225,f2950,f1334,f8378]) ).
fof(f8378,plain,
( spl0_413
<=> ! [X0,X1] :
( c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f2950,plain,
( spl0_268
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f3225,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) )
| ~ spl0_129
| ~ spl0_268 ),
inference(duplicate_literal_removal,[],[f3212]) ).
fof(f3212,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) )
| ~ spl0_129
| ~ spl0_268 ),
inference(resolution,[],[f2951,f1335]) ).
fof(f2951,plain,
( ! [X3,X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_268 ),
inference(avatar_component_clause,[],[f2950]) ).
fof(f8376,plain,
( spl0_412
| ~ spl0_103
| ~ spl0_231 ),
inference(avatar_split_clause,[],[f2622,f2566,f1184,f8374]) ).
fof(f8374,plain,
( spl0_412
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f2622,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
| ~ spl0_103
| ~ spl0_231 ),
inference(trivial_inequality_removal,[],[f2619]) ).
fof(f2619,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
| ~ spl0_103
| ~ spl0_231 ),
inference(superposition,[],[f2567,f1185]) ).
fof(f8372,plain,
( spl0_411
| ~ spl0_92
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2228,f1986,f1136,f8370]) ).
fof(f8370,plain,
( spl0_411
<=> ! [X0,X1] :
( c_lessequals(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f2228,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
| ~ spl0_92
| ~ spl0_199 ),
inference(superposition,[],[f1987,f1137]) ).
fof(f8368,plain,
( spl0_410
| ~ spl0_91
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2206,f1982,f1132,f8366]) ).
fof(f8366,plain,
( spl0_410
<=> ! [X0,X1] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_lessequals(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f2206,plain,
( ! [X0,X1] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_lessequals(X1,X0,tc_nat) )
| ~ spl0_91
| ~ spl0_198 ),
inference(superposition,[],[f1983,f1133]) ).
fof(f8364,plain,
( spl0_409
| ~ spl0_57
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f2020,f1923,f971,f8362]) ).
fof(f8362,plain,
( spl0_409
<=> ! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f971,plain,
( spl0_57
<=> c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f2020,plain,
( ! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),c_HOL_Ozero__class_Ozero(tc_nat),X0) )
| ~ spl0_57
| ~ spl0_185 ),
inference(resolution,[],[f1924,f973]) ).
fof(f973,plain,
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f971]) ).
fof(f8360,plain,
( spl0_408
| ~ spl0_102
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1705,f1652,f1180,f8358]) ).
fof(f8358,plain,
( spl0_408
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(X2,X1,tc_nat)
| c_lessequals(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f1705,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(X2,X1,tc_nat)
| c_lessequals(X0,X2,tc_nat) )
| ~ spl0_102
| ~ spl0_164 ),
inference(resolution,[],[f1653,f1181]) ).
fof(f8356,plain,
( ~ spl0_407
| ~ spl0_95
| spl0_392 ),
inference(avatar_split_clause,[],[f8161,f7308,f1151,f8353]) ).
fof(f8353,plain,
( spl0_407
<=> class_Ring__and__Field_Oordered__semidom(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f8161,plain,
( ~ class_Ring__and__Field_Oordered__semidom(t_a)
| ~ spl0_95
| spl0_392 ),
inference(resolution,[],[f7309,f1152]) ).
fof(f8183,plain,
( ~ spl0_18
| spl0_406
| ~ spl0_78
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2139,f1970,f1073,f8181,f776]) ).
fof(f8181,plain,
( spl0_406
<=> ! [X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f2139,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| c_lessequals(X0,X1,tc_nat) )
| ~ spl0_78
| ~ spl0_195 ),
inference(resolution,[],[f1971,f1074]) ).
fof(f8179,plain,
( spl0_405
| ~ spl0_94
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1702,f1652,f1145,f8177]) ).
fof(f8177,plain,
( spl0_405
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f1702,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat) )
| ~ spl0_94
| ~ spl0_164 ),
inference(resolution,[],[f1653,f1146]) ).
fof(f8175,plain,
( spl0_404
| ~ spl0_115
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f1682,f1644,f1245,f8173]) ).
fof(f8173,plain,
( spl0_404
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f1682,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) )
| ~ spl0_115
| ~ spl0_162 ),
inference(resolution,[],[f1645,f1246]) ).
fof(f8171,plain,
( spl0_403
| ~ spl0_102
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1617,f1526,f1180,f8169]) ).
fof(f8169,plain,
( spl0_403
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)
| c_lessequals(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f1617,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)
| c_lessequals(X1,X0,tc_nat) )
| ~ spl0_102
| ~ spl0_156 ),
inference(resolution,[],[f1527,f1181]) ).
fof(f8167,plain,
( spl0_402
| ~ spl0_97
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1541,f1493,f1159,f8165]) ).
fof(f8165,plain,
( spl0_402
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f1541,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat) )
| ~ spl0_97
| ~ spl0_148 ),
inference(resolution,[],[f1494,f1160]) ).
fof(f7993,plain,
( spl0_401
| ~ spl0_18
| ~ spl0_102
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f2039,f1927,f1180,f776,f7991]) ).
fof(f7991,plain,
( spl0_401
<=> ! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f2039,plain,
( ! [X0,X1] :
( ~ class_Orderings_Opreorder(tc_nat)
| c_lessequals(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
| ~ spl0_102
| ~ spl0_186 ),
inference(duplicate_literal_removal,[],[f2029]) ).
fof(f2029,plain,
( ! [X0,X1] :
( ~ class_Orderings_Opreorder(tc_nat)
| c_lessequals(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_lessequals(X0,X1,tc_nat) )
| ~ spl0_102
| ~ spl0_186 ),
inference(resolution,[],[f1928,f1181]) ).
fof(f7989,plain,
( spl0_400
| ~ spl0_98
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f1683,f1644,f1163,f7987]) ).
fof(f7987,plain,
( spl0_400
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f1683,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) )
| ~ spl0_98
| ~ spl0_162 ),
inference(resolution,[],[f1645,f1164]) ).
fof(f7985,plain,
( spl0_399
| ~ spl0_94
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1614,f1526,f1145,f7983]) ).
fof(f7983,plain,
( spl0_399
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f1614,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat)
| ~ spl0_94
| ~ spl0_156 ),
inference(resolution,[],[f1527,f1146]) ).
fof(f7981,plain,
( spl0_398
| ~ spl0_135
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1466,f1383,f1359,f7979]) ).
fof(f7979,plain,
( spl0_398
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f1466,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X1,X2,X0) )
| ~ spl0_135
| ~ spl0_141 ),
inference(duplicate_literal_removal,[],[f1465]) ).
fof(f1465,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_135
| ~ spl0_141 ),
inference(resolution,[],[f1384,f1360]) ).
fof(f7488,plain,
( spl0_397
| ~ spl0_92
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1608,f1522,f1136,f7486]) ).
fof(f7486,plain,
( spl0_397
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != X0
| c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f1608,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != X0
| c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
| ~ spl0_92
| ~ spl0_155 ),
inference(superposition,[],[f1523,f1137]) ).
fof(f7484,plain,
( spl0_396
| ~ spl0_91
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1550,f1493,f1132,f7482]) ).
fof(f7482,plain,
( spl0_396
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f1550,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
| ~ spl0_91
| ~ spl0_148 ),
inference(superposition,[],[f1494,f1133]) ).
fof(f7480,plain,
( spl0_395
| ~ spl0_34
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1538,f1489,f856,f7478]) ).
fof(f7478,plain,
( spl0_395
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f1538,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Int_Oint)
| ~ spl0_34
| ~ spl0_147 ),
inference(resolution,[],[f1490,f858]) ).
fof(f7476,plain,
( spl0_394
| ~ spl0_9
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1537,f1489,f731,f7474]) ).
fof(f7474,plain,
( spl0_394
<=> ! [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_394])]) ).
fof(f1537,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat)
| ~ spl0_9
| ~ spl0_147 ),
inference(resolution,[],[f1490,f733]) ).
fof(f7433,plain,
( spl0_393
| ~ spl0_1
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f5188,f5185,f691,f7431]) ).
fof(f7431,plain,
( spl0_393
<=> ! [X0,X3,X2,X1] :
( c_HOL_Ozero__class_Ozero(t_a) = X0
| c_HOL_Ozero__class_Ozero(t_a) = X1
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X2,X0,t_a),c_HOL_Oinverse__class_Odivide(X3,X1,t_a),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X1,t_a),c_HOL_Otimes__class_Otimes(X3,X0,t_a),t_a),c_HOL_Otimes__class_Otimes(X0,X1,t_a),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f5185,plain,
( spl0_359
<=> ! [X4,X11,X0,X12,X2] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X11
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X2,X4,X0),c_HOL_Oinverse__class_Odivide(X12,X11,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X11,X0),c_HOL_Otimes__class_Otimes(X12,X4,X0),X0),c_HOL_Otimes__class_Otimes(X4,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f5188,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Ozero__class_Ozero(t_a) = X0
| c_HOL_Ozero__class_Ozero(t_a) = X1
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X2,X0,t_a),c_HOL_Oinverse__class_Odivide(X3,X1,t_a),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X1,t_a),c_HOL_Otimes__class_Otimes(X3,X0,t_a),t_a),c_HOL_Otimes__class_Otimes(X0,X1,t_a),t_a) )
| ~ spl0_1
| ~ spl0_359 ),
inference(resolution,[],[f5186,f693]) ).
fof(f5186,plain,
( ! [X2,X0,X11,X4,X12] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X11
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X2,X4,X0),c_HOL_Oinverse__class_Odivide(X12,X11,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X11,X0),c_HOL_Otimes__class_Otimes(X12,X4,X0),X0),c_HOL_Otimes__class_Otimes(X4,X11,X0),X0) )
| ~ spl0_359 ),
inference(avatar_component_clause,[],[f5185]) ).
fof(f7311,plain,
( ~ spl0_391
| spl0_392
| ~ spl0_129
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f3530,f3010,f1334,f7308,f7304]) ).
fof(f7304,plain,
( spl0_391
<=> class_Ring__and__Field_Oordered__ring__strict(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f3530,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(t_a),c_HOL_Oone__class_Oone(t_a),t_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(t_a)
| ~ spl0_129
| ~ spl0_283 ),
inference(superposition,[],[f1335,f3011]) ).
fof(f6671,plain,
( ~ spl0_389
| spl0_368
| ~ spl0_390
| ~ spl0_103
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2243,f1994,f1184,f6668,f5557,f6664]) ).
fof(f6664,plain,
( spl0_389
<=> class_Int_Onumber__ring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f5557,plain,
( spl0_368
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f6668,plain,
( spl0_390
<=> class_Ring__and__Field_Oidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f1994,plain,
( spl0_201
<=> ! [X4,X0,X2] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X2 = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X2,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f2243,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oidom(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_Int_Onumber__ring(tc_nat) )
| ~ spl0_103
| ~ spl0_201 ),
inference(trivial_inequality_removal,[],[f2242]) ).
fof(f2242,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_Int_Onumber__ring(tc_nat) )
| ~ spl0_103
| ~ spl0_201 ),
inference(superposition,[],[f1995,f1185]) ).
fof(f1995,plain,
( ! [X2,X0,X4] :
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X2,X4,X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X2 = X4
| ~ class_Int_Onumber__ring(X0) )
| ~ spl0_201 ),
inference(avatar_component_clause,[],[f1994]) ).
fof(f6662,plain,
( spl0_388
| ~ spl0_45
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1418,f1346,f911,f6660]) ).
fof(f6660,plain,
( spl0_388
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Int_Oint),X0,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f911,plain,
( spl0_45
<=> class_OrderedGroup_Omonoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f1346,plain,
( spl0_132
<=> ! [X9,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1418,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Int_Oint),X0,tc_Int_Oint)
| ~ spl0_45
| ~ spl0_132 ),
inference(resolution,[],[f1347,f913]) ).
fof(f913,plain,
( class_OrderedGroup_Omonoid__mult(tc_Int_Oint)
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f911]) ).
fof(f1347,plain,
( ! [X0,X9] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X9,X0) )
| ~ spl0_132 ),
inference(avatar_component_clause,[],[f1346]) ).
fof(f6588,plain,
( spl0_387
| ~ spl0_17
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1417,f1346,f771,f6586]) ).
fof(f6586,plain,
( spl0_387
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f771,plain,
( spl0_17
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f1417,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ spl0_17
| ~ spl0_132 ),
inference(resolution,[],[f1347,f773]) ).
fof(f773,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f771]) ).
fof(f6584,plain,
( spl0_386
| ~ spl0_34
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1409,f1338,f856,f6582]) ).
fof(f6582,plain,
( spl0_386
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f1338,plain,
( spl0_130
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f1409,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint)
| ~ spl0_34
| ~ spl0_130 ),
inference(resolution,[],[f1339,f858]) ).
fof(f1339,plain,
( ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X0) )
| ~ spl0_130 ),
inference(avatar_component_clause,[],[f1338]) ).
fof(f6580,plain,
( spl0_385
| ~ spl0_9
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1408,f1338,f731,f6578]) ).
fof(f6578,plain,
( spl0_385
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f1408,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_9
| ~ spl0_130 ),
inference(resolution,[],[f1339,f733]) ).
fof(f6576,plain,
( spl0_384
| ~ spl0_43
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1401,f1310,f901,f6574]) ).
fof(f6574,plain,
( spl0_384
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f901,plain,
( spl0_43
<=> class_Ring__and__Field_Omult__zero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f1310,plain,
( spl0_123
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1401,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint)
| ~ spl0_43
| ~ spl0_123 ),
inference(resolution,[],[f1311,f903]) ).
fof(f903,plain,
( class_Ring__and__Field_Omult__zero(tc_Int_Oint)
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f901]) ).
fof(f1311,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) )
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f1310]) ).
fof(f6572,plain,
( spl0_383
| ~ spl0_15
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1400,f1310,f761,f6570]) ).
fof(f6570,plain,
( spl0_383
<=> ! [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_383])]) ).
fof(f761,plain,
( spl0_15
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f1400,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_15
| ~ spl0_123 ),
inference(resolution,[],[f1311,f763]) ).
fof(f763,plain,
( class_Ring__and__Field_Omult__zero(tc_nat)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f761]) ).
fof(f6568,plain,
( spl0_382
| ~ spl0_43
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1399,f1301,f901,f6566]) ).
fof(f6566,plain,
( spl0_382
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f1301,plain,
( spl0_121
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f1399,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| ~ spl0_43
| ~ spl0_121 ),
inference(resolution,[],[f1302,f903]) ).
fof(f1302,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f1301]) ).
fof(f6564,plain,
( spl0_381
| ~ spl0_15
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1398,f1301,f761,f6562]) ).
fof(f6562,plain,
( spl0_381
<=> ! [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_381])]) ).
fof(f1398,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_15
| ~ spl0_121 ),
inference(resolution,[],[f1302,f763]) ).
fof(f5784,plain,
( spl0_380
| ~ spl0_58
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1539,f1493,f976,f5782]) ).
fof(f5782,plain,
( spl0_380
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f976,plain,
( spl0_58
<=> ! [X2] : ~ c_HOL_Oord__class_Oless(X2,X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f1539,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ spl0_58
| ~ spl0_148 ),
inference(resolution,[],[f1494,f977]) ).
fof(f977,plain,
( ! [X2] : ~ c_HOL_Oord__class_Oless(X2,X2,tc_nat)
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f976]) ).
fof(f5780,plain,
( spl0_379
| ~ spl0_46
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f1298,f1257,f916,f5778]) ).
fof(f5778,plain,
( spl0_379
<=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f916,plain,
( spl0_46
<=> class_OrderedGroup_Ogroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f1257,plain,
( spl0_118
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f1298,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X0
| ~ spl0_46
| ~ spl0_118 ),
inference(resolution,[],[f1258,f918]) ).
fof(f918,plain,
( class_OrderedGroup_Ogroup__add(tc_Int_Oint)
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f916]) ).
fof(f1258,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 )
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f1257]) ).
fof(f5776,plain,
( spl0_378
| ~ spl0_42
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f1297,f1253,f896,f5774]) ).
fof(f5774,plain,
( spl0_378
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f896,plain,
( spl0_42
<=> class_OrderedGroup_Oab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f1253,plain,
( spl0_117
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f1297,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Int_Oint)
| ~ spl0_42
| ~ spl0_117 ),
inference(resolution,[],[f1254,f898]) ).
fof(f898,plain,
( class_OrderedGroup_Oab__group__add(tc_Int_Oint)
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f896]) ).
fof(f1254,plain,
( ! [X2,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X2,X2,X0) )
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f1253]) ).
fof(f5772,plain,
( spl0_377
| ~ spl0_34
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1271,f1216,f856,f5770]) ).
fof(f5770,plain,
( spl0_377
<=> ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f1216,plain,
( spl0_108
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f1271,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) = X0
| ~ spl0_34
| ~ spl0_108 ),
inference(resolution,[],[f1217,f858]) ).
fof(f1217,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 )
| ~ spl0_108 ),
inference(avatar_component_clause,[],[f1216]) ).
fof(f5625,plain,
( spl0_376
| ~ spl0_9
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1270,f1216,f731,f5623]) ).
fof(f5623,plain,
( spl0_376
<=> ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f1270,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
| ~ spl0_9
| ~ spl0_108 ),
inference(resolution,[],[f1217,f733]) ).
fof(f5621,plain,
( spl0_375
| ~ spl0_34
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1269,f1212,f856,f5619]) ).
fof(f5619,plain,
( spl0_375
<=> ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Int_Oint),X0,tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f1212,plain,
( spl0_107
<=> ! [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_107])]) ).
fof(f1269,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Int_Oint),X0,tc_Int_Oint) = X0
| ~ spl0_34
| ~ spl0_107 ),
inference(resolution,[],[f1213,f858]) ).
fof(f1213,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_107 ),
inference(avatar_component_clause,[],[f1212]) ).
fof(f5617,plain,
( spl0_374
| ~ spl0_9
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1268,f1212,f731,f5615]) ).
fof(f5615,plain,
( spl0_374
<=> ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f1268,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = X0
| ~ spl0_9
| ~ spl0_107 ),
inference(resolution,[],[f1213,f733]) ).
fof(f5613,plain,
( spl0_373
| ~ spl0_45
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f1265,f1204,f911,f5611]) ).
fof(f5611,plain,
( spl0_373
<=> ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f1204,plain,
( spl0_105
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1265,plain,
( ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_Int_Oint) = X0
| ~ spl0_45
| ~ spl0_105 ),
inference(resolution,[],[f1205,f913]) ).
fof(f1205,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X0) = X1 )
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f1204]) ).
fof(f5609,plain,
( spl0_372
| ~ spl0_17
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f1264,f1204,f771,f5607]) ).
fof(f5607,plain,
( spl0_372
<=> ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f1264,plain,
( ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
| ~ spl0_17
| ~ spl0_105 ),
inference(resolution,[],[f1205,f773]) ).
fof(f5572,plain,
( ~ spl0_370
| spl0_371
| ~ spl0_77
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f1997,f1915,f1069,f5570,f5566]) ).
fof(f5566,plain,
( spl0_370
<=> class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f5570,plain,
( spl0_371
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f1069,plain,
( spl0_77
<=> ! [X19] : ~ c_HOL_Oord__class_Oless(X19,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f1997,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) )
| ~ spl0_77
| ~ spl0_183 ),
inference(resolution,[],[f1916,f1070]) ).
fof(f1070,plain,
( ! [X19] : ~ c_HOL_Oord__class_Oless(X19,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f1069]) ).
fof(f5564,plain,
( ~ spl0_369
| spl0_368
| ~ spl0_103
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f1723,f1669,f1184,f5557,f5561]) ).
fof(f5561,plain,
( spl0_369
<=> class_OrderedGroup_Ogroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f1669,plain,
( spl0_168
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f1723,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_OrderedGroup_Ogroup__add(tc_nat) )
| ~ spl0_103
| ~ spl0_168 ),
inference(trivial_inequality_removal,[],[f1722]) ).
fof(f1722,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_OrderedGroup_Ogroup__add(tc_nat) )
| ~ spl0_103
| ~ spl0_168 ),
inference(superposition,[],[f1670,f1185]) ).
fof(f1670,plain,
( ! [X3,X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X3,X0)
| X1 = X3
| ~ class_OrderedGroup_Ogroup__add(X0) )
| ~ spl0_168 ),
inference(avatar_component_clause,[],[f1669]) ).
fof(f5559,plain,
( ~ spl0_367
| spl0_368
| ~ spl0_103
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f1714,f1665,f1184,f5557,f5553]) ).
fof(f5553,plain,
( spl0_367
<=> class_OrderedGroup_Oab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f1665,plain,
( spl0_167
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f1714,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_103
| ~ spl0_167 ),
inference(trivial_inequality_removal,[],[f1713]) ).
fof(f1713,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_103
| ~ spl0_167 ),
inference(superposition,[],[f1666,f1185]) ).
fof(f1666,plain,
( ! [X3,X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X3,X0)
| X1 = X3
| ~ class_OrderedGroup_Oab__group__add(X0) )
| ~ spl0_167 ),
inference(avatar_component_clause,[],[f1665]) ).
fof(f5551,plain,
( spl0_366
| ~ spl0_84
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1436,f1359,f1102,f5549]) ).
fof(f5549,plain,
( spl0_366
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f1102,plain,
( spl0_84
<=> ! [X2,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f1436,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_84
| ~ spl0_135 ),
inference(duplicate_literal_removal,[],[f1432]) ).
fof(f1432,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_84
| ~ spl0_135 ),
inference(resolution,[],[f1360,f1103]) ).
fof(f1103,plain,
( ! [X2,X0] :
( ~ c_HOL_Oord__class_Oless(X2,X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_84 ),
inference(avatar_component_clause,[],[f1102]) ).
fof(f5536,plain,
( spl0_365
| ~ spl0_1
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f4737,f4684,f691,f5534]) ).
fof(f5534,plain,
( spl0_365
<=> ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(t_a) = X0
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X0,t_a),X2,t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X2,t_a),c_Power_Opower__class_Opower(X0,X2,t_a),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f4684,plain,
( spl0_336
<=> ! [X3,X0,X9,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X3,X0),X9,X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X3,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f4737,plain,
( ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(t_a) = X0
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X0,t_a),X2,t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X2,t_a),c_Power_Opower__class_Opower(X0,X2,t_a),t_a) )
| ~ spl0_1
| ~ spl0_336 ),
inference(resolution,[],[f4685,f693]) ).
fof(f4685,plain,
( ! [X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X3,X0),X9,X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X3,X9,X0),X0) )
| ~ spl0_336 ),
inference(avatar_component_clause,[],[f4684]) ).
fof(f5499,plain,
( spl0_364
| ~ spl0_1
| ~ spl0_282 ),
inference(avatar_split_clause,[],[f3379,f3006,f691,f5497]) ).
fof(f3006,plain,
( spl0_282
<=> ! [X13,X0,X3,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X3,X0),X13,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X13,X0),c_HOL_Oinverse__class_Odivide(X3,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f3379,plain,
( ! [X2,X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X0,X1,t_a),X2,t_a) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X0,X2,t_a),c_HOL_Oinverse__class_Odivide(X1,X2,t_a),t_a)
| ~ spl0_1
| ~ spl0_282 ),
inference(resolution,[],[f3007,f693]) ).
fof(f3007,plain,
( ! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X3,X0),X13,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X13,X0),c_HOL_Oinverse__class_Odivide(X3,X13,X0),X0) )
| ~ spl0_282 ),
inference(avatar_component_clause,[],[f3006]) ).
fof(f5481,plain,
( spl0_363
| ~ spl0_1
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f2300,f2245,f691,f5479]) ).
fof(f2245,plain,
( spl0_202
<=> ! [X13,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X13
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X13,X0),X13,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f2300,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(t_a) = X0
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X0,t_a),X0,t_a) = X1 )
| ~ spl0_1
| ~ spl0_202 ),
inference(resolution,[],[f2246,f693]) ).
fof(f2246,plain,
( ! [X0,X1,X13] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X13
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X13,X0),X13,X0) = X1 )
| ~ spl0_202 ),
inference(avatar_component_clause,[],[f2245]) ).
fof(f5207,plain,
( spl0_362
| ~ spl0_1
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1775,f1729,f691,f5205]) ).
fof(f5205,plain,
( spl0_362
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(t_a) = X0
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Oinverse__class_Odivide(X0,X0,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f1729,plain,
( spl0_171
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f1775,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(t_a) = X0
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Oinverse__class_Odivide(X0,X0,t_a) )
| ~ spl0_1
| ~ spl0_171 ),
inference(resolution,[],[f1730,f693]) ).
fof(f1730,plain,
( ! [X2,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X2,X2,X0) )
| ~ spl0_171 ),
inference(avatar_component_clause,[],[f1729]) ).
fof(f5203,plain,
( spl0_361
| ~ spl0_1
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1774,f1725,f691,f5201]) ).
fof(f1725,plain,
( spl0_170
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X1,X3,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f1774,plain,
( ! [X0,X1] : c_HOL_Oinverse__class_Odivide(X0,X1,t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X1,t_a),t_a)
| ~ spl0_1
| ~ spl0_170 ),
inference(resolution,[],[f1726,f693]) ).
fof(f1726,plain,
( ! [X3,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X1,X3,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X3,X0),X0) )
| ~ spl0_170 ),
inference(avatar_component_clause,[],[f1725]) ).
fof(f5192,plain,
( spl0_360
| ~ spl0_1
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f1564,f1501,f691,f5190]) ).
fof(f1501,plain,
( spl0_150
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Oinverse(X1,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f1564,plain,
( ! [X0] : c_HOL_Oinverse__class_Oinverse(X0,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),X0,t_a)
| ~ spl0_1
| ~ spl0_150 ),
inference(resolution,[],[f1502,f693]) ).
fof(f1502,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Oinverse(X1,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0) )
| ~ spl0_150 ),
inference(avatar_component_clause,[],[f1501]) ).
fof(f5187,plain,
spl0_359,
inference(avatar_split_clause,[],[f177,f5185]) ).
fof(f177,axiom,
! [X2,X0,X11,X4,X12] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X11
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X2,X4,X0),c_HOL_Oinverse__class_Odivide(X12,X11,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X11,X0),c_HOL_Otimes__class_Otimes(X12,X4,X0),X0),c_HOL_Otimes__class_Otimes(X4,X11,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__frac__eq_0) ).
fof(f5182,plain,
spl0_358,
inference(avatar_split_clause,[],[f181,f5180]) ).
fof(f5180,plain,
( spl0_358
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ominus__class_Ominus(X3,X1,X0),X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f181,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ominus__class_Ominus(X3,X1,X0),X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_division__ring__inverse__diff_0) ).
fof(f5124,plain,
( spl0_357
| ~ spl0_132
| ~ spl0_146 ),
inference(avatar_split_clause,[],[f2549,f1468,f1346,f5122]) ).
fof(f5122,plain,
( spl0_357
<=> ! [X0] : c_HOL_Oone__class_Oone(t_a) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f1468,plain,
( spl0_146
<=> class_OrderedGroup_Omonoid__mult(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f2549,plain,
( ! [X0] : c_HOL_Oone__class_Oone(t_a) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X0,t_a)
| ~ spl0_132
| ~ spl0_146 ),
inference(resolution,[],[f1470,f1347]) ).
fof(f1470,plain,
( class_OrderedGroup_Omonoid__mult(t_a)
| ~ spl0_146 ),
inference(avatar_component_clause,[],[f1468]) ).
fof(f4985,plain,
spl0_356,
inference(avatar_split_clause,[],[f110,f4983]) ).
fof(f4983,plain,
( spl0_356
<=> ! [X0,X14,X13,X3,X1] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(X13,X14,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f110,axiom,
! [X3,X0,X1,X14,X13] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(X13,X14,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
fof(f4981,plain,
spl0_355,
inference(avatar_split_clause,[],[f109,f4979]) ).
fof(f4979,plain,
( spl0_355
<=> ! [X0,X14,X13,X3,X1] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(X13,X14,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f109,axiom,
! [X3,X0,X1,X14,X13] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(X13,X14,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_0) ).
fof(f4977,plain,
spl0_354,
inference(avatar_split_clause,[],[f32,f4975]) ).
fof(f32,axiom,
! [X3,X0,X1,X14,X13] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).
fof(f4973,plain,
spl0_353,
inference(avatar_split_clause,[],[f27,f4971]) ).
fof(f27,axiom,
! [X3,X0,X1,X14,X13] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).
fof(f4969,plain,
spl0_352,
inference(avatar_split_clause,[],[f26,f4967]) ).
fof(f26,axiom,
! [X3,X0,X1,X14,X13] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).
fof(f4965,plain,
spl0_351,
inference(avatar_split_clause,[],[f25,f4963]) ).
fof(f25,axiom,
! [X3,X0,X1,X14,X13] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(X13,X14,X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).
fof(f4961,plain,
( spl0_350
| ~ spl0_93
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1935,f1338,f1140,f4959]) ).
fof(f1935,plain,
( ! [X0] : c_HOL_Oone__class_Oone(t_a) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),t_a)
| ~ spl0_93
| ~ spl0_130 ),
inference(resolution,[],[f1142,f1339]) ).
fof(f4951,plain,
spl0_349,
inference(avatar_split_clause,[],[f515,f4949]) ).
fof(f4949,plain,
( spl0_349
<=> ! [X3,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X1 = X3
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_Power_Opower__class_Opower(X1,X9,X0) != c_Power_Opower__class_Opower(X3,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f515,axiom,
! [X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X1 = X3
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_Power_Opower__class_Opower(X1,X9,X0) != c_Power_Opower__class_Opower(X3,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).
fof(f4857,plain,
spl0_348,
inference(avatar_split_clause,[],[f603,f4855]) ).
fof(f603,axiom,
! [X0,X1,X19,X9] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ c_lessequals(X9,X19,tc_nat)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(X19,X9,tc_nat),X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X19,X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__diff_0) ).
fof(f4853,plain,
spl0_347,
inference(avatar_split_clause,[],[f132,f4851]) ).
fof(f132,axiom,
! [X3,X0,X1,X20] :
( ~ class_Ring__and__Field_Oring(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X3,X0),c_Int_Onumber__class_Onumber__of(X20,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X20,X0),X0),c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X20,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__diff__distrib__number__of_0) ).
fof(f4849,plain,
spl0_346,
inference(avatar_split_clause,[],[f131,f4847]) ).
fof(f131,axiom,
! [X3,X0,X13,X20] :
( ~ class_Ring__and__Field_Oring(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X20,X0),c_HOL_Ominus__class_Ominus(X3,X13,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X20,X0),X3,X0),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X20,X0),X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__diff__distrib__number__of_0) ).
fof(f4845,plain,
( spl0_345
| ~ spl0_79
| ~ spl0_126 ),
inference(avatar_split_clause,[],[f1761,f1322,f1077,f4843]) ).
fof(f4843,plain,
( spl0_345
<=> ! [X0] : c_HOL_Ozero__class_Ozero(t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(t_a),X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f1077,plain,
( spl0_79
<=> class_Ring__and__Field_Oring__no__zero__divisors(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f1322,plain,
( spl0_126
<=> ! [X0,X3] :
( ~ 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),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1761,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(t_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(t_a),X0,t_a)
| ~ spl0_79
| ~ spl0_126 ),
inference(resolution,[],[f1079,f1323]) ).
fof(f1323,plain,
( ! [X3,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),X3,X0) )
| ~ spl0_126 ),
inference(avatar_component_clause,[],[f1322]) ).
fof(f1079,plain,
( class_Ring__and__Field_Oring__no__zero__divisors(t_a)
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f1077]) ).
fof(f4841,plain,
spl0_344,
inference(avatar_split_clause,[],[f129,f4839]) ).
fof(f4839,plain,
( spl0_344
<=> ! [X4,X11,X0,X12,X2] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X11
| c_HOL_Otimes__class_Otimes(X2,X11,X0) != c_HOL_Otimes__class_Otimes(X12,X4,X0)
| c_HOL_Oinverse__class_Odivide(X2,X4,X0) = c_HOL_Oinverse__class_Odivide(X12,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f129,axiom,
! [X2,X0,X11,X4,X12] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X11
| c_HOL_Otimes__class_Otimes(X2,X11,X0) != c_HOL_Otimes__class_Otimes(X12,X4,X0)
| c_HOL_Oinverse__class_Odivide(X2,X4,X0) = c_HOL_Oinverse__class_Odivide(X12,X11,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).
fof(f4837,plain,
spl0_343,
inference(avatar_split_clause,[],[f128,f4835]) ).
fof(f4835,plain,
( spl0_343
<=> ! [X4,X11,X0,X12,X2] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X11
| c_HOL_Oinverse__class_Odivide(X2,X4,X0) != c_HOL_Oinverse__class_Odivide(X12,X11,X0)
| c_HOL_Otimes__class_Otimes(X2,X11,X0) = c_HOL_Otimes__class_Otimes(X12,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f128,axiom,
! [X2,X0,X11,X4,X12] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X11
| c_HOL_Oinverse__class_Odivide(X2,X4,X0) != c_HOL_Oinverse__class_Odivide(X12,X11,X0)
| c_HOL_Otimes__class_Otimes(X2,X11,X0) = c_HOL_Otimes__class_Otimes(X12,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).
fof(f4773,plain,
spl0_342,
inference(avatar_split_clause,[],[f516,f4771]) ).
fof(f516,axiom,
! [X0,X1,X9,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X9,X24,tc_nat)
| ~ c_lessequals(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X24,X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__decreasing_0) ).
fof(f4769,plain,
spl0_341,
inference(avatar_split_clause,[],[f489,f4767]) ).
fof(f489,axiom,
! [X0,X1,X9,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X9,X24,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X24,X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).
fof(f4765,plain,
spl0_340,
inference(avatar_split_clause,[],[f241,f4763]) ).
fof(f241,axiom,
! [X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X3,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
fof(f4749,plain,
( spl0_339
| ~ spl0_79
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1760,f1326,f1077,f4747]) ).
fof(f4747,plain,
( spl0_339
<=> ! [X0] : c_HOL_Ozero__class_Ozero(t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f1326,plain,
( spl0_127
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f1760,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(t_a) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(t_a),t_a)
| ~ spl0_79
| ~ spl0_127 ),
inference(resolution,[],[f1079,f1327]) ).
fof(f1327,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f1326]) ).
fof(f4745,plain,
spl0_338,
inference(avatar_split_clause,[],[f237,f4743]) ).
fof(f237,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X9,X0),X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).
fof(f4741,plain,
spl0_337,
inference(avatar_split_clause,[],[f134,f4739]) ).
fof(f4739,plain,
( spl0_337
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X3,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f134,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X3,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__mult__distrib_0) ).
fof(f4686,plain,
spl0_336,
inference(avatar_split_clause,[],[f528,f4684]) ).
fof(f528,axiom,
! [X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X3,X0),X9,X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X3,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).
fof(f4682,plain,
spl0_335,
inference(avatar_split_clause,[],[f140,f4680]) ).
fof(f140,axiom,
! [X2,X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).
fof(f4678,plain,
spl0_334,
inference(avatar_split_clause,[],[f139,f4676]) ).
fof(f139,axiom,
! [X2,X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).
fof(f4592,plain,
spl0_333,
inference(avatar_split_clause,[],[f609,f4590]) ).
fof(f609,axiom,
! [X19,X9,X23] :
( ~ c_lessequals(X23,X19,tc_nat)
| ~ c_lessequals(X23,X9,tc_nat)
| c_HOL_Ominus__class_Ominus(X19,X9,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X19,X23,tc_nat),c_HOL_Ominus__class_Ominus(X9,X23,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).
fof(f4588,plain,
spl0_332,
inference(avatar_split_clause,[],[f48,f4586]) ).
fof(f48,axiom,
! [X0,X18,X16,X17,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X15,X16,X0),c_HOL_Otimes__class_Otimes(X17,X18,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X15,X17,X0),c_HOL_Otimes__class_Otimes(X16,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
fof(f4443,plain,
spl0_331,
inference(avatar_split_clause,[],[f589,f4441]) ).
fof(f589,axiom,
! [X19,X9,X23] :
( ~ c_lessequals(X23,X19,tc_nat)
| ~ c_lessequals(X23,X9,tc_nat)
| c_lessequals(X19,X9,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X19,X23,tc_nat),c_HOL_Ominus__class_Ominus(X9,X23,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).
fof(f4439,plain,
spl0_330,
inference(avatar_split_clause,[],[f412,f4437]) ).
fof(f412,axiom,
! [X2,X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X9
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_Power_Opower__class_Opower(X2,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_4) ).
fof(f4435,plain,
( spl0_329
| ~ spl0_1
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1487,f1395,f691,f4433]) ).
fof(f1395,plain,
( spl0_144
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1487,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(t_a),X0,t_a)
| ~ spl0_1
| ~ spl0_144 ),
inference(resolution,[],[f1396,f693]) ).
fof(f1396,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X1,X0) )
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f1395]) ).
fof(f4431,plain,
spl0_328,
inference(avatar_split_clause,[],[f368,f4429]) ).
fof(f4429,plain,
( spl0_328
<=> ! [X9,X23,X19] :
( ~ c_lessequals(X23,X19,tc_nat)
| ~ c_lessequals(X23,X9,tc_nat)
| c_HOL_Oord__class_Oless(X19,X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X19,X23,tc_nat),c_HOL_Ominus__class_Ominus(X9,X23,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f368,axiom,
! [X19,X9,X23] :
( ~ c_lessequals(X23,X19,tc_nat)
| ~ c_lessequals(X23,X9,tc_nat)
| c_HOL_Oord__class_Oless(X19,X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X19,X23,tc_nat),c_HOL_Ominus__class_Ominus(X9,X23,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).
fof(f4427,plain,
spl0_327,
inference(avatar_split_clause,[],[f256,f4425]) ).
fof(f256,axiom,
! [X2,X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X9
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_0) ).
fof(f4423,plain,
spl0_326,
inference(avatar_split_clause,[],[f83,f4421]) ).
fof(f83,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
fof(f4419,plain,
spl0_325,
inference(avatar_split_clause,[],[f82,f4417]) ).
fof(f82,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
fof(f3606,plain,
spl0_324,
inference(avatar_split_clause,[],[f593,f3604]) ).
fof(f593,axiom,
! [X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X3,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono_0) ).
fof(f3602,plain,
spl0_323,
inference(avatar_split_clause,[],[f503,f3600]) ).
fof(f503,axiom,
! [X2,X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X2,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X2,X0),c_Power_Opower__class_Opower(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).
fof(f3598,plain,
spl0_322,
inference(avatar_split_clause,[],[f502,f3596]) ).
fof(f502,axiom,
! [X0,X1,X9,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X9,X24,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X1,X24,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).
fof(f3594,plain,
spl0_321,
inference(avatar_split_clause,[],[f410,f3592]) ).
fof(f410,axiom,
! [X0,X1,X9,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X9,X24,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X1,X24,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing_0) ).
fof(f3590,plain,
spl0_320,
inference(avatar_split_clause,[],[f403,f3588]) ).
fof(f403,axiom,
! [X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X9
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_2) ).
fof(f3586,plain,
spl0_319,
inference(avatar_split_clause,[],[f379,f3584]) ).
fof(f379,axiom,
! [X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X3,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
fof(f3582,plain,
spl0_318,
inference(avatar_split_clause,[],[f251,f3580]) ).
fof(f251,axiom,
! [X2,X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X2,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0)
| c_lessequals(c_Power_Opower__class_Opower(X3,X2,X0),c_Power_Opower__class_Opower(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing__iff_1) ).
fof(f3578,plain,
spl0_317,
inference(avatar_split_clause,[],[f249,f3576]) ).
fof(f249,axiom,
! [X0,X1,X19,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(X19,X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X19,X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__imp__le__exp_0) ).
fof(f3574,plain,
spl0_316,
inference(avatar_split_clause,[],[f138,f3572]) ).
fof(f138,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
fof(f3570,plain,
spl0_315,
inference(avatar_split_clause,[],[f97,f3568]) ).
fof(f97,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_lessequals(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
fof(f3529,plain,
spl0_314,
inference(avatar_split_clause,[],[f96,f3527]) ).
fof(f96,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_lessequals(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
fof(f3525,plain,
spl0_313,
inference(avatar_split_clause,[],[f95,f3523]) ).
fof(f95,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
fof(f3521,plain,
spl0_312,
inference(avatar_split_clause,[],[f94,f3519]) ).
fof(f94,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
fof(f3517,plain,
spl0_311,
inference(avatar_split_clause,[],[f93,f3515]) ).
fof(f93,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Omult__mono1(X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
fof(f3513,plain,
spl0_310,
inference(avatar_split_clause,[],[f88,f3511]) ).
fof(f88,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
fof(f3509,plain,
spl0_309,
inference(avatar_split_clause,[],[f87,f3507]) ).
fof(f87,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
fof(f3505,plain,
spl0_308,
inference(avatar_split_clause,[],[f86,f3503]) ).
fof(f86,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
fof(f3501,plain,
spl0_307,
inference(avatar_split_clause,[],[f85,f3499]) ).
fof(f85,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
fof(f3497,plain,
spl0_306,
inference(avatar_split_clause,[],[f74,f3495]) ).
fof(f74,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
fof(f3493,plain,
spl0_305,
inference(avatar_split_clause,[],[f72,f3491]) ).
fof(f72,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
fof(f3461,plain,
spl0_304,
inference(avatar_split_clause,[],[f71,f3459]) ).
fof(f71,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
fof(f3457,plain,
spl0_303,
inference(avatar_split_clause,[],[f70,f3455]) ).
fof(f70,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
fof(f3453,plain,
spl0_302,
inference(avatar_split_clause,[],[f68,f3451]) ).
fof(f68,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
fof(f3449,plain,
spl0_301,
inference(avatar_split_clause,[],[f67,f3447]) ).
fof(f67,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
fof(f3445,plain,
spl0_300,
inference(avatar_split_clause,[],[f66,f3443]) ).
fof(f66,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).
fof(f3441,plain,
spl0_299,
inference(avatar_split_clause,[],[f64,f3439]) ).
fof(f64,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
fof(f3437,plain,
spl0_298,
inference(avatar_split_clause,[],[f62,f3435]) ).
fof(f62,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
fof(f3433,plain,
spl0_297,
inference(avatar_split_clause,[],[f37,f3431]) ).
fof(f37,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
fof(f3429,plain,
spl0_296,
inference(avatar_split_clause,[],[f36,f3427]) ).
fof(f36,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
fof(f3425,plain,
spl0_295,
inference(avatar_split_clause,[],[f35,f3423]) ).
fof(f35,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
fof(f3421,plain,
( spl0_294
| ~ spl0_118
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f2585,f1517,f1257,f3419]) ).
fof(f3419,plain,
( spl0_294
<=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(t_a),t_a) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f1517,plain,
( spl0_154
<=> class_OrderedGroup_Ogroup__add(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f2585,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(t_a),t_a) = X0
| ~ spl0_118
| ~ spl0_154 ),
inference(resolution,[],[f1519,f1258]) ).
fof(f1519,plain,
( class_OrderedGroup_Ogroup__add(t_a)
| ~ spl0_154 ),
inference(avatar_component_clause,[],[f1517]) ).
fof(f3417,plain,
spl0_293,
inference(avatar_split_clause,[],[f34,f3415]) ).
fof(f34,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
fof(f3413,plain,
spl0_292,
inference(avatar_split_clause,[],[f33,f3411]) ).
fof(f33,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
fof(f3409,plain,
spl0_291,
inference(avatar_split_clause,[],[f31,f3407]) ).
fof(f31,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
fof(f3405,plain,
spl0_290,
inference(avatar_split_clause,[],[f30,f3403]) ).
fof(f30,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
fof(f3401,plain,
spl0_289,
inference(avatar_split_clause,[],[f29,f3399]) ).
fof(f29,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
fof(f3397,plain,
spl0_288,
inference(avatar_split_clause,[],[f28,f3395]) ).
fof(f28,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
fof(f3373,plain,
( spl0_287
| ~ spl0_117
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f2370,f1350,f1253,f3371]) ).
fof(f1350,plain,
( spl0_133
<=> class_OrderedGroup_Oab__group__add(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f2370,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(t_a) = c_HOL_Ominus__class_Ominus(X0,X0,t_a)
| ~ spl0_117
| ~ spl0_133 ),
inference(resolution,[],[f1352,f1254]) ).
fof(f1352,plain,
( class_OrderedGroup_Oab__group__add(t_a)
| ~ spl0_133 ),
inference(avatar_component_clause,[],[f1350]) ).
fof(f3211,plain,
( spl0_286
| ~ spl0_112
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f2160,f1240,f1232,f3208]) ).
fof(f1232,plain,
( spl0_112
<=> ! [X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f2160,plain,
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a)
| ~ spl0_112
| ~ spl0_114 ),
inference(resolution,[],[f1242,f1233]) ).
fof(f1233,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) )
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f1232]) ).
fof(f3090,plain,
( spl0_285
| ~ spl0_93
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1932,f1216,f1140,f3088]) ).
fof(f1932,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(t_a),t_a) = X0
| ~ spl0_93
| ~ spl0_108 ),
inference(resolution,[],[f1142,f1217]) ).
fof(f3016,plain,
spl0_284,
inference(avatar_split_clause,[],[f594,f3014]) ).
fof(f594,axiom,
! [X19,X9,X23] :
( X9 = X19
| ~ c_lessequals(X23,X19,tc_nat)
| ~ c_lessequals(X23,X9,tc_nat)
| c_HOL_Ominus__class_Ominus(X19,X23,tc_nat) != c_HOL_Ominus__class_Ominus(X9,X23,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).
fof(f3012,plain,
( spl0_283
| ~ spl0_93
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1931,f1212,f1140,f3010]) ).
fof(f1931,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),X0,t_a) = X0
| ~ spl0_93
| ~ spl0_107 ),
inference(resolution,[],[f1142,f1213]) ).
fof(f3008,plain,
spl0_282,
inference(avatar_split_clause,[],[f572,f3006]) ).
fof(f572,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X3,X0),X13,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X13,X0),c_HOL_Oinverse__class_Odivide(X3,X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).
fof(f3004,plain,
spl0_281,
inference(avatar_split_clause,[],[f561,f3002]) ).
fof(f3002,plain,
( spl0_281
<=> ! [X9,X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X9
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f561,axiom,
! [X0,X9] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X9
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
fof(f3000,plain,
spl0_280,
inference(avatar_split_clause,[],[f557,f2998]) ).
fof(f2998,plain,
( spl0_280
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| X1 = X3
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oinverse__class_Oinverse(X1,X0) != c_HOL_Oinverse__class_Oinverse(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f557,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| X1 = X3
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oinverse__class_Oinverse(X1,X0) != c_HOL_Oinverse__class_Oinverse(X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).
fof(f2996,plain,
spl0_279,
inference(avatar_split_clause,[],[f475,f2994]) ).
fof(f475,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__power_0) ).
fof(f2992,plain,
spl0_278,
inference(avatar_split_clause,[],[f175,f2990]) ).
fof(f175,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X9,X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X9,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).
fof(f2988,plain,
spl0_277,
inference(avatar_split_clause,[],[f118,f2986]) ).
fof(f118,axiom,
! [X0,X19,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X19,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X19,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
fof(f2984,plain,
spl0_276,
inference(avatar_split_clause,[],[f116,f2982]) ).
fof(f116,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).
fof(f2980,plain,
spl0_275,
inference(avatar_split_clause,[],[f113,f2978]) ).
fof(f113,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).
fof(f2976,plain,
spl0_274,
inference(avatar_split_clause,[],[f112,f2974]) ).
fof(f112,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
fof(f2972,plain,
spl0_273,
inference(avatar_split_clause,[],[f111,f2970]) ).
fof(f111,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
fof(f2968,plain,
( spl0_272
| ~ spl0_93
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f1930,f1208,f1140,f2966]) ).
fof(f2966,plain,
( spl0_272
<=> ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),t_a) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f1208,plain,
( spl0_106
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(X2,c_HOL_Oone__class_Oone(tc_nat),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1930,plain,
( ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),t_a) = X0
| ~ spl0_93
| ~ spl0_106 ),
inference(resolution,[],[f1142,f1209]) ).
fof(f1209,plain,
( ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(X2,c_HOL_Oone__class_Oone(tc_nat),X0) = X2 )
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f1208]) ).
fof(f2964,plain,
spl0_271,
inference(avatar_split_clause,[],[f108,f2962]) ).
fof(f2962,plain,
( spl0_271
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f108,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
fof(f2960,plain,
spl0_270,
inference(avatar_split_clause,[],[f107,f2958]) ).
fof(f2958,plain,
( spl0_270
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f107,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
fof(f2956,plain,
spl0_269,
inference(avatar_split_clause,[],[f106,f2954]) ).
fof(f2954,plain,
( spl0_269
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f106,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
fof(f2952,plain,
spl0_268,
inference(avatar_split_clause,[],[f105,f2950]) ).
fof(f105,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
fof(f2948,plain,
spl0_267,
inference(avatar_split_clause,[],[f104,f2946]) ).
fof(f104,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
fof(f2944,plain,
spl0_266,
inference(avatar_split_clause,[],[f103,f2942]) ).
fof(f103,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).
fof(f2940,plain,
spl0_265,
inference(avatar_split_clause,[],[f102,f2938]) ).
fof(f102,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
fof(f2936,plain,
spl0_264,
inference(avatar_split_clause,[],[f100,f2934]) ).
fof(f100,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).
fof(f2932,plain,
spl0_263,
inference(avatar_split_clause,[],[f98,f2930]) ).
fof(f98,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).
fof(f2928,plain,
spl0_262,
inference(avatar_split_clause,[],[f92,f2926]) ).
fof(f2926,plain,
( spl0_262
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f92,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
fof(f2923,plain,
spl0_261,
inference(avatar_split_clause,[],[f91,f2921]) ).
fof(f2921,plain,
( spl0_261
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f91,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
fof(f2919,plain,
spl0_260,
inference(avatar_split_clause,[],[f90,f2917]) ).
fof(f2917,plain,
( spl0_260
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f90,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
fof(f2915,plain,
spl0_259,
inference(avatar_split_clause,[],[f89,f2913]) ).
fof(f2913,plain,
( spl0_259
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f89,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
fof(f2911,plain,
spl0_258,
inference(avatar_split_clause,[],[f80,f2909]) ).
fof(f80,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
fof(f2907,plain,
spl0_257,
inference(avatar_split_clause,[],[f79,f2905]) ).
fof(f79,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).
fof(f2903,plain,
spl0_256,
inference(avatar_split_clause,[],[f78,f2901]) ).
fof(f78,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
fof(f2899,plain,
spl0_255,
inference(avatar_split_clause,[],[f77,f2897]) ).
fof(f77,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
fof(f2895,plain,
spl0_254,
inference(avatar_split_clause,[],[f76,f2893]) ).
fof(f76,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
fof(f2891,plain,
spl0_253,
inference(avatar_split_clause,[],[f75,f2889]) ).
fof(f75,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
fof(f2887,plain,
spl0_252,
inference(avatar_split_clause,[],[f61,f2885]) ).
fof(f61,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X13,X0),c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
fof(f2883,plain,
( spl0_251
| ~ spl0_1
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1283,f1236,f691,f2881]) ).
fof(f1236,plain,
( spl0_113
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f1283,plain,
( ! [X0] : c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(t_a),t_a) = X0
| ~ spl0_1
| ~ spl0_113 ),
inference(resolution,[],[f1237,f693]) ).
fof(f1237,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 )
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f1236]) ).
fof(f2879,plain,
spl0_250,
inference(avatar_split_clause,[],[f60,f2877]) ).
fof(f60,axiom,
! [X3,X0,X1,X13] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X1,X0),c_HOL_Otimes__class_Otimes(X13,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
fof(f2875,plain,
spl0_249,
inference(avatar_split_clause,[],[f21,f2873]) ).
fof(f2873,plain,
( spl0_249
<=> ! [X4,X0,X10,X2] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X4,X0),X10,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X10,X0),c_Power_Opower__class_Opower(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f21,axiom,
! [X2,X10,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X4,X0),X10,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X10,X0),c_Power_Opower__class_Opower(X4,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
fof(f2871,plain,
spl0_248,
inference(avatar_split_clause,[],[f20,f2869]) ).
fof(f20,axiom,
! [X3,X0,X1,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X3,X0),X9,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X3,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
fof(f2819,plain,
spl0_247,
inference(avatar_split_clause,[],[f597,f2817]) ).
fof(f597,axiom,
! [X2,X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_3) ).
fof(f2815,plain,
spl0_246,
inference(avatar_split_clause,[],[f563,f2813]) ).
fof(f2813,plain,
( spl0_246
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f563,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
fof(f2811,plain,
spl0_245,
inference(avatar_split_clause,[],[f554,f2809]) ).
fof(f2809,plain,
( spl0_245
<=> ! [X2,X4,X0,X25,X26] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X26,X25,X0)
| c_lessequals(X4,X2,X0)
| c_HOL_Ominus__class_Ominus(X2,X4,X0) != c_HOL_Ominus__class_Ominus(X25,X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f554,axiom,
! [X2,X0,X26,X4,X25] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X26,X25,X0)
| c_lessequals(X4,X2,X0)
| c_HOL_Ominus__class_Ominus(X2,X4,X0) != c_HOL_Ominus__class_Ominus(X25,X26,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).
fof(f2807,plain,
spl0_244,
inference(avatar_split_clause,[],[f536,f2805]) ).
fof(f536,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X9,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__power__inverse_0) ).
fof(f2803,plain,
spl0_243,
inference(avatar_split_clause,[],[f497,f2801]) ).
fof(f2801,plain,
( spl0_243
<=> ! [X19,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X9 = X19
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_Power_Opower__class_Opower(X1,X9,X0) != c_Power_Opower__class_Opower(X1,X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f497,axiom,
! [X0,X1,X19,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X9 = X19
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_Power_Opower__class_Opower(X1,X9,X0) != c_Power_Opower__class_Opower(X1,X19,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
fof(f2799,plain,
spl0_242,
inference(avatar_split_clause,[],[f423,f2797]) ).
fof(f2797,plain,
( spl0_242
<=> ! [X4,X0,X25,X2,X26] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0)
| c_HOL_Oord__class_Oless(X25,X26,X0)
| c_HOL_Ominus__class_Ominus(X2,X4,X0) != c_HOL_Ominus__class_Ominus(X25,X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f423,axiom,
! [X2,X0,X26,X4,X25] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0)
| c_HOL_Oord__class_Oless(X25,X26,X0)
| c_HOL_Ominus__class_Ominus(X2,X4,X0) != c_HOL_Ominus__class_Ominus(X25,X26,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).
fof(f2795,plain,
spl0_241,
inference(avatar_split_clause,[],[f345,f2793]) ).
fof(f345,axiom,
! [X2,X0,X9,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_lessequals(X2,X4,X0)
| c_lessequals(c_Power_Opower__class_Opower(X2,X9,X0),c_Power_Opower__class_Opower(X4,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono__odd_0) ).
fof(f2658,plain,
spl0_240,
inference(avatar_split_clause,[],[f514,f2656]) ).
fof(f514,axiom,
! [X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X9
| c_lessequals(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_5) ).
fof(f2654,plain,
spl0_239,
inference(avatar_split_clause,[],[f446,f2652]) ).
fof(f446,axiom,
! [X2,X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_5) ).
fof(f2650,plain,
spl0_238,
inference(avatar_split_clause,[],[f445,f2648]) ).
fof(f445,axiom,
! [X2,X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__zero__eq_2) ).
fof(f2646,plain,
spl0_237,
inference(avatar_split_clause,[],[f376,f2644]) ).
fof(f376,axiom,
! [X2,X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_2) ).
fof(f2642,plain,
spl0_236,
inference(avatar_split_clause,[],[f375,f2640]) ).
fof(f2640,plain,
( spl0_236
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f375,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power__iff_0) ).
fof(f2638,plain,
spl0_235,
inference(avatar_split_clause,[],[f370,f2636]) ).
fof(f370,axiom,
! [X3,X1,X13] :
( ~ c_lessequals(X13,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X13,tc_nat),c_HOL_Ominus__class_Ominus(X3,X13,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).
fof(f2634,plain,
spl0_234,
inference(avatar_split_clause,[],[f279,f2632]) ).
fof(f279,axiom,
! [X21,X19,X9] :
( ~ c_HOL_Oord__class_Oless(X19,X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(X19,X21,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X21,X9,tc_nat),c_HOL_Ominus__class_Ominus(X21,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
fof(f2630,plain,
spl0_233,
inference(avatar_split_clause,[],[f259,f2628]) ).
fof(f259,axiom,
! [X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X9
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_1) ).
fof(f2626,plain,
spl0_232,
inference(avatar_split_clause,[],[f176,f2624]) ).
fof(f176,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X9,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).
fof(f2568,plain,
spl0_231,
inference(avatar_split_clause,[],[f566,f2566]) ).
fof(f566,axiom,
! [X19,X9] :
( X9 = X19
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X19,X9,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X9,X19,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
fof(f2564,plain,
spl0_230,
inference(avatar_split_clause,[],[f447,f2562]) ).
fof(f2562,plain,
( spl0_230
<=> ! [X9,X0,X2] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f447,axiom,
! [X2,X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_4) ).
fof(f2560,plain,
spl0_229,
inference(avatar_split_clause,[],[f378,f2558]) ).
fof(f2558,plain,
( spl0_229
<=> ! [X9,X0,X2] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Ozero__class_Ozero(X0) = X2
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f378,axiom,
! [X2,X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Ozero__class_Ozero(X0) = X2
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_1) ).
fof(f2556,plain,
spl0_228,
inference(avatar_split_clause,[],[f363,f2554]) ).
fof(f363,axiom,
! [X19,X9] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X19,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X19,X9,tc_nat),X19,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less_0) ).
fof(f2548,plain,
spl0_227,
inference(avatar_split_clause,[],[f57,f2546]) ).
fof(f57,axiom,
! [X0,X18,X17,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X15,c_HOL_Otimes__class_Otimes(X17,X18,X0),X0) = c_HOL_Otimes__class_Otimes(X17,c_HOL_Otimes__class_Otimes(X15,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(f2544,plain,
spl0_226,
inference(avatar_split_clause,[],[f56,f2542]) ).
fof(f2542,plain,
( spl0_226
<=> ! [X18,X0,X17,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X15,c_HOL_Otimes__class_Otimes(X17,X18,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X15,X17,X0),X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f56,axiom,
! [X0,X18,X17,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X15,c_HOL_Otimes__class_Otimes(X17,X18,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X15,X17,X0),X18,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
fof(f2540,plain,
spl0_225,
inference(avatar_split_clause,[],[f54,f2538]) ).
fof(f54,axiom,
! [X0,X16,X17,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X15,X16,X0),X17,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X15,X17,X0),X16,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(f2536,plain,
spl0_224,
inference(avatar_split_clause,[],[f53,f2534]) ).
fof(f53,axiom,
! [X3,X0,X1,X13] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X3,X0),X13,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X3,X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(f2532,plain,
spl0_223,
inference(avatar_split_clause,[],[f19,f2530]) ).
fof(f2530,plain,
( spl0_223
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X9,X0),X1,X0) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f19,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X9,X0),X1,X0) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__commutes_0) ).
fof(f2528,plain,
spl0_222,
inference(avatar_split_clause,[],[f12,f2526]) ).
fof(f2526,plain,
( spl0_222
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f12,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X1,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
fof(f2524,plain,
spl0_221,
inference(avatar_split_clause,[],[f10,f2522]) ).
fof(f2522,plain,
( spl0_221
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f10,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X1,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
fof(f2490,plain,
spl0_220,
inference(avatar_split_clause,[],[f584,f2488]) ).
fof(f2488,plain,
( spl0_220
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f584,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
fof(f2486,plain,
spl0_219,
inference(avatar_split_clause,[],[f560,f2484]) ).
fof(f560,axiom,
! [X0,X9] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X9
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).
fof(f2482,plain,
spl0_218,
inference(avatar_split_clause,[],[f507,f2480]) ).
fof(f507,axiom,
! [X2,X4] :
( ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
| c_HOL_Oord__class_Oless(X2,X4,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X2,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__difference__nat_1) ).
fof(f2478,plain,
spl0_217,
inference(avatar_split_clause,[],[f506,f2476]) ).
fof(f506,axiom,
! [X2,X4] :
( ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X4,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X2,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__difference__nat_0) ).
fof(f2474,plain,
spl0_216,
inference(avatar_split_clause,[],[f327,f2472]) ).
fof(f327,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| X1 = X3
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oone__class_Oone(X0) != c_HOL_Oinverse__class_Odivide(X1,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).
fof(f2299,plain,
spl0_215,
inference(avatar_split_clause,[],[f608,f2297]) ).
fof(f608,axiom,
! [X27,X22,X23] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X27,X22,tc_nat),X23,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X27,X23,tc_nat),X22,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).
fof(f2295,plain,
spl0_214,
inference(avatar_split_clause,[],[f542,f2293]) ).
fof(f542,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power__iff_1) ).
fof(f2291,plain,
spl0_213,
inference(avatar_split_clause,[],[f541,f2289]) ).
fof(f541,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
fof(f2287,plain,
spl0_212,
inference(avatar_split_clause,[],[f382,f2285]) ).
fof(f382,axiom,
! [X2,X0,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ class_OrderedGroup_Omonoid__mult(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__even__power_0) ).
fof(f2283,plain,
spl0_211,
inference(avatar_split_clause,[],[f344,f2281]) ).
fof(f344,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__power_0) ).
fof(f2279,plain,
spl0_210,
inference(avatar_split_clause,[],[f311,f2277]) ).
fof(f311,axiom,
! [X9] :
( ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X9,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__num__iff_0) ).
fof(f2275,plain,
spl0_209,
inference(avatar_split_clause,[],[f310,f2273]) ).
fof(f310,axiom,
! [X9] :
( c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X9,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__num__iff_1) ).
fof(f2271,plain,
spl0_208,
inference(avatar_split_clause,[],[f244,f2269]) ).
fof(f244,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
fof(f2267,plain,
spl0_207,
inference(avatar_split_clause,[],[f243,f2265]) ).
fof(f243,axiom,
! [X2,X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__zero__eq_1) ).
fof(f2263,plain,
spl0_206,
inference(avatar_split_clause,[],[f182,f2261]) ).
fof(f182,axiom,
! [X2,X0] :
( ~ class_Int_Onumber__ring(X0)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0) = c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__one__odd__power_0) ).
fof(f2259,plain,
spl0_205,
inference(avatar_split_clause,[],[f180,f2257]) ).
fof(f2257,plain,
( spl0_205
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f180,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__inverse_0) ).
fof(f2255,plain,
spl0_204,
inference(avatar_split_clause,[],[f179,f2253]) ).
fof(f179,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__inverse_0) ).
fof(f2251,plain,
spl0_203,
inference(avatar_split_clause,[],[f178,f2249]) ).
fof(f178,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse_0) ).
fof(f2247,plain,
spl0_202,
inference(avatar_split_clause,[],[f124,f2245]) ).
fof(f124,axiom,
! [X0,X1,X13] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X13
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X13,X0),X13,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).
fof(f1996,plain,
spl0_201,
inference(avatar_split_clause,[],[f602,f1994]) ).
fof(f602,axiom,
! [X2,X0,X4] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X2 = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X2,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
fof(f1992,plain,
spl0_200,
inference(avatar_split_clause,[],[f595,f1990]) ).
fof(f1990,plain,
( spl0_200
<=> ! [X2,X0,X25,X26] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X25 = X26
| c_HOL_Ominus__class_Ominus(X25,X26,X0) != c_HOL_Ominus__class_Ominus(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f595,axiom,
! [X2,X0,X26,X25] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X25 = X26
| c_HOL_Ominus__class_Ominus(X25,X26,X0) != c_HOL_Ominus__class_Ominus(X2,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
fof(f1988,plain,
spl0_199,
inference(avatar_split_clause,[],[f592,f1986]) ).
fof(f592,axiom,
! [X21,X19,X9] :
( ~ c_lessequals(X19,X9,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X21,X9,tc_nat),c_HOL_Ominus__class_Ominus(X21,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
fof(f1984,plain,
spl0_198,
inference(avatar_split_clause,[],[f591,f1982]) ).
fof(f591,axiom,
! [X21,X19,X9] :
( ~ c_lessequals(X19,X9,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X19,X21,tc_nat),c_HOL_Ominus__class_Ominus(X9,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
fof(f1980,plain,
spl0_197,
inference(avatar_split_clause,[],[f535,f1978]) ).
fof(f535,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,X3,X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
fof(f1976,plain,
spl0_196,
inference(avatar_split_clause,[],[f534,f1974]) ).
fof(f534,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
fof(f1972,plain,
spl0_195,
inference(avatar_split_clause,[],[f521,f1970]) ).
fof(f521,axiom,
! [X2,X0,X11,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X2,X4,X0)
| ~ c_lessequals(X4,X11,X0)
| c_lessequals(X2,X11,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f1968,plain,
spl0_194,
inference(avatar_split_clause,[],[f520,f1966]) ).
fof(f520,axiom,
! [X2,X0,X11,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X4,X2,X0)
| ~ c_lessequals(X11,X4,X0)
| c_lessequals(X11,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f1964,plain,
spl0_193,
inference(avatar_split_clause,[],[f479,f1962]) ).
fof(f479,axiom,
! [X2,X0,X11,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X2,X0)
| ~ c_HOL_Oord__class_Oless(X11,X4,X0)
| c_HOL_Oord__class_Oless(X11,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f1960,plain,
spl0_192,
inference(avatar_split_clause,[],[f478,f1958]) ).
fof(f478,axiom,
! [X2,X0,X11,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X11,X0)
| c_HOL_Oord__class_Oless(X2,X11,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f1956,plain,
spl0_191,
inference(avatar_split_clause,[],[f476,f1954]) ).
fof(f1954,plain,
( spl0_191
<=> ! [X4,X0,X2] :
( ~ class_Int_Oring__char__0(X0)
| ~ class_Int_Onumber__ring(X0)
| X2 = X4
| c_Int_Onumber__class_Onumber__of(X2,X0) != c_Int_Onumber__class_Onumber__of(X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f476,axiom,
! [X2,X0,X4] :
( ~ class_Int_Oring__char__0(X0)
| ~ class_Int_Onumber__ring(X0)
| X2 = X4
| c_Int_Onumber__class_Onumber__of(X2,X0) != c_Int_Onumber__class_Onumber__of(X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__number__of_0) ).
fof(f1952,plain,
spl0_190,
inference(avatar_split_clause,[],[f470,f1950]) ).
fof(f470,axiom,
! [X2,X0,X11,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X11,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X2,X0)
| c_HOL_Oord__class_Oless(X11,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
fof(f1948,plain,
spl0_189,
inference(avatar_split_clause,[],[f469,f1946]) ).
fof(f469,axiom,
! [X2,X0,X11,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X4,X2,X0)
| ~ c_HOL_Oord__class_Oless(X11,X4,X0)
| c_HOL_Oord__class_Oless(X11,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
fof(f1944,plain,
spl0_188,
inference(avatar_split_clause,[],[f468,f1942]) ).
fof(f468,axiom,
! [X2,X0,X11,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X4,X11,X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0)
| c_HOL_Oord__class_Oless(X2,X11,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f1940,plain,
spl0_187,
inference(avatar_split_clause,[],[f467,f1938]) ).
fof(f467,axiom,
! [X2,X0,X11,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X2,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X11,X0)
| c_HOL_Oord__class_Oless(X2,X11,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f1929,plain,
spl0_186,
inference(avatar_split_clause,[],[f464,f1927]) ).
fof(f464,axiom,
! [X2,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X2,X4,X0)
| c_lessequals(X4,X2,X0)
| c_HOL_Oord__class_Oless(X2,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
fof(f1925,plain,
spl0_185,
inference(avatar_split_clause,[],[f312,f1923]) ).
fof(f312,axiom,
! [X2,X0] :
( ~ class_Int_Onumber__ring(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__one__even__power_0) ).
fof(f1921,plain,
spl0_184,
inference(avatar_split_clause,[],[f246,f1919]) ).
fof(f246,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
fof(f1917,plain,
spl0_183,
inference(avatar_split_clause,[],[f245,f1915]) ).
fof(f245,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
fof(f1913,plain,
spl0_182,
inference(avatar_split_clause,[],[f135,f1911]) ).
fof(f135,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oinverse__class_Oinverse(X1,X0) = X3
| c_HOL_Otimes__class_Otimes(X1,X3,X0) != c_HOL_Oone__class_Oone(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__unique_0) ).
fof(f1773,plain,
spl0_181,
inference(avatar_split_clause,[],[f567,f1771]) ).
fof(f567,axiom,
! [X2,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| X2 = X4
| ~ c_lessequals(X2,X4,X0)
| ~ c_lessequals(X4,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
fof(f1769,plain,
spl0_180,
inference(avatar_split_clause,[],[f562,f1767]) ).
fof(f1767,plain,
( spl0_180
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f562,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
fof(f1765,plain,
spl0_179,
inference(avatar_split_clause,[],[f549,f1763]) ).
fof(f549,axiom,
! [X9,X27] :
( ~ c_lessequals(X27,X9,tc_nat)
| c_HOL_Ominus__class_Ominus(X9,c_HOL_Ominus__class_Ominus(X9,X27,tc_nat),tc_nat) = X27 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
fof(f1759,plain,
spl0_178,
inference(avatar_split_clause,[],[f547,f1757]) ).
fof(f547,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).
fof(f1755,plain,
spl0_177,
inference(avatar_split_clause,[],[f486,f1753]) ).
fof(f486,axiom,
! [X2,X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X2 = X4
| c_HOL_Oord__class_Oless(X2,X4,X0)
| c_HOL_Oord__class_Oless(X4,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
fof(f1751,plain,
spl0_176,
inference(avatar_split_clause,[],[f484,f1749]) ).
fof(f484,axiom,
! [X2,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| X2 = X4
| c_HOL_Oord__class_Oless(X4,X2,X0)
| c_HOL_Oord__class_Oless(X2,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
fof(f1747,plain,
spl0_175,
inference(avatar_split_clause,[],[f460,f1745]) ).
fof(f460,axiom,
! [X2,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| X2 = X4
| ~ c_lessequals(X2,X4,X0)
| c_HOL_Oord__class_Oless(X2,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
fof(f1743,plain,
spl0_174,
inference(avatar_split_clause,[],[f459,f1741]) ).
fof(f459,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X3
| ~ c_lessequals(X1,X3,X0)
| c_HOL_Oord__class_Oless(X1,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
fof(f1739,plain,
spl0_173,
inference(avatar_split_clause,[],[f444,f1737]) ).
fof(f444,axiom,
! [X2,X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__zero__eq_0) ).
fof(f1735,plain,
spl0_172,
inference(avatar_split_clause,[],[f380,f1733]) ).
fof(f380,axiom,
! [X2,X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power__eq_1) ).
fof(f1731,plain,
spl0_171,
inference(avatar_split_clause,[],[f337,f1729]) ).
fof(f337,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X2,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).
fof(f1727,plain,
spl0_170,
inference(avatar_split_clause,[],[f136,f1725]) ).
fof(f136,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X1,X3,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
fof(f1719,plain,
( spl0_169
| ~ spl0_1
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f1067,f1044,f691,f1716]) ).
fof(f1044,plain,
( spl0_75
<=> ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Power_Opower(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1067,plain,
( class_Power_Opower(t_a)
| ~ spl0_1
| ~ spl0_75 ),
inference(resolution,[],[f1045,f693]) ).
fof(f1045,plain,
( ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Power_Opower(X28) )
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f1044]) ).
fof(f1671,plain,
spl0_168,
inference(avatar_split_clause,[],[f601,f1669]) ).
fof(f601,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
fof(f1667,plain,
spl0_167,
inference(avatar_split_clause,[],[f600,f1665]) ).
fof(f600,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
fof(f1663,plain,
spl0_166,
inference(avatar_split_clause,[],[f529,f1661]) ).
fof(f1661,plain,
( spl0_166
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oinverse__class_Oinverse(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f529,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oinverse__class_Oinverse(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).
fof(f1659,plain,
( spl0_165
| ~ spl0_1
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f1066,f1040,f691,f1656]) ).
fof(f1656,plain,
( spl0_165
<=> class_Ring__and__Field_Oidom(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f1040,plain,
( spl0_74
<=> ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Oidom(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f1066,plain,
( class_Ring__and__Field_Oidom(t_a)
| ~ spl0_1
| ~ spl0_74 ),
inference(resolution,[],[f1041,f693]) ).
fof(f1041,plain,
( ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Oidom(X28) )
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f1040]) ).
fof(f1654,plain,
spl0_164,
inference(avatar_split_clause,[],[f523,f1652]) ).
fof(f523,axiom,
! [X27,X22,X23] :
( ~ c_lessequals(X27,X22,tc_nat)
| ~ c_lessequals(X22,X23,tc_nat)
| c_lessequals(X27,X23,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).
fof(f1650,plain,
spl0_163,
inference(avatar_split_clause,[],[f365,f1648]) ).
fof(f365,axiom,
! [X19,X9] :
( ~ c_HOL_Oord__class_Oless(X19,X9,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X9,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
fof(f1646,plain,
spl0_162,
inference(avatar_split_clause,[],[f364,f1644]) ).
fof(f364,axiom,
! [X19,X9] :
( c_HOL_Oord__class_Oless(X19,X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X9,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
fof(f1642,plain,
spl0_161,
inference(avatar_split_clause,[],[f278,f1640]) ).
fof(f278,axiom,
! [X2,X4] :
( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X2,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__difference__nat_4) ).
fof(f1638,plain,
spl0_160,
inference(avatar_split_clause,[],[f277,f1636]) ).
fof(f277,axiom,
! [X2,X4] :
( ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X2,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__difference__nat_3) ).
fof(f1602,plain,
( spl0_159
| ~ spl0_1
| ~ spl0_73 ),
inference(avatar_split_clause,[],[f1065,f1036,f691,f1599]) ).
fof(f1599,plain,
( spl0_159
<=> class_Ring__and__Field_Oring(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1036,plain,
( spl0_73
<=> ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Oring(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f1065,plain,
( class_Ring__and__Field_Oring(t_a)
| ~ spl0_1
| ~ spl0_73 ),
inference(resolution,[],[f1037,f693]) ).
fof(f1037,plain,
( ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Oring(X28) )
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f1036]) ).
fof(f1536,plain,
spl0_158,
inference(avatar_split_clause,[],[f578,f1534]) ).
fof(f1534,plain,
( spl0_158
<=> ! [X2,X0] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f578,axiom,
! [X2,X0] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X2,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
fof(f1532,plain,
spl0_157,
inference(avatar_split_clause,[],[f565,f1530]) ).
fof(f565,axiom,
! [X19,X9] :
( X9 = X19
| ~ c_lessequals(X19,X9,tc_nat)
| ~ c_lessequals(X9,X19,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).
fof(f1528,plain,
spl0_156,
inference(avatar_split_clause,[],[f544,f1526]) ).
fof(f544,axiom,
! [X19,X9] :
( ~ c_lessequals(X19,X9,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X19,X9,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).
fof(f1524,plain,
spl0_155,
inference(avatar_split_clause,[],[f543,f1522]) ).
fof(f543,axiom,
! [X19,X9] :
( c_lessequals(X19,X9,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X19,X9,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).
fof(f1520,plain,
( spl0_154
| ~ spl0_1
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f1064,f1032,f691,f1517]) ).
fof(f1032,plain,
( spl0_72
<=> ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_OrderedGroup_Ogroup__add(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f1064,plain,
( class_OrderedGroup_Ogroup__add(t_a)
| ~ spl0_1
| ~ spl0_72 ),
inference(resolution,[],[f1033,f693]) ).
fof(f1033,plain,
( ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_OrderedGroup_Ogroup__add(X28) )
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f1032]) ).
fof(f1515,plain,
spl0_153,
inference(avatar_split_clause,[],[f531,f1513]) ).
fof(f531,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_0) ).
fof(f1511,plain,
spl0_152,
inference(avatar_split_clause,[],[f481,f1509]) ).
fof(f481,axiom,
! [X2,X4] :
( X2 = X4
| c_HOL_Oord__class_Oless(X2,X4,tc_nat)
| c_HOL_Oord__class_Oless(X4,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
fof(f1507,plain,
spl0_151,
inference(avatar_split_clause,[],[f401,f1505]) ).
fof(f401,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_3) ).
fof(f1503,plain,
spl0_150,
inference(avatar_split_clause,[],[f366,f1501]) ).
fof(f366,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Oinverse(X1,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
fof(f1499,plain,
spl0_149,
inference(avatar_split_clause,[],[f281,f1497]) ).
fof(f281,axiom,
! [X19,X9] :
( X9 = X19
| ~ c_lessequals(X19,X9,tc_nat)
| c_HOL_Oord__class_Oless(X19,X9,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).
fof(f1495,plain,
spl0_148,
inference(avatar_split_clause,[],[f280,f1493]) ).
fof(f280,axiom,
! [X9,X22,X23] :
( ~ c_HOL_Oord__class_Oless(X22,X23,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X22,X9,tc_nat),X23,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
fof(f1491,plain,
spl0_147,
inference(avatar_split_clause,[],[f40,f1489]) ).
fof(f40,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,X3,X0) = c_HOL_Otimes__class_Otimes(X3,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(f1471,plain,
( spl0_146
| ~ spl0_1
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f1063,f1028,f691,f1468]) ).
fof(f1028,plain,
( spl0_71
<=> ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_OrderedGroup_Omonoid__mult(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f1063,plain,
( class_OrderedGroup_Omonoid__mult(t_a)
| ~ spl0_1
| ~ spl0_71 ),
inference(resolution,[],[f1029,f693]) ).
fof(f1029,plain,
( ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_OrderedGroup_Omonoid__mult(X28) )
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f1028]) ).
fof(f1414,plain,
( spl0_145
| ~ spl0_1
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f1062,f1024,f691,f1411]) ).
fof(f1411,plain,
( spl0_145
<=> class_Ring__and__Field_Omult__zero(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1024,plain,
( spl0_70
<=> ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Omult__zero(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f1062,plain,
( class_Ring__and__Field_Omult__zero(t_a)
| ~ spl0_1
| ~ spl0_70 ),
inference(resolution,[],[f1025,f693]) ).
fof(f1025,plain,
( ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Omult__zero(X28) )
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f1024]) ).
fof(f1397,plain,
spl0_144,
inference(avatar_split_clause,[],[f604,f1395]) ).
fof(f604,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
fof(f1393,plain,
spl0_143,
inference(avatar_split_clause,[],[f518,f1391]) ).
fof(f518,axiom,
! [X2,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X2,X4,X0)
| c_lessequals(X4,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f1389,plain,
spl0_142,
inference(avatar_split_clause,[],[f512,f1387]) ).
fof(f512,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f1385,plain,
spl0_141,
inference(avatar_split_clause,[],[f511,f1383]) ).
fof(f511,axiom,
! [X2,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f1381,plain,
spl0_140,
inference(avatar_split_clause,[],[f509,f1379]) ).
fof(f509,axiom,
! [X2,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
fof(f1377,plain,
spl0_139,
inference(avatar_split_clause,[],[f473,f1375]) ).
fof(f473,axiom,
! [X2,X4] :
( ~ c_HOL_Oord__class_Oless(X2,X4,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X2,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__difference__nat_2) ).
fof(f1373,plain,
spl0_138,
inference(avatar_split_clause,[],[f466,f1371]) ).
fof(f466,axiom,
! [X2,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0)
| c_lessequals(X2,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f1369,plain,
spl0_137,
inference(avatar_split_clause,[],[f465,f1367]) ).
fof(f465,axiom,
! [X2,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0)
| c_lessequals(X2,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f1365,plain,
spl0_136,
inference(avatar_split_clause,[],[f455,f1363]) ).
fof(f455,axiom,
! [X2,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X4,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f1361,plain,
spl0_135,
inference(avatar_split_clause,[],[f454,f1359]) ).
fof(f454,axiom,
! [X2,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X4,X2,X0)
| c_HOL_Oord__class_Oless(X2,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
fof(f1357,plain,
spl0_134,
inference(avatar_split_clause,[],[f451,f1355]) ).
fof(f451,axiom,
! [X2,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X4,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
fof(f1353,plain,
( spl0_133
| ~ spl0_1
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f1056,f1020,f691,f1350]) ).
fof(f1020,plain,
( spl0_69
<=> ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_OrderedGroup_Oab__group__add(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1056,plain,
( class_OrderedGroup_Oab__group__add(t_a)
| ~ spl0_1
| ~ spl0_69 ),
inference(resolution,[],[f1021,f693]) ).
fof(f1021,plain,
( ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_OrderedGroup_Oab__group__add(X28) )
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f1020]) ).
fof(f1348,plain,
spl0_132,
inference(avatar_split_clause,[],[f419,f1346]) ).
fof(f419,axiom,
! [X0,X9] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).
fof(f1344,plain,
spl0_131,
inference(avatar_split_clause,[],[f347,f1342]) ).
fof(f1342,plain,
( spl0_131
<=> ! [X0,X1] :
( ~ class_Power_Opower(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f347,axiom,
! [X0,X1] :
( ~ class_Power_Opower(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).
fof(f1340,plain,
spl0_130,
inference(avatar_split_clause,[],[f346,f1338]) ).
fof(f346,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
fof(f1336,plain,
spl0_129,
inference(avatar_split_clause,[],[f101,f1334]) ).
fof(f101,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
fof(f1332,plain,
spl0_128,
inference(avatar_split_clause,[],[f84,f1330]) ).
fof(f84,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
fof(f1328,plain,
spl0_127,
inference(avatar_split_clause,[],[f39,f1326]) ).
fof(f39,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
fof(f1324,plain,
spl0_126,
inference(avatar_split_clause,[],[f38,f1322]) ).
fof(f38,axiom,
! [X3,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),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
fof(f1320,plain,
spl0_125,
inference(avatar_split_clause,[],[f9,f1318]) ).
fof(f1318,plain,
( spl0_125
<=> ! [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_125])]) ).
fof(f9,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_Osemiring__rules_I9_J_0) ).
fof(f1316,plain,
spl0_124,
inference(avatar_split_clause,[],[f8,f1314]) ).
fof(f1314,plain,
( spl0_124
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f8,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f1312,plain,
spl0_123,
inference(avatar_split_clause,[],[f2,f1310]) ).
fof(f2,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
fof(f1308,plain,
( spl0_122
| ~ spl0_1
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f1055,f1016,f691,f1305]) ).
fof(f1016,plain,
( spl0_68
<=> ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Osemiring__0(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f1055,plain,
( class_Ring__and__Field_Osemiring__0(t_a)
| ~ spl0_1
| ~ spl0_68 ),
inference(resolution,[],[f1017,f693]) ).
fof(f1017,plain,
( ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Osemiring__0(X28) )
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f1016]) ).
fof(f1303,plain,
spl0_121,
inference(avatar_split_clause,[],[f1,f1301]) ).
fof(f1,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
fof(f1278,plain,
( spl0_120
| ~ spl0_1
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f1054,f1012,f691,f1275]) ).
fof(f1275,plain,
( spl0_120
<=> class_Ring__and__Field_Ozero__neq__one(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1012,plain,
( spl0_67
<=> ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Ozero__neq__one(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f1054,plain,
( class_Ring__and__Field_Ozero__neq__one(t_a)
| ~ spl0_1
| ~ spl0_67 ),
inference(resolution,[],[f1013,f693]) ).
fof(f1013,plain,
( ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Ozero__neq__one(X28) )
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f1012]) ).
fof(f1263,plain,
spl0_119,
inference(avatar_split_clause,[],[f577,f1261]) ).
fof(f1261,plain,
( spl0_119
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f577,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self_0) ).
fof(f1259,plain,
spl0_118,
inference(avatar_split_clause,[],[f576,f1257]) ).
fof(f576,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
fof(f1255,plain,
spl0_117,
inference(avatar_split_clause,[],[f574,f1253]) ).
fof(f574,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X2,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
fof(f1251,plain,
spl0_116,
inference(avatar_split_clause,[],[f570,f1249]) ).
fof(f570,axiom,
! [X9] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X9
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
fof(f1247,plain,
spl0_115,
inference(avatar_split_clause,[],[f427,f1245]) ).
fof(f427,axiom,
! [X9] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X9
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
fof(f1243,plain,
( spl0_114
| ~ spl0_1
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f1053,f1008,f691,f1240]) ).
fof(f1008,plain,
( spl0_66
<=> ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Odivision__ring(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f1053,plain,
( class_Ring__and__Field_Odivision__ring(t_a)
| ~ spl0_1
| ~ spl0_66 ),
inference(resolution,[],[f1009,f693]) ).
fof(f1009,plain,
( ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Odivision__ring(X28) )
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f1008]) ).
fof(f1238,plain,
spl0_113,
inference(avatar_split_clause,[],[f418,f1236]) ).
fof(f418,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__1_0) ).
fof(f1234,plain,
spl0_112,
inference(avatar_split_clause,[],[f276,f1232]) ).
fof(f276,axiom,
! [X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__1_0) ).
fof(f1230,plain,
spl0_111,
inference(avatar_split_clause,[],[f47,f1228]) ).
fof(f1228,plain,
( spl0_111
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f47,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
fof(f1226,plain,
spl0_110,
inference(avatar_split_clause,[],[f46,f1224]) ).
fof(f1224,plain,
( spl0_110
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f46,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
fof(f1222,plain,
spl0_109,
inference(avatar_split_clause,[],[f45,f1220]) ).
fof(f1220,plain,
( spl0_109
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f45,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).
fof(f1218,plain,
spl0_108,
inference(avatar_split_clause,[],[f43,f1216]) ).
fof(f43,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
fof(f1214,plain,
spl0_107,
inference(avatar_split_clause,[],[f42,f1212]) ).
fof(f42,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
fof(f1210,plain,
spl0_106,
inference(avatar_split_clause,[],[f18,f1208]) ).
fof(f18,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(X2,c_HOL_Oone__class_Oone(tc_nat),X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
fof(f1206,plain,
spl0_105,
inference(avatar_split_clause,[],[f17,f1204]) ).
fof(f17,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__right_0) ).
fof(f1201,plain,
( spl0_104
| ~ spl0_1
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f1052,f1004,f691,f1198]) ).
fof(f1198,plain,
( spl0_104
<=> class_OrderedGroup_Ocomm__monoid__mult(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1004,plain,
( spl0_65
<=> ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_OrderedGroup_Ocomm__monoid__mult(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f1052,plain,
( class_OrderedGroup_Ocomm__monoid__mult(t_a)
| ~ spl0_1
| ~ spl0_65 ),
inference(resolution,[],[f1005,f693]) ).
fof(f1005,plain,
( ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_OrderedGroup_Ocomm__monoid__mult(X28) )
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f1004]) ).
fof(f1186,plain,
spl0_103,
inference(avatar_split_clause,[],[f598,f1184]) ).
fof(f598,axiom,
! [X9] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
fof(f1182,plain,
spl0_102,
inference(avatar_split_clause,[],[f517,f1180]) ).
fof(f517,axiom,
! [X19,X9] :
( c_lessequals(X19,X9,tc_nat)
| c_lessequals(X9,X19,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
fof(f1178,plain,
spl0_101,
inference(avatar_split_clause,[],[f496,f1176]) ).
fof(f1176,plain,
( spl0_101
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f496,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
fof(f1174,plain,
( spl0_100
| ~ spl0_1
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f1051,f1000,f691,f1171]) ).
fof(f1000,plain,
( spl0_64
<=> ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_OrderedGroup_Oab__semigroup__mult(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f1051,plain,
( class_OrderedGroup_Oab__semigroup__mult(t_a)
| ~ spl0_1
| ~ spl0_64 ),
inference(resolution,[],[f1001,f693]) ).
fof(f1001,plain,
( ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_OrderedGroup_Oab__semigroup__mult(X28) )
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f1000]) ).
fof(f1169,plain,
spl0_99,
inference(avatar_split_clause,[],[f490,f1167]) ).
fof(f1167,plain,
( spl0_99
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f490,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
fof(f1165,plain,
spl0_98,
inference(avatar_split_clause,[],[f474,f1163]) ).
fof(f474,axiom,
! [X9] :
( c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__pos_0) ).
fof(f1161,plain,
spl0_97,
inference(avatar_split_clause,[],[f416,f1159]) ).
fof(f416,axiom,
! [X2,X4] :
( ~ c_HOL_Oord__class_Oless(X2,X4,tc_nat)
| c_lessequals(X2,X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
fof(f1157,plain,
spl0_96,
inference(avatar_split_clause,[],[f248,f1155]) ).
fof(f1155,plain,
( spl0_96
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f248,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
fof(f1153,plain,
spl0_95,
inference(avatar_split_clause,[],[f247,f1151]) ).
fof(f247,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
fof(f1147,plain,
spl0_94,
inference(avatar_split_clause,[],[f599,f1145]) ).
fof(f599,axiom,
! [X19,X9] : c_lessequals(c_HOL_Ominus__class_Ominus(X19,X9,tc_nat),X19,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
fof(f1143,plain,
( spl0_93
| ~ spl0_1
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f1050,f996,f691,f1140]) ).
fof(f996,plain,
( spl0_63
<=> ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Ocomm__semiring__1(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f1050,plain,
( class_Ring__and__Field_Ocomm__semiring__1(t_a)
| ~ spl0_1
| ~ spl0_63 ),
inference(resolution,[],[f997,f693]) ).
fof(f997,plain,
( ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Ocomm__semiring__1(X28) )
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f996]) ).
fof(f1138,plain,
spl0_92,
inference(avatar_split_clause,[],[f580,f1136]) ).
fof(f580,axiom,
! [X19] : c_HOL_Ominus__class_Ominus(X19,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
fof(f1134,plain,
spl0_91,
inference(avatar_split_clause,[],[f579,f1132]) ).
fof(f579,axiom,
! [X19] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X19,X19,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
fof(f1130,plain,
spl0_90,
inference(avatar_split_clause,[],[f471,f1128]) ).
fof(f1128,plain,
( spl0_90
<=> ! [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_90])]) ).
fof(f471,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_one__neq__zero_0) ).
fof(f1126,plain,
( spl0_89
| ~ spl0_1
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f1049,f992,f691,f1123]) ).
fof(f1123,plain,
( spl0_89
<=> class_Ring__and__Field_Ono__zero__divisors(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f992,plain,
( spl0_62
<=> ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Ono__zero__divisors(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f1049,plain,
( class_Ring__and__Field_Ono__zero__divisors(t_a)
| ~ spl0_1
| ~ spl0_62 ),
inference(resolution,[],[f993,f693]) ).
fof(f993,plain,
( ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Ono__zero__divisors(X28) )
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f992]) ).
fof(f1121,plain,
( ~ spl0_88
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f571,f691,f1118]) ).
fof(f571,axiom,
( ~ class_Ring__and__Field_Ofield(t_a)
| v_a != c_HOL_Ozero__class_Ozero(t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nz_0) ).
fof(f1116,plain,
spl0_87,
inference(avatar_split_clause,[],[f526,f1114]) ).
fof(f1114,plain,
( spl0_87
<=> ! [X2,X0] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f526,axiom,
! [X2,X0] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X2,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1112,plain,
spl0_86,
inference(avatar_split_clause,[],[f525,f1110]) ).
fof(f1110,plain,
( spl0_86
<=> ! [X2,X0] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f525,axiom,
! [X2,X0] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X2,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1108,plain,
spl0_85,
inference(avatar_split_clause,[],[f495,f1106]) ).
fof(f1106,plain,
( spl0_85
<=> ! [X2,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f495,axiom,
! [X2,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f1104,plain,
spl0_84,
inference(avatar_split_clause,[],[f494,f1102]) ).
fof(f494,axiom,
! [X2,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f1100,plain,
spl0_83,
inference(avatar_split_clause,[],[f491,f1098]) ).
fof(f1098,plain,
( spl0_83
<=> ! [X2,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f491,axiom,
! [X2,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f1096,plain,
spl0_82,
inference(avatar_split_clause,[],[f133,f1093]) ).
fof(f1093,plain,
( spl0_82
<=> c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f133,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__number__of__Min_0) ).
fof(f1091,plain,
( ~ spl0_81
| spl0_80 ),
inference(avatar_split_clause,[],[f1086,f1082,f1088]) ).
fof(f1082,plain,
( spl0_80
<=> c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f1086,plain,
( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_x,t_a)
| spl0_80 ),
inference(forward_demodulation,[],[f1084,f580]) ).
fof(f1084,plain,
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a)
| spl0_80 ),
inference(avatar_component_clause,[],[f1082]) ).
fof(f1085,plain,
~ spl0_80,
inference(avatar_split_clause,[],[f615,f1082]) ).
fof(f615,axiom,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1080,plain,
( spl0_79
| ~ spl0_1
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f1048,f988,f691,f1077]) ).
fof(f988,plain,
( spl0_61
<=> ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Oring__no__zero__divisors(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f1048,plain,
( class_Ring__and__Field_Oring__no__zero__divisors(t_a)
| ~ spl0_1
| ~ spl0_61 ),
inference(resolution,[],[f989,f693]) ).
fof(f989,plain,
( ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Oring__no__zero__divisors(X28) )
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f988]) ).
fof(f1075,plain,
spl0_78,
inference(avatar_split_clause,[],[f612,f1073]) ).
fof(f612,axiom,
! [X9] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le0_0) ).
fof(f1071,plain,
spl0_77,
inference(avatar_split_clause,[],[f424,f1069]) ).
fof(f424,axiom,
! [X19] : ~ c_HOL_Oord__class_Oless(X19,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
fof(f1061,plain,
( spl0_76
| ~ spl0_1
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f1047,f984,f691,f1058]) ).
fof(f1058,plain,
( spl0_76
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f984,plain,
( spl0_60
<=> ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Oring__1__no__zero__divisors(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f1047,plain,
( class_Ring__and__Field_Oring__1__no__zero__divisors(t_a)
| ~ spl0_1
| ~ spl0_60 ),
inference(resolution,[],[f985,f693]) ).
fof(f985,plain,
( ! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Oring__1__no__zero__divisors(X28) )
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f984]) ).
fof(f1046,plain,
spl0_75,
inference(avatar_split_clause,[],[f631,f1044]) ).
fof(f631,axiom,
! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Power_Opower(X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Power_Opower) ).
fof(f1042,plain,
spl0_74,
inference(avatar_split_clause,[],[f630,f1040]) ).
fof(f630,axiom,
! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Oidom(X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Oidom) ).
fof(f1038,plain,
spl0_73,
inference(avatar_split_clause,[],[f629,f1036]) ).
fof(f629,axiom,
! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Oring(X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Oring) ).
fof(f1034,plain,
spl0_72,
inference(avatar_split_clause,[],[f628,f1032]) ).
fof(f628,axiom,
! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_OrderedGroup_Ogroup__add(X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_OrderedGroup_Ogroup__add) ).
fof(f1030,plain,
spl0_71,
inference(avatar_split_clause,[],[f627,f1028]) ).
fof(f627,axiom,
! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_OrderedGroup_Omonoid__mult(X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_OrderedGroup_Omonoid__mult) ).
fof(f1026,plain,
spl0_70,
inference(avatar_split_clause,[],[f626,f1024]) ).
fof(f626,axiom,
! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Omult__zero(X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Omult__zero) ).
fof(f1022,plain,
spl0_69,
inference(avatar_split_clause,[],[f625,f1020]) ).
fof(f625,axiom,
! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_OrderedGroup_Oab__group__add(X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_OrderedGroup_Oab__group__add) ).
fof(f1018,plain,
spl0_68,
inference(avatar_split_clause,[],[f624,f1016]) ).
fof(f624,axiom,
! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Osemiring__0(X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Osemiring__0) ).
fof(f1014,plain,
spl0_67,
inference(avatar_split_clause,[],[f623,f1012]) ).
fof(f623,axiom,
! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Ozero__neq__one(X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Ozero__neq__one) ).
fof(f1010,plain,
spl0_66,
inference(avatar_split_clause,[],[f622,f1008]) ).
fof(f622,axiom,
! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Odivision__ring(X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Odivision__ring) ).
fof(f1006,plain,
spl0_65,
inference(avatar_split_clause,[],[f621,f1004]) ).
fof(f621,axiom,
! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_OrderedGroup_Ocomm__monoid__mult(X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_OrderedGroup_Ocomm__monoid__mult) ).
fof(f1002,plain,
spl0_64,
inference(avatar_split_clause,[],[f620,f1000]) ).
fof(f620,axiom,
! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_OrderedGroup_Oab__semigroup__mult(X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_OrderedGroup_Oab__semigroup__mult) ).
fof(f998,plain,
spl0_63,
inference(avatar_split_clause,[],[f619,f996]) ).
fof(f619,axiom,
! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Ocomm__semiring__1(X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Ocomm__semiring__1) ).
fof(f994,plain,
spl0_62,
inference(avatar_split_clause,[],[f618,f992]) ).
fof(f618,axiom,
! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Ono__zero__divisors(X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Ono__zero__divisors) ).
fof(f990,plain,
spl0_61,
inference(avatar_split_clause,[],[f617,f988]) ).
fof(f617,axiom,
! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Oring__no__zero__divisors(X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Oring__no__zero__divisors) ).
fof(f986,plain,
spl0_60,
inference(avatar_split_clause,[],[f616,f984]) ).
fof(f616,axiom,
! [X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| class_Ring__and__Field_Oring__1__no__zero__divisors(X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f982,plain,
spl0_59,
inference(avatar_split_clause,[],[f522,f980]) ).
fof(f522,axiom,
! [X9] : c_lessequals(X9,X9,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).
fof(f978,plain,
spl0_58,
inference(avatar_split_clause,[],[f493,f976]) ).
fof(f493,axiom,
! [X2] : ~ c_HOL_Oord__class_Oless(X2,X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
fof(f974,plain,
spl0_57,
inference(avatar_split_clause,[],[f426,f971]) ).
fof(f426,axiom,
c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__zero__nat_0) ).
fof(f969,plain,
~ spl0_56,
inference(avatar_split_clause,[],[f59,f966]) ).
fof(f966,plain,
( spl0_56
<=> c_Parity_Oeven__odd__class_Oeven(c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f59,axiom,
~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__1__nat_0) ).
fof(f964,plain,
spl0_55,
inference(avatar_split_clause,[],[f685,f961]) ).
fof(f685,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).
fof(f959,plain,
spl0_54,
inference(avatar_split_clause,[],[f684,f956]) ).
fof(f684,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Power_Opower) ).
fof(f954,plain,
spl0_53,
inference(avatar_split_clause,[],[f683,f951]) ).
fof(f683,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).
fof(f949,plain,
spl0_52,
inference(avatar_split_clause,[],[f682,f946]) ).
fof(f946,plain,
( spl0_52
<=> class_Int_Oring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f682,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).
fof(f944,plain,
spl0_51,
inference(avatar_split_clause,[],[f681,f941]) ).
fof(f941,plain,
( spl0_51
<=> class_Orderings_Oorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f681,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).
fof(f939,plain,
spl0_50,
inference(avatar_split_clause,[],[f680,f936]) ).
fof(f936,plain,
( spl0_50
<=> class_Orderings_Olinorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f680,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).
fof(f934,plain,
spl0_49,
inference(avatar_split_clause,[],[f679,f931]) ).
fof(f931,plain,
( spl0_49
<=> class_Orderings_Opreorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f679,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).
fof(f929,plain,
spl0_48,
inference(avatar_split_clause,[],[f678,f926]) ).
fof(f926,plain,
( spl0_48
<=> class_Ring__and__Field_Oidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f678,axiom,
class_Ring__and__Field_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).
fof(f924,plain,
spl0_47,
inference(avatar_split_clause,[],[f677,f921]) ).
fof(f677,axiom,
class_Ring__and__Field_Oring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring) ).
fof(f919,plain,
spl0_46,
inference(avatar_split_clause,[],[f676,f916]) ).
fof(f676,axiom,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).
fof(f914,plain,
spl0_45,
inference(avatar_split_clause,[],[f675,f911]) ).
fof(f675,axiom,
class_OrderedGroup_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).
fof(f909,plain,
spl0_44,
inference(avatar_split_clause,[],[f674,f906]) ).
fof(f906,plain,
( spl0_44
<=> class_Ring__and__Field_Omult__mono(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f674,axiom,
class_Ring__and__Field_Omult__mono(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono) ).
fof(f904,plain,
spl0_43,
inference(avatar_split_clause,[],[f673,f901]) ).
fof(f673,axiom,
class_Ring__and__Field_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).
fof(f899,plain,
spl0_42,
inference(avatar_split_clause,[],[f672,f896]) ).
fof(f672,axiom,
class_OrderedGroup_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).
fof(f894,plain,
spl0_41,
inference(avatar_split_clause,[],[f671,f891]) ).
fof(f891,plain,
( spl0_41
<=> class_Ring__and__Field_Omult__mono1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f671,axiom,
class_Ring__and__Field_Omult__mono1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono1) ).
fof(f889,plain,
spl0_40,
inference(avatar_split_clause,[],[f670,f886]) ).
fof(f670,axiom,
class_Ring__and__Field_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__0) ).
fof(f884,plain,
spl0_39,
inference(avatar_split_clause,[],[f669,f881]) ).
fof(f881,plain,
( spl0_39
<=> class_Ring__and__Field_Oordered__idom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f669,axiom,
class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).
fof(f879,plain,
spl0_38,
inference(avatar_split_clause,[],[f668,f876]) ).
fof(f876,plain,
( spl0_38
<=> class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f668,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).
fof(f874,plain,
spl0_37,
inference(avatar_split_clause,[],[f667,f871]) ).
fof(f871,plain,
( spl0_37
<=> class_Ring__and__Field_Opordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f667,axiom,
class_Ring__and__Field_Opordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__ring) ).
fof(f869,plain,
spl0_36,
inference(avatar_split_clause,[],[f666,f866]) ).
fof(f666,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) ).
fof(f864,plain,
spl0_35,
inference(avatar_split_clause,[],[f665,f861]) ).
fof(f665,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) ).
fof(f859,plain,
spl0_34,
inference(avatar_split_clause,[],[f664,f856]) ).
fof(f664,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).
fof(f854,plain,
spl0_33,
inference(avatar_split_clause,[],[f663,f851]) ).
fof(f851,plain,
( spl0_33
<=> class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f663,axiom,
class_Ring__and__Field_Oordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).
fof(f849,plain,
spl0_32,
inference(avatar_split_clause,[],[f662,f846]) ).
fof(f846,plain,
( spl0_32
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f662,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).
fof(f844,plain,
spl0_31,
inference(avatar_split_clause,[],[f661,f841]) ).
fof(f841,plain,
( spl0_31
<=> class_Ring__and__Field_Oordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f661,axiom,
class_Ring__and__Field_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) ).
fof(f839,plain,
spl0_30,
inference(avatar_split_clause,[],[f660,f836]) ).
fof(f836,plain,
( spl0_30
<=> class_Ring__and__Field_Opordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f660,axiom,
class_Ring__and__Field_Opordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) ).
fof(f834,plain,
spl0_29,
inference(avatar_split_clause,[],[f659,f831]) ).
fof(f831,plain,
( spl0_29
<=> class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f659,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).
fof(f829,plain,
spl0_28,
inference(avatar_split_clause,[],[f658,f826]) ).
fof(f826,plain,
( spl0_28
<=> class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f658,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) ).
fof(f824,plain,
spl0_27,
inference(avatar_split_clause,[],[f657,f821]) ).
fof(f821,plain,
( spl0_27
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f657,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f819,plain,
spl0_26,
inference(avatar_split_clause,[],[f656,f816]) ).
fof(f816,plain,
( spl0_26
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f656,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) ).
fof(f814,plain,
spl0_25,
inference(avatar_split_clause,[],[f655,f811]) ).
fof(f811,plain,
( spl0_25
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f655,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f809,plain,
spl0_24,
inference(avatar_split_clause,[],[f654,f806]) ).
fof(f806,plain,
( spl0_24
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f654,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f804,plain,
spl0_23,
inference(avatar_split_clause,[],[f653,f801]) ).
fof(f801,plain,
( spl0_23
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f653,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f799,plain,
spl0_22,
inference(avatar_split_clause,[],[f652,f796]) ).
fof(f652,axiom,
class_Int_Onumber(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).
fof(f794,plain,
spl0_21,
inference(avatar_split_clause,[],[f651,f791]) ).
fof(f651,axiom,
class_Power_Opower(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
fof(f789,plain,
spl0_20,
inference(avatar_split_clause,[],[f650,f786]) ).
fof(f650,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f784,plain,
spl0_19,
inference(avatar_split_clause,[],[f649,f781]) ).
fof(f649,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f779,plain,
spl0_18,
inference(avatar_split_clause,[],[f648,f776]) ).
fof(f648,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f774,plain,
spl0_17,
inference(avatar_split_clause,[],[f647,f771]) ).
fof(f647,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(f769,plain,
spl0_16,
inference(avatar_split_clause,[],[f646,f766]) ).
fof(f646,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
fof(f764,plain,
spl0_15,
inference(avatar_split_clause,[],[f645,f761]) ).
fof(f645,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f759,plain,
spl0_14,
inference(avatar_split_clause,[],[f644,f756]) ).
fof(f644,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
fof(f754,plain,
spl0_13,
inference(avatar_split_clause,[],[f643,f751]) ).
fof(f643,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
fof(f749,plain,
spl0_12,
inference(avatar_split_clause,[],[f642,f746]) ).
fof(f746,plain,
( spl0_12
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f642,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(f744,plain,
spl0_11,
inference(avatar_split_clause,[],[f641,f741]) ).
fof(f641,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
fof(f739,plain,
spl0_10,
inference(avatar_split_clause,[],[f640,f736]) ).
fof(f640,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f734,plain,
spl0_9,
inference(avatar_split_clause,[],[f639,f731]) ).
fof(f639,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(f729,plain,
spl0_8,
inference(avatar_split_clause,[],[f638,f726]) ).
fof(f638,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f724,plain,
spl0_7,
inference(avatar_split_clause,[],[f637,f721]) ).
fof(f721,plain,
( spl0_7
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f637,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(f719,plain,
spl0_6,
inference(avatar_split_clause,[],[f636,f716]) ).
fof(f716,plain,
( spl0_6
<=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f636,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
fof(f714,plain,
spl0_5,
inference(avatar_split_clause,[],[f635,f711]) ).
fof(f711,plain,
( spl0_5
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f635,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
fof(f709,plain,
spl0_4,
inference(avatar_split_clause,[],[f634,f706]) ).
fof(f634,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
fof(f704,plain,
spl0_3,
inference(avatar_split_clause,[],[f633,f701]) ).
fof(f633,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f699,plain,
spl0_2,
inference(avatar_split_clause,[],[f632,f696]) ).
fof(f696,plain,
( spl0_2
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f632,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f694,plain,
spl0_1,
inference(avatar_split_clause,[],[f613,f691]) ).
fof(f613,axiom,
class_Ring__and__Field_Ofield(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SWV674-1 : TPTP v8.2.0. Released v4.1.0.
% 0.10/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n018.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 : Sun May 19 08:58:38 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (5629)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.41 % (5632)WARNING: value z3 for option sas not known
% 0.15/0.41 % (5633)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.41 % (5631)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.41 % (5632)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)
% 0.15/0.41 % (5630)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.41 % (5634)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)
% 0.15/0.41 % (5635)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)
% 0.15/0.41 % (5636)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)
% 0.22/0.45 TRYING [1]
% 0.22/0.46 TRYING [2]
% 0.22/0.55 TRYING [3]
% 1.50/0.60 TRYING [1]
% 1.50/0.62 TRYING [2]
% 3.99/0.98 TRYING [4]
% 4.45/1.01 TRYING [3]
% 7.91/1.53 TRYING [1]
% 8.11/1.53 TRYING [2]
% 8.11/1.59 TRYING [3]
% 12.25/2.17 TRYING [4]
% 13.02/2.28 TRYING [5]
% 15.69/2.62 TRYING [4]
% 22.13/3.55 TRYING [5]
% 38.90/5.99 TRYING [6]
% 47.57/7.23 TRYING [6]
% 55.92/8.42 % (5634)First to succeed.
% 56.57/8.46 % (5634)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-5629"
% 56.57/8.47 % (5634)Refutation found. Thanks to Tanya!
% 56.57/8.47 % SZS status Unsatisfiable for theBenchmark
% 56.57/8.47 % SZS output start Proof for theBenchmark
% See solution above
% 56.57/8.49 % (5634)------------------------------
% 56.57/8.49 % (5634)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 56.57/8.49 % (5634)Termination reason: Refutation
% 56.57/8.49
% 56.57/8.49 % (5634)Memory used [KB]: 47281
% 56.57/8.49 % (5634)Time elapsed: 8.048 s
% 56.57/8.49 % (5634)Instructions burned: 27867 (million)
% 56.57/8.49 % (5629)Success in time 8.026 s
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