TSTP Solution File: SWV716-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV716-1 : 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 : n009.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 06:35:14 EDT 2024
% Result : Unsatisfiable 15.46s 2.68s
% Output : Refutation 15.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2322
% Syntax : Number of formulae : 3836 (1367 unt; 0 def)
% Number of atoms : 9069 (1572 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 9083 (3850 ~;4020 |; 0 &)
% (1213 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of predicates : 1283 (1281 usr;1214 prp; 0-6 aty)
% Number of functors : 31 ( 31 usr; 10 con; 0-5 aty)
% Number of variables : 5988 (5988 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f34732,plain,
$false,
inference(avatar_sat_refutation,[],[f1690,f1695,f1700,f1705,f1710,f1715,f1720,f1725,f1730,f1735,f1740,f1745,f1750,f1755,f1760,f1765,f1770,f1775,f1780,f1785,f1790,f1795,f1800,f1805,f1810,f1815,f1820,f1825,f1830,f1835,f1840,f1845,f1850,f1855,f1860,f1865,f1870,f1875,f1880,f1885,f1890,f1895,f1900,f1905,f1910,f1915,f1920,f1925,f1930,f1935,f1940,f1945,f1950,f1955,f1960,f1965,f1970,f1975,f1980,f1985,f1990,f1995,f2000,f2005,f2010,f2015,f2020,f2025,f2030,f2035,f2040,f2045,f2050,f2055,f2060,f2065,f2070,f2075,f2080,f2085,f2090,f2095,f2100,f2105,f2110,f2115,f2120,f2125,f2130,f2135,f2140,f2145,f2150,f2155,f2160,f2165,f2170,f2175,f2180,f2185,f2190,f2195,f2200,f2205,f2210,f2215,f2220,f2225,f2230,f2235,f2240,f2245,f2250,f2255,f2260,f2265,f2270,f2275,f2280,f2285,f2290,f2295,f2300,f2305,f2310,f2315,f2319,f2324,f2328,f2333,f2337,f2342,f2346,f2350,f2355,f2359,f2365,f2369,f2373,f2377,f2383,f2387,f2392,f2396,f2400,f2404,f2408,f2413,f2418,f2422,f2426,f2430,f2434,f2438,f2442,f2446,f2450,f2455,f2459,f2463,f2467,f2471,f2475,f2479,f2483,f2487,f2491,f2495,f2499,f2508,f2512,f2516,f2520,f2524,f2528,f2532,f2536,f2540,f2544,f2548,f2552,f2556,f2560,f2586,f2596,f2600,f2604,f2608,f2612,f2616,f2620,f2624,f2628,f2632,f2636,f2640,f2644,f2648,f2652,f2657,f2661,f2665,f2669,f2673,f2677,f2681,f2685,f2689,f2693,f2697,f2701,f2705,f2709,f2714,f2718,f2722,f2726,f2730,f2734,f2738,f2742,f2746,f2751,f2756,f2761,f2765,f2769,f2773,f2778,f2782,f2786,f2791,f2857,f2880,f2884,f2888,f2892,f2896,f2900,f2904,f2908,f2912,f2916,f2920,f2924,f2928,f2932,f2936,f2940,f2944,f2948,f2952,f2956,f2960,f2964,f2968,f2972,f2976,f2980,f2984,f2988,f2992,f2996,f3000,f3004,f3008,f3012,f3016,f3020,f3024,f3028,f3032,f3036,f3040,f3044,f3048,f3052,f3056,f3060,f3064,f3068,f3080,f3197,f3344,f3472,f3477,f3481,f3485,f3489,f3493,f3497,f3501,f3505,f3509,f3513,f3518,f3522,f3526,f3530,f3534,f3538,f3542,f3546,f3550,f3554,f3558,f3563,f3568,f3572,f3576,f3580,f3584,f3588,f3593,f3599,f3603,f3607,f3611,f3615,f3619,f3623,f3627,f3631,f3636,f3640,f3645,f3852,f4003,f4007,f4011,f4015,f4019,f4023,f4027,f4031,f4035,f4039,f4043,f4047,f4051,f4055,f4059,f4063,f4074,f4079,f4084,f4088,f4092,f4096,f4100,f4104,f4108,f4112,f4117,f4121,f4125,f4129,f4133,f4137,f4141,f4145,f4149,f4153,f4157,f4168,f4172,f4176,f4180,f4184,f4188,f4192,f4196,f4200,f4204,f4216,f4220,f4224,f4228,f4232,f4237,f4285,f4463,f4509,f4667,f4671,f4675,f4679,f4683,f4688,f4692,f4696,f4700,f4704,f4708,f4712,f4716,f4720,f4724,f4728,f4732,f4736,f4741,f4746,f4750,f4754,f4758,f4762,f4766,f4770,f4775,f4779,f4783,f4787,f4791,f4795,f4799,f4803,f4807,f4811,f4816,f4820,f4824,f4828,f4832,f4836,f4840,f4844,f4848,f4852,f4856,f4874,f4878,f4882,f4886,f4890,f4895,f4900,f4946,f5183,f5504,f5775,f5779,f5783,f5792,f5796,f5800,f5804,f5808,f5812,f5816,f5820,f5824,f5828,f5832,f5836,f5840,f5844,f5848,f5852,f5856,f5860,f5864,f5868,f5872,f5880,f5884,f5888,f5892,f5896,f5900,f5904,f5908,f5912,f5916,f5940,f5944,f5948,f5952,f5956,f5960,f5964,f5968,f5972,f5976,f5981,f5985,f5989,f5993,f5997,f6001,f6005,f6009,f6013,f6017,f6021,f6029,f6033,f6037,f6041,f6045,f6049,f6053,f6057,f6061,f6065,f6070,f6074,f6078,f6082,f6086,f6090,f6094,f6098,f6172,f6311,f6874,f7287,f7387,f7391,f7395,f7399,f7403,f7407,f7411,f7415,f7419,f7423,f7427,f7431,f7435,f7448,f7452,f7456,f7460,f7464,f7468,f7472,f7476,f7480,f7484,f7488,f7492,f7496,f7500,f7504,f7508,f7513,f7517,f7521,f7525,f8019,f8060,f8064,f8068,f8072,f8076,f8080,f8084,f8088,f8092,f8126,f8130,f8134,f8138,f8142,f8146,f8150,f8154,f8158,f8162,f8167,f8171,f8175,f8179,f8183,f8187,f8191,f8195,f8199,f8203,f8207,f8211,f8215,f8219,f8223,f8227,f8231,f8235,f8239,f8243,f8247,f8251,f8288,f8292,f8296,f8300,f8304,f8308,f8312,f8316,f8343,f8574,f9097,f9376,f9380,f9384,f9388,f9392,f9396,f9400,f9404,f9408,f9412,f9416,f9420,f9424,f9428,f9432,f9436,f9475,f9479,f9483,f9487,f9491,f9495,f9499,f9503,f9507,f9511,f9516,f9520,f9524,f9528,f9532,f9536,f9540,f9544,f9548,f9552,f9556,f9564,f9568,f9572,f9576,f9580,f9584,f9588,f9592,f9596,f9600,f9605,f9609,f9614,f9618,f9622,f9626,f9889,f10073,f10829,f10916,f10920,f10924,f10928,f10932,f10936,f10946,f10950,f10954,f10958,f10962,f10966,f10970,f10974,f10978,f10982,f10999,f11003,f11007,f11011,f11015,f11019,f11023,f11027,f11031,f11035,f11039,f11043,f11047,f11051,f11506,f12050,f12054,f12058,f12062,f12066,f12070,f12074,f12078,f12082,f12086,f12090,f12094,f12098,f12102,f12106,f12110,f12114,f12118,f12122,f12156,f12160,f12164,f12168,f12172,f12176,f12180,f12184,f12188,f12192,f12196,f12200,f12204,f12208,f12212,f12216,f12220,f12224,f12228,f12232,f12236,f12240,f12244,f12248,f12252,f12796,f13127,f13131,f13135,f13139,f13143,f13147,f13152,f13156,f13160,f13164,f13168,f13172,f13176,f13180,f13184,f13188,f13192,f13218,f13222,f13226,f13230,f13234,f13238,f13242,f13246,f13250,f13254,f13259,f13263,f13267,f13271,f13275,f13279,f13283,f13287,f13291,f13295,f13299,f13304,f13308,f13312,f13316,f13320,f13324,f13328,f14288,f15004,f15008,f15013,f15017,f15021,f15025,f15029,f15033,f15037,f15041,f15045,f15049,f15053,f15107,f15111,f15115,f15119,f15123,f15127,f15131,f15135,f15139,f15143,f15147,f15329,f15505,f15535,f15539,f15543,f15547,f15551,f15555,f15559,f15563,f15592,f15596,f15600,f15604,f15608,f15612,f15616,f15620,f15624,f15628,f15632,f15636,f15640,f15644,f15648,f15652,f15656,f15660,f15664,f15668,f15672,f15703,f15707,f15711,f15715,f15719,f15723,f15727,f15731,f15735,f15739,f15772,f15776,f15780,f15784,f15788,f15792,f15796,f15800,f15804,f15808,f15853,f15857,f15861,f15865,f15869,f15873,f15877,f15881,f15885,f15889,f15894,f15898,f15902,f15906,f15910,f15914,f15918,f15922,f15926,f15930,f15934,f16236,f16568,f17383,f17901,f18128,f18132,f18136,f18140,f18144,f18148,f18152,f18156,f18160,f18164,f18168,f18172,f18176,f18180,f18184,f18188,f18192,f18196,f18200,f18204,f18208,f18212,f18216,f18220,f18224,f18228,f18232,f18242,f18246,f18250,f18254,f20602,f20606,f20610,f20614,f20618,f20622,f20626,f20630,f20634,f20638,f20642,f20646,f20650,f20654,f20658,f20662,f20666,f20670,f20707,f20711,f20715,f20719,f20723,f20727,f20731,f20735,f20739,f20743,f20747,f21191,f21708,f21712,f21716,f21724,f21728,f21732,f21736,f21740,f21744,f21748,f21752,f21756,f21760,f21764,f21768,f21772,f21776,f21780,f21784,f21788,f21792,f21796,f21800,f21808,f21812,f21816,f21820,f21824,f21828,f21832,f21836,f21840,f21844,f21849,f21853,f21857,f21861,f21865,f21869,f21873,f21877,f21881,f21885,f21889,f21900,f21904,f21908,f21912,f21916,f21920,f21924,f21928,f21932,f21936,f21941,f21948,f21952,f21956,f21960,f21964,f21968,f21972,f21976,f21980,f21984,f21993,f22493,f24291,f24295,f24299,f24303,f24307,f24308,f24313,f24317,f24321,f24325,f24329,f24333,f24337,f24341,f24345,f24349,f24353,f24357,f24361,f24365,f24369,f24373,f24377,f24381,f24385,f24389,f24393,f24400,f24478,f24482,f24486,f24490,f24494,f24506,f24746,f25323,f25327,f25331,f25335,f25384,f25388,f25392,f25396,f25506,f25515,f25519,f25523,f25527,f25531,f25535,f25539,f26078,f26083,f26128,f26133,f26137,f26141,f26246,f26250,f26254,f26258,f26262,f26275,f26279,f26283,f26287,f26291,f26295,f26299,f26303,f26307,f26311,f26315,f26319,f26323,f26327,f26331,f26335,f26339,f26343,f26347,f26351,f26732,f26996,f27000,f27004,f27008,f27012,f27016,f27020,f27024,f27028,f27032,f27036,f27040,f27044,f27048,f27052,f27509,f27573,f27577,f27581,f27585,f27589,f27593,f27597,f27601,f27605,f27615,f27619,f27822,f28118,f28122,f28126,f28130,f28134,f28242,f28246,f28250,f28254,f28258,f28262,f28266,f28270,f28274,f28278,f28282,f28286,f28290,f28294,f28298,f28302,f28306,f28310,f28881,f29125,f29129,f29133,f29137,f29141,f29145,f29149,f29720,f29724,f29728,f29938,f29944,f29953,f29957,f29961,f29965,f29969,f29973,f30298,f30302,f30306,f30481,f30485,f30504,f30508,f30512,f30516,f30977,f30982,f31289,f31293,f31297,f31301,f31305,f31309,f31313,f31317,f31321,f31339,f31343,f31347,f32377,f32875,f32879,f33503,f33509,f33513,f33517,f33521,f33525,f33529,f33533,f33913,f34646,f34654,f34659,f34706,f34713,f34724,f34731]) ).
fof(f34731,plain,
( ~ spl0_14
| ~ spl0_97
| ~ spl0_158
| ~ spl0_553
| ~ spl0_875
| ~ spl0_1127
| spl0_1213 ),
inference(avatar_contradiction_clause,[],[f34730]) ).
fof(f34730,plain,
( $false
| ~ spl0_14
| ~ spl0_97
| ~ spl0_158
| ~ spl0_553
| ~ spl0_875
| ~ spl0_1127
| spl0_1213 ),
inference(trivial_inequality_removal,[],[f34729]) ).
fof(f34729,plain,
( c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____))),tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),tc_Complex_Ocomplex) != c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____))),tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),tc_Complex_Ocomplex)
| ~ spl0_14
| ~ spl0_97
| ~ spl0_158
| ~ spl0_553
| ~ spl0_875
| ~ spl0_1127
| spl0_1213 ),
inference(forward_demodulation,[],[f34728,f28110]) ).
fof(f28110,plain,
( ! [X0] : c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X0,c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,X0),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))
| ~ spl0_158
| ~ spl0_1127 ),
inference(resolution,[],[f27618,f2454]) ).
fof(f2454,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)
| ~ spl0_158 ),
inference(avatar_component_clause,[],[f2452]) ).
fof(f2452,plain,
( spl0_158
<=> c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f27618,plain,
( ! [X16,X4] :
( ~ c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)
| c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X4,X16) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,X4),X16) )
| ~ spl0_1127 ),
inference(avatar_component_clause,[],[f27617]) ).
fof(f27617,plain,
( spl0_1127
<=> ! [X4,X16] :
( ~ c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)
| c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X4,X16) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,X4),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f34728,plain,
( c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____))),tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),tc_Complex_Ocomplex) != c_HOL_Ominus__class_Ominus(c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____))),tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),tc_Complex_Ocomplex)
| ~ spl0_14
| ~ spl0_97
| ~ spl0_158
| ~ spl0_553
| ~ spl0_875
| ~ spl0_1127
| spl0_1213 ),
inference(forward_demodulation,[],[f34727,f7938]) ).
fof(f7938,plain,
( ! [X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X0)
| ~ spl0_97
| ~ spl0_553 ),
inference(resolution,[],[f7516,f2169]) ).
fof(f2169,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f2167]) ).
fof(f2167,plain,
( spl0_97
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f7516,plain,
( ! [X3,X6,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X4) )
| ~ spl0_553 ),
inference(avatar_component_clause,[],[f7515]) ).
fof(f7515,plain,
( spl0_553
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f34727,plain,
( c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____))),tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),tc_Complex_Ocomplex) != c_HOL_Ominus__class_Ominus(c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____))),tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),tc_Complex_Ocomplex)
| ~ spl0_14
| ~ spl0_97
| ~ spl0_158
| ~ spl0_553
| ~ spl0_875
| ~ spl0_1127
| spl0_1213 ),
inference(forward_demodulation,[],[f34726,f28110]) ).
fof(f34726,plain,
( c_HOL_Ominus__class_Ominus(c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____))),tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),tc_Complex_Ocomplex) != c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____))),tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),tc_Complex_Ocomplex)
| ~ spl0_14
| ~ spl0_97
| ~ spl0_553
| ~ spl0_875
| spl0_1213 ),
inference(forward_demodulation,[],[f34725,f17837]) ).
fof(f17837,plain,
( ! [X0,X1] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X0),hAPP(c_Suc,X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X0),X1))
| ~ spl0_14
| ~ spl0_875 ),
inference(resolution,[],[f15901,f1754]) ).
fof(f1754,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f1752]) ).
fof(f1752,plain,
( spl0_14
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f15901,plain,
( ! [X2,X3,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),hAPP(c_Suc,X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2)) )
| ~ spl0_875 ),
inference(avatar_component_clause,[],[f15900]) ).
fof(f15900,plain,
( spl0_875
<=> ! [X2,X9,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),hAPP(c_Suc,X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f34725,plain,
( c_HOL_Ominus__class_Ominus(c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),tc_Complex_Ocomplex) != c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),tc_Complex_Ocomplex)
| ~ spl0_97
| ~ spl0_553
| spl0_1213 ),
inference(forward_demodulation,[],[f34723,f7938]) ).
fof(f34723,plain,
( c_HOL_Ominus__class_Ominus(c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),tc_Complex_Ocomplex) != c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),tc_Complex_Ocomplex)
| spl0_1213 ),
inference(avatar_component_clause,[],[f34721]) ).
fof(f34721,plain,
( spl0_1213
<=> c_HOL_Ominus__class_Ominus(c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).
fof(f34724,plain,
~ spl0_1213,
inference(avatar_split_clause,[],[f1445,f34721]) ).
fof(f1445,axiom,
c_HOL_Ominus__class_Ominus(c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),tc_Complex_Ocomplex) != c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f34713,plain,
spl0_1212,
inference(avatar_split_clause,[],[f1293,f34711]) ).
fof(f34711,plain,
( spl0_1212
<=> ! [X9,X17,X3] :
( ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ominus__class_Ominus(X9,X17,X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X3)),X9)),X17),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).
fof(f1293,axiom,
! [X3,X9,X17] :
( ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ominus__class_Ominus(X9,X17,X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X3)),X9)),X17),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power2__diff_0) ).
fof(f34706,plain,
spl0_1211,
inference(avatar_split_clause,[],[f646,f34704]) ).
fof(f34704,plain,
( spl0_1211
<=> ! [X17,X4,X9,X6,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X9,X4,X3)),c_HOL_Ominus__class_Ominus(X17,X6,X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X9,X4,X3)),X6))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_HOL_Ominus__class_Ominus(X17,X6,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).
fof(f646,axiom,
! [X3,X6,X9,X4,X17] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X9,X4,X3)),c_HOL_Ominus__class_Ominus(X17,X6,X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X9,X4,X3)),X6))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_HOL_Ominus__class_Ominus(X17,X6,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).
fof(f34659,plain,
spl0_1210,
inference(avatar_split_clause,[],[f1099,f34657]) ).
fof(f34657,plain,
( spl0_1210
<=> ! [X4,X0,X14,X16,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X14)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X16)),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X14),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X0),X3)),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).
fof(f1099,axiom,
! [X3,X0,X16,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X14)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X16)),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X14),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X0),X3)),X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__divides__special_0) ).
fof(f34654,plain,
spl0_1209,
inference(avatar_split_clause,[],[f1083,f34652]) ).
fof(f34652,plain,
( spl0_1209
<=> ! [X3,X4,X7,X6,X5,X43] :
( ~ class_RealVector_Oreal__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X7),X3),X43,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X6,X7,X3),X43,X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X4,X5,X3),X43,X3)),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).
fof(f1083,axiom,
! [X3,X6,X7,X4,X5,X43] :
( ~ class_RealVector_Oreal__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X7),X3),X43,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X6,X7,X3),X43,X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X4,X5,X3),X43,X3)),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__mult__lemma_0) ).
fof(f34646,plain,
spl0_1208,
inference(avatar_split_clause,[],[f811,f34644]) ).
fof(f34644,plain,
( spl0_1208
<=> ! [X17,X9,X3,X22,X24] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| c_HOL_Ozero__class_Ozero(X3) = X22
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oinverse__class_Odivide(X9,X17,X3)),c_HOL_Oinverse__class_Odivide(X24,X22,X3)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X22)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X24),X17)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X22),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).
fof(f811,axiom,
! [X3,X9,X17,X24,X22] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| c_HOL_Ozero__class_Ozero(X3) = X22
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oinverse__class_Odivide(X9,X17,X3)),c_HOL_Oinverse__class_Odivide(X24,X22,X3)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X22)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X24),X17)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X22),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__frac__eq_0) ).
fof(f33913,plain,
( ~ spl0_86
| spl0_1207
| ~ spl0_483
| ~ spl0_1183 ),
inference(avatar_split_clause,[],[f31330,f30979,f5962,f33911,f2112]) ).
fof(f2112,plain,
( spl0_86
<=> class_Orderings_Oorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f33911,plain,
( spl0_1207
<=> ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).
fof(f5962,plain,
( spl0_483
<=> ! [X17,X3,X9,X22] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X22,X17,X3)
| ~ c_HOL_Oord__class_Oless(X17,X9,X3)
| c_HOL_Oord__class_Oless(X22,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f30979,plain,
( spl0_1183
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).
fof(f31330,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| ~ class_Orderings_Oorder(tc_Int_Oint)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) )
| ~ spl0_483
| ~ spl0_1183 ),
inference(resolution,[],[f30981,f5963]) ).
fof(f5963,plain,
( ! [X3,X9,X17,X22] :
( ~ c_HOL_Oord__class_Oless(X17,X9,X3)
| ~ c_lessequals(X22,X17,X3)
| ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X22,X9,X3) )
| ~ spl0_483 ),
inference(avatar_component_clause,[],[f5962]) ).
fof(f30981,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint)
| ~ spl0_1183 ),
inference(avatar_component_clause,[],[f30979]) ).
fof(f33533,plain,
spl0_1206,
inference(avatar_split_clause,[],[f1171,f33531]) ).
fof(f33531,plain,
( spl0_1206
<=> ! [X14,X16,X25,X2,X1] :
( ~ c_lessequals(X14,X16,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X16,X14,tc_nat)),X25)),X1),X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).
fof(f1171,axiom,
! [X2,X1,X16,X14,X25] :
( ~ c_lessequals(X14,X16,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X16,X14,tc_nat)),X25)),X1),X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff1_0) ).
fof(f33529,plain,
spl0_1205,
inference(avatar_split_clause,[],[f1170,f33527]) ).
fof(f33527,plain,
( spl0_1205
<=> ! [X14,X16,X25,X2,X1] :
( ~ c_lessequals(X14,X16,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X16,X14,tc_nat)),X25)),X1),X2,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).
fof(f1170,axiom,
! [X2,X1,X16,X14,X25] :
( ~ c_lessequals(X14,X16,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X16,X14,tc_nat)),X25)),X1),X2,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff1_1) ).
fof(f33525,plain,
spl0_1204,
inference(avatar_split_clause,[],[f1169,f33523]) ).
fof(f33523,plain,
( spl0_1204
<=> ! [X14,X16,X25,X2,X1] :
( ~ c_lessequals(X16,X14,tc_nat)
| c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X14,X16,tc_nat)),X25)),X2),tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).
fof(f1169,axiom,
! [X2,X1,X16,X14,X25] :
( ~ c_lessequals(X16,X14,tc_nat)
| c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X14,X16,tc_nat)),X25)),X2),tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff2_0) ).
fof(f33521,plain,
spl0_1203,
inference(avatar_split_clause,[],[f1168,f33519]) ).
fof(f33519,plain,
( spl0_1203
<=> ! [X14,X16,X25,X2,X1] :
( ~ c_lessequals(X16,X14,tc_nat)
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X14,X16,tc_nat)),X25)),X2),tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).
fof(f1168,axiom,
! [X2,X1,X16,X14,X25] :
( ~ c_lessequals(X16,X14,tc_nat)
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X14,X16,tc_nat)),X25)),X2),tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff2_1) ).
fof(f33517,plain,
spl0_1202,
inference(avatar_split_clause,[],[f500,f33515]) ).
fof(f33515,plain,
( spl0_1202
<=> ! [X14,X16,X25,X2,X1] :
( ~ c_lessequals(X16,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X14,X16,tc_nat)),X25)),X2),tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).
fof(f500,axiom,
! [X2,X1,X16,X14,X25] :
( ~ c_lessequals(X16,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X14,X16,tc_nat)),X25)),X2),tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff2_1) ).
fof(f33513,plain,
spl0_1201,
inference(avatar_split_clause,[],[f499,f33511]) ).
fof(f33511,plain,
( spl0_1201
<=> ! [X14,X16,X25,X2,X1] :
( ~ c_lessequals(X16,X14,tc_nat)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X14,X16,tc_nat)),X25)),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).
fof(f499,axiom,
! [X2,X1,X16,X14,X25] :
( ~ c_lessequals(X16,X14,tc_nat)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X14,X16,tc_nat)),X25)),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff2_0) ).
fof(f33509,plain,
spl0_1200,
inference(avatar_split_clause,[],[f498,f33507]) ).
fof(f33507,plain,
( spl0_1200
<=> ! [X14,X16,X25,X2,X1] :
( ~ c_lessequals(X14,X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X16,X14,tc_nat)),X25)),X1),X2,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).
fof(f498,axiom,
! [X2,X1,X16,X14,X25] :
( ~ c_lessequals(X14,X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X16,X14,tc_nat)),X25)),X1),X2,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff1_1) ).
fof(f33503,plain,
spl0_1199,
inference(avatar_split_clause,[],[f497,f33501]) ).
fof(f33501,plain,
( spl0_1199
<=> ! [X14,X16,X25,X2,X1] :
( ~ c_lessequals(X14,X16,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X16,X14,tc_nat)),X25)),X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).
fof(f497,axiom,
! [X2,X1,X16,X14,X25] :
( ~ c_lessequals(X14,X16,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X16,X14,tc_nat)),X25)),X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff1_0) ).
fof(f32879,plain,
spl0_1198,
inference(avatar_split_clause,[],[f1624,f32877]) ).
fof(f32877,plain,
( spl0_1198
<=> ! [X14,X16,X25,X2,X1] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X16,X14,tc_nat)),X25)),X1),X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25),tc_nat),X2,tc_nat)
| ~ c_lessequals(X14,X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).
fof(f1624,plain,
! [X2,X1,X16,X14,X25] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X16,X14,tc_nat)),X25)),X1),X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25),tc_nat),X2,tc_nat)
| ~ c_lessequals(X14,X16,tc_nat) ),
inference(forward_demodulation,[],[f1175,f1191]) ).
fof(f1191,axiom,
! [X0,X16,X14] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X16,X14,tc_nat),X0,tc_nat) = c_HOL_Ominus__class_Ominus(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X0),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).
fof(f1175,axiom,
! [X2,X1,X16,X14,X25] :
( ~ c_lessequals(X14,X16,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X2),tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X16,X14,tc_nat)),X25)),X1),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__add__eq1_0) ).
fof(f32875,plain,
spl0_1197,
inference(avatar_split_clause,[],[f1600,f32873]) ).
fof(f32873,plain,
( spl0_1197
<=> ! [X4,X5] : c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X4),X5,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(X4,X5,tc_nat)),c_Divides_Odiv__class_Odiv(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X5,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(X4,X5,tc_nat)),c_Divides_Odiv__class_Omod(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X5,tc_nat)),X5,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).
fof(f1600,plain,
! [X4,X5] : c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X4),X5,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(X4,X5,tc_nat)),c_Divides_Odiv__class_Odiv(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X5,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(X4,X5,tc_nat)),c_Divides_Odiv__class_Omod(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X5,tc_nat)),X5,tc_nat)),
inference(forward_demodulation,[],[f138,f421]) ).
fof(f421,axiom,
hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Fact_Ofact__0__nat_0) ).
fof(f138,axiom,
! [X4,X5] : c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X4),X5,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(X4,X5,tc_nat)),c_Divides_Odiv__class_Odiv(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(X4,X5,tc_nat)),c_Divides_Odiv__class_Omod(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)),X5,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__Suc_0) ).
fof(f32377,plain,
( ~ spl0_83
| ~ spl0_1196
| ~ spl0_245
| ~ spl0_1183 ),
inference(avatar_split_clause,[],[f31325,f30979,f2922,f32374,f2097]) ).
fof(f2097,plain,
( spl0_83
<=> class_Orderings_Opreorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f32374,plain,
( spl0_1196
<=> c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f2922,plain,
( spl0_245
<=> ! [X9,X17,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X17,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X17,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f31325,plain,
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| ~ class_Orderings_Opreorder(tc_Int_Oint)
| ~ spl0_245
| ~ spl0_1183 ),
inference(resolution,[],[f30981,f2923]) ).
fof(f2923,plain,
( ! [X3,X9,X17] :
( ~ c_HOL_Oord__class_Oless(X9,X17,X3)
| ~ c_lessequals(X17,X9,X3)
| ~ class_Orderings_Opreorder(X3) )
| ~ spl0_245 ),
inference(avatar_component_clause,[],[f2922]) ).
fof(f31347,plain,
spl0_1195,
inference(avatar_split_clause,[],[f1310,f31345]) ).
fof(f31345,plain,
( spl0_1195
<=> ! [X16,X1,X14] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X14))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f1310,axiom,
! [X1,X16,X14] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X14))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__cancel1_0) ).
fof(f31343,plain,
spl0_1194,
inference(avatar_split_clause,[],[f1177,f31341]) ).
fof(f31341,plain,
( spl0_1194
<=> ! [X14,X16,X25,X2,X1] :
( ~ c_lessequals(X14,X16,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X16,X14,tc_nat)),X25)),X1) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f1177,axiom,
! [X2,X1,X16,X14,X25] :
( ~ c_lessequals(X14,X16,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X16,X14,tc_nat)),X25)),X1) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__eq__add__iff1_0) ).
fof(f31339,plain,
spl0_1193,
inference(avatar_split_clause,[],[f1082,f31337]) ).
fof(f31337,plain,
( spl0_1193
<=> ! [X17,X9,X3,X22,X24] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| c_HOL_Ozero__class_Ozero(X3) = X22
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X9,X17,X3),c_HOL_Oinverse__class_Odivide(X24,X22,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X22),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X24),X17),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X22),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f1082,axiom,
! [X3,X9,X17,X24,X22] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| c_HOL_Ozero__class_Ozero(X3) = X22
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X9,X17,X3),c_HOL_Oinverse__class_Odivide(X24,X22,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X22),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X24),X17),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X22),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__frac__eq_0) ).
fof(f31321,plain,
spl0_1192,
inference(avatar_split_clause,[],[f934,f31319]) ).
fof(f31319,plain,
( spl0_1192
<=> ! [X5,X37,X4,X7,X6,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_HOL_Oord__class_Oless(X5,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X6,X4,X3)),X37)),X7),X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X37)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X37)),X7),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).
fof(f934,axiom,
! [X3,X37,X6,X7,X4,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_HOL_Oord__class_Oless(X5,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X6,X4,X3)),X37)),X7),X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X37)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X37)),X7),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).
fof(f31317,plain,
spl0_1191,
inference(avatar_split_clause,[],[f933,f31315]) ).
fof(f31315,plain,
( spl0_1191
<=> ! [X5,X37,X4,X7,X6,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_HOL_Oord__class_Oless(X5,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X6,X4,X3)),X37)),X7),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X37)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X37)),X7),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f933,axiom,
! [X3,X37,X6,X7,X4,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_HOL_Oord__class_Oless(X5,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X6,X4,X3)),X37)),X7),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X37)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X37)),X7),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
fof(f31313,plain,
spl0_1190,
inference(avatar_split_clause,[],[f932,f31311]) ).
fof(f31311,plain,
( spl0_1190
<=> ! [X37,X4,X7,X6,X5,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X4,X6,X3)),X37)),X5),X7,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X37)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X37)),X7),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f932,axiom,
! [X3,X37,X6,X7,X4,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X4,X6,X3)),X37)),X5),X7,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X37)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X37)),X7),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
fof(f31309,plain,
spl0_1189,
inference(avatar_split_clause,[],[f931,f31307]) ).
fof(f31307,plain,
( spl0_1189
<=> ! [X37,X4,X7,X6,X5,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X4,X6,X3)),X37)),X5),X7,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X37)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X37)),X7),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).
fof(f931,axiom,
! [X3,X37,X6,X7,X4,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X4,X6,X3)),X37)),X5),X7,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X37)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X37)),X7),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
fof(f31305,plain,
spl0_1188,
inference(avatar_split_clause,[],[f760,f31303]) ).
fof(f31303,plain,
( spl0_1188
<=> ! [X37,X4,X7,X6,X5,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X4,X6,X3)),X37)),X5),X7,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X37)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X37)),X7),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
fof(f760,axiom,
! [X3,X37,X6,X7,X4,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X4,X6,X3)),X37)),X5),X7,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X37)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X37)),X7),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).
fof(f31301,plain,
spl0_1187,
inference(avatar_split_clause,[],[f759,f31299]) ).
fof(f31299,plain,
( spl0_1187
<=> ! [X37,X4,X7,X6,X5,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X4,X6,X3)),X37)),X5),X7,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X37)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X37)),X7),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).
fof(f759,axiom,
! [X3,X37,X6,X7,X4,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X4,X6,X3)),X37)),X5),X7,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X37)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X37)),X7),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).
fof(f31297,plain,
spl0_1186,
inference(avatar_split_clause,[],[f758,f31295]) ).
fof(f31295,plain,
( spl0_1186
<=> ! [X5,X37,X4,X7,X6,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(X5,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X6,X4,X3)),X37)),X7),X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X37)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X37)),X7),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).
fof(f758,axiom,
! [X3,X37,X6,X7,X4,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(X5,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X6,X4,X3)),X37)),X7),X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X37)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X37)),X7),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).
fof(f31293,plain,
spl0_1185,
inference(avatar_split_clause,[],[f757,f31291]) ).
fof(f31291,plain,
( spl0_1185
<=> ! [X5,X37,X4,X7,X6,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(X5,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X6,X4,X3)),X37)),X7),X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X37)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X37)),X7),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f757,axiom,
! [X3,X37,X6,X7,X4,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(X5,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X6,X4,X3)),X37)),X7),X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X37)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X37)),X7),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).
fof(f31289,plain,
spl0_1184,
inference(avatar_split_clause,[],[f625,f31287]) ).
fof(f31287,plain,
( spl0_1184
<=> ! [X5,X4,X7,X6,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X4 = X6
| X5 = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X7)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f625,axiom,
! [X3,X6,X7,X4,X5] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X4 = X6
| X5 = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X7)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
fof(f30982,plain,
( spl0_1183
| ~ spl0_84
| spl0_1153
| ~ spl0_416
| ~ spl0_1061 ),
inference(avatar_split_clause,[],[f25587,f25503,f4793,f28878,f2102,f30979]) ).
fof(f2102,plain,
( spl0_84
<=> class_Orderings_Olinorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f28878,plain,
( spl0_1153
<=> c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f4793,plain,
( spl0_416
<=> ! [X9,X17,X3] :
( ~ class_Orderings_Olinorder(X3)
| X9 = X17
| ~ c_lessequals(X9,X17,X3)
| c_HOL_Oord__class_Oless(X9,X17,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f25503,plain,
( spl0_1061
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f25587,plain,
( c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint)
| ~ class_Orderings_Olinorder(tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint)
| ~ spl0_416
| ~ spl0_1061 ),
inference(resolution,[],[f25505,f4794]) ).
fof(f4794,plain,
( ! [X3,X9,X17] :
( ~ c_lessequals(X9,X17,X3)
| X9 = X17
| ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X9,X17,X3) )
| ~ spl0_416 ),
inference(avatar_component_clause,[],[f4793]) ).
fof(f25505,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint)
| ~ spl0_1061 ),
inference(avatar_component_clause,[],[f25503]) ).
fof(f30977,plain,
spl0_1182,
inference(avatar_split_clause,[],[f1623,f30975]) ).
fof(f30975,plain,
( spl0_1182
<=> ! [X14,X16,X25,X2,X1] :
( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X14,X16,tc_nat)),X25),tc_nat),X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25),tc_nat),X2,tc_nat)
| ~ c_lessequals(X16,X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f1623,plain,
! [X2,X1,X16,X14,X25] :
( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X14,X16,tc_nat)),X25),tc_nat),X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25),tc_nat),X2,tc_nat)
| ~ c_lessequals(X16,X14,tc_nat) ),
inference(forward_demodulation,[],[f1622,f1191]) ).
fof(f1622,plain,
! [X2,X1,X16,X14,X25] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X2),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X14,X16,tc_nat)),X25),tc_nat),X2,tc_nat)
| ~ c_lessequals(X16,X14,tc_nat) ),
inference(forward_demodulation,[],[f1174,f1191]) ).
fof(f1174,axiom,
! [X2,X1,X16,X14,X25] :
( ~ c_lessequals(X16,X14,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X14,X16,tc_nat)),X25)),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__add__eq2_0) ).
fof(f30516,plain,
spl0_1181,
inference(avatar_split_clause,[],[f1317,f30514]) ).
fof(f30514,plain,
( spl0_1181
<=> ! [X2,X9,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f1317,axiom,
! [X2,X3,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I37_J_0) ).
fof(f30512,plain,
spl0_1180,
inference(avatar_split_clause,[],[f1284,f30510]) ).
fof(f30510,plain,
( spl0_1180
<=> ! [X2,X10,X11,X9,X13,X12,X3,X8] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X8,X9),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2))) = hAPP(hAPP(X12,X9),hAPP(hAPP(X12,hAPP(hAPP(X8,X9),X2)),hAPP(hAPP(X8,X9),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).
fof(f1284,axiom,
! [X2,X3,X10,X11,X8,X9,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X8,X9),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2))) = hAPP(hAPP(X12,X9),hAPP(hAPP(X12,hAPP(hAPP(X8,X9),X2)),hAPP(hAPP(X8,X9),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I37_J_0) ).
fof(f30508,plain,
spl0_1179,
inference(avatar_split_clause,[],[f649,f30506]) ).
fof(f30506,plain,
( spl0_1179
<=> ! [X37,X4,X7,X6,X5,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X4,X6,X3)),X37)),X5) = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X37)),X7) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X37)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f649,axiom,
! [X3,X37,X6,X7,X4,X5] :
( ~ class_Ring__and__Field_Oring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X4,X6,X3)),X37)),X5) = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X37)),X7) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X37)),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).
fof(f30504,plain,
spl0_1178,
inference(avatar_split_clause,[],[f43,f30502]) ).
fof(f30502,plain,
( spl0_1178
<=> ! [X6,X4,X5] : c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X6),X5,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(X4,X5,tc_nat)),c_Divides_Odiv__class_Odiv(X6,X5,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(X4,X5,tc_nat)),c_Divides_Odiv__class_Omod(X6,X5,tc_nat)),X5,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).
fof(f43,axiom,
! [X6,X4,X5] : c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X6),X5,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(X4,X5,tc_nat)),c_Divides_Odiv__class_Odiv(X6,X5,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(X4,X5,tc_nat)),c_Divides_Odiv__class_Omod(X6,X5,tc_nat)),X5,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add1__eq_0) ).
fof(f30485,plain,
spl0_1177,
inference(avatar_split_clause,[],[f1301,f30483]) ).
fof(f30483,plain,
( spl0_1177
<=> ! [X2,X4,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f1301,axiom,
! [X2,X3,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__odd__eq_0) ).
fof(f30481,plain,
spl0_1176,
inference(avatar_split_clause,[],[f751,f30479]) ).
fof(f30479,plain,
( spl0_1176
<=> ! [X5,X37,X4,X6,X3] :
( ~ class_Ring__and__Field_Osemiring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X37)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X37)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6)),X37)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).
fof(f751,axiom,
! [X3,X37,X6,X4,X5] :
( ~ class_Ring__and__Field_Osemiring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X37)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X37)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6)),X37)),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
fof(f30306,plain,
spl0_1175,
inference(avatar_split_clause,[],[f1042,f30304]) ).
fof(f30304,plain,
( spl0_1175
<=> ! [X5,X4,X7,X6] :
( X4 = X6
| X5 = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X6),X7)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X6),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
fof(f1042,axiom,
! [X6,X7,X4,X5] :
( X4 = X6
| X5 = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X6),X7)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X6),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_0) ).
fof(f30302,plain,
spl0_1174,
inference(avatar_split_clause,[],[f622,f30300]) ).
fof(f30300,plain,
( spl0_1174
<=> ! [X5,X31,X4,X6,X29,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,X5,X3) != c_Divides_Odiv__class_Omod(X29,X5,X3)
| c_Divides_Odiv__class_Omod(X6,X5,X3) != c_Divides_Odiv__class_Omod(X31,X5,X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X5,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X29),X31),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f622,axiom,
! [X31,X3,X29,X6,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,X5,X3) != c_Divides_Odiv__class_Omod(X29,X5,X3)
| c_Divides_Odiv__class_Omod(X6,X5,X3) != c_Divides_Odiv__class_Omod(X31,X5,X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X5,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X29),X31),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__cong_0) ).
fof(f30298,plain,
spl0_1173,
inference(avatar_split_clause,[],[f287,f30296]) ).
fof(f30296,plain,
( spl0_1173
<=> ! [X5,X31,X4,X6,X29,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,X5,X3) != c_Divides_Odiv__class_Omod(X29,X5,X3)
| c_Divides_Odiv__class_Omod(X6,X5,X3) != c_Divides_Odiv__class_Omod(X31,X5,X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X5,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X31),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f287,axiom,
! [X31,X3,X29,X6,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,X5,X3) != c_Divides_Odiv__class_Omod(X29,X5,X3)
| c_Divides_Odiv__class_Omod(X6,X5,X3) != c_Divides_Odiv__class_Omod(X31,X5,X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X5,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X31),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).
fof(f29973,plain,
spl0_1172,
inference(avatar_split_clause,[],[f1290,f29971]) ).
fof(f29971,plain,
( spl0_1172
<=> ! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat)),X2) = hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat)),X2),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f1290,axiom,
! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat)),X2) = hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat)),X2),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lemma__Suc__Suc__4n__diff__2_0) ).
fof(f29969,plain,
spl0_1171,
inference(avatar_split_clause,[],[f1162,f29967]) ).
fof(f29967,plain,
( spl0_1171
<=> ! [X0,X14,X16,X25] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X0)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14)),X25)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f1162,axiom,
! [X0,X16,X14,X25] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X0)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14)),X25)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__add__mult__distrib_0) ).
fof(f29965,plain,
spl0_1170,
inference(avatar_split_clause,[],[f879,f29963]) ).
fof(f29963,plain,
( spl0_1170
<=> ! [X4,X3,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_lessequals(X2,X1,tc_nat)
| c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X4,X3)),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f879,axiom,
! [X2,X3,X1,X4] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_lessequals(X2,X1,tc_nat)
| c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X4,X3)),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__diff__rev__if_1) ).
fof(f29961,plain,
spl0_1169,
inference(avatar_split_clause,[],[f648,f29959]) ).
fof(f29959,plain,
( spl0_1169
<=> ! [X5,X37,X4,X6,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X37)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X37)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X4,X6,X3)),X37)),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f648,axiom,
! [X3,X37,X6,X4,X5] :
( ~ class_Ring__and__Field_Oring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X37)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X37)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X4,X6,X3)),X37)),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).
fof(f29957,plain,
spl0_1168,
inference(avatar_split_clause,[],[f645,f29955]) ).
fof(f29955,plain,
( spl0_1168
<=> ! [X4,X34,X6,X3] :
( ~ class_Ring__and__Field_Osemiring(X3)
| ~ class_Int_Onumber(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6)),c_Int_Onumber__class_Onumber__of(X34,X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_Int_Onumber__class_Onumber__of(X34,X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),c_Int_Onumber__class_Onumber__of(X34,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f645,axiom,
! [X3,X6,X4,X34] :
( ~ class_Ring__and__Field_Osemiring(X3)
| ~ class_Int_Onumber(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6)),c_Int_Onumber__class_Onumber__of(X34,X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_Int_Onumber__class_Onumber__of(X34,X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),c_Int_Onumber__class_Onumber__of(X34,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__distrib__number__of_0) ).
fof(f29953,plain,
( ~ spl0_91
| spl0_1166
| ~ spl0_1167
| ~ spl0_544
| ~ spl0_1052 ),
inference(avatar_split_clause,[],[f25376,f24743,f7478,f29950,f29946,f2137]) ).
fof(f2137,plain,
( spl0_91
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f29946,plain,
( spl0_1166
<=> c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f29950,plain,
( spl0_1167
<=> c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f7478,plain,
( spl0_544
<=> ! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f24743,plain,
( spl0_1052
<=> c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Complex_Ocomplex)),v_ka____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
fof(f25376,plain,
( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex)
| ~ spl0_544
| ~ spl0_1052 ),
inference(inner_rewriting,[],[f25338]) ).
fof(f25338,plain,
( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex)
| ~ spl0_544
| ~ spl0_1052 ),
inference(superposition,[],[f7479,f24745]) ).
fof(f24745,plain,
( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Complex_Ocomplex)),v_ka____)
| ~ spl0_1052 ),
inference(avatar_component_clause,[],[f24743]) ).
fof(f7479,plain,
( ! [X2,X3,X4] :
( c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)
| c_HOL_Ozero__class_Ozero(X3) = X4
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X3) )
| ~ spl0_544 ),
inference(avatar_component_clause,[],[f7478]) ).
fof(f29944,plain,
spl0_1165,
inference(avatar_split_clause,[],[f644,f29942]) ).
fof(f29942,plain,
( spl0_1165
<=> ! [X5,X34,X6,X3] :
( ~ class_Ring__and__Field_Osemiring(X3)
| ~ class_Int_Onumber(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Int_Onumber__class_Onumber__of(X34,X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Int_Onumber__class_Onumber__of(X34,X3)),X6)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Int_Onumber__class_Onumber__of(X34,X3)),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f644,axiom,
! [X3,X6,X34,X5] :
( ~ class_Ring__and__Field_Osemiring(X3)
| ~ class_Int_Onumber(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Int_Onumber__class_Onumber__of(X34,X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Int_Onumber__class_Onumber__of(X34,X3)),X6)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Int_Onumber__class_Onumber__of(X34,X3)),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__distrib__number__of_0) ).
fof(f29938,plain,
spl0_1164,
inference(avatar_split_clause,[],[f750,f29936]) ).
fof(f29936,plain,
( spl0_1164
<=> ! [X5,X7,X9,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X7)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f750,axiom,
! [X3,X9,X7,X5] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X7)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
fof(f29728,plain,
spl0_1163,
inference(avatar_split_clause,[],[f1291,f29726]) ).
fof(f29726,plain,
( spl0_1163
<=> ! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2) = hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).
fof(f1291,axiom,
! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2) = hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__Suc__mult__two__diff__two_0) ).
fof(f29724,plain,
spl0_1162,
inference(avatar_split_clause,[],[f924,f29722]) ).
fof(f29722,plain,
( spl0_1162
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| X9 = X17
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X17,X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).
fof(f924,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| X9 = X17
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X17,X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power2__eq__imp__eq_0) ).
fof(f29720,plain,
spl0_1161,
inference(avatar_split_clause,[],[f245,f29718]) ).
fof(f29718,plain,
( spl0_1161
<=> ! [X5,X4,X7,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X7),X3),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X5,X3),X3)),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X6,X7,X3),X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f245,axiom,
! [X3,X6,X7,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X7),X3),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X5,X3),X3)),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X6,X7,X3),X3)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__diff__triangle__ineq_0) ).
fof(f29149,plain,
spl0_1160,
inference(avatar_split_clause,[],[f1620,f29147]) ).
fof(f29147,plain,
( spl0_1160
<=> ! [X14,X16,X25,X2] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Ominus__class_Ominus(X14,X16,tc_nat))),X25)),X2)
| ~ c_lessequals(X16,X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f1620,plain,
! [X2,X16,X14,X25] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Ominus__class_Ominus(X14,X16,tc_nat))),X25)),X2)
| ~ c_lessequals(X16,X14,tc_nat) ),
inference(forward_demodulation,[],[f1172,f1162]) ).
fof(f1172,axiom,
! [X2,X16,X14,X25] :
( ~ c_lessequals(X16,X14,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X25)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X25)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X14,X16,tc_nat)),X25)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__eq__add__iff2_1) ).
fof(f29145,plain,
spl0_1159,
inference(avatar_split_clause,[],[f1394,f29143]) ).
fof(f29143,plain,
( spl0_1159
<=> ! [X18,X19,X20,X3,X21] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X18),X19)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X20),X21)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X18),X20)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f1394,axiom,
! [X21,X3,X18,X19,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X18),X19)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X20),X21)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X18),X20)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
fof(f29141,plain,
spl0_1158,
inference(avatar_split_clause,[],[f1286,f29139]) ).
fof(f29139,plain,
( spl0_1158
<=> ! [X2,X4,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(X4,X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).
fof(f1286,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(X4,X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__ring__1__class_Opower__minus__even_0) ).
fof(f29137,plain,
spl0_1157,
inference(avatar_split_clause,[],[f1276,f29135]) ).
fof(f29135,plain,
( spl0_1157
<=> ! [X2,X10,X11,X9,X13,X12,X3,X8] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X8,X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2)) = hAPP(hAPP(X12,hAPP(hAPP(X8,X9),X2)),hAPP(hAPP(X8,X9),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f1276,axiom,
! [X2,X3,X10,X11,X8,X9,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X8,X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2)) = hAPP(hAPP(X12,hAPP(hAPP(X8,X9),X2)),hAPP(hAPP(X8,X9),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I36_J_0) ).
fof(f29133,plain,
spl0_1156,
inference(avatar_split_clause,[],[f764,f29131]) ).
fof(f29131,plain,
( spl0_1156
<=> ! [X5,X31,X4,X6,X29,X3] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(X4,X5,X3) != c_Divides_Odiv__class_Omod(X29,X5,X3)
| c_Divides_Odiv__class_Omod(X6,X5,X3) != c_Divides_Odiv__class_Omod(X31,X5,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,X6,X3),X5,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X29,X31,X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).
fof(f764,axiom,
! [X31,X3,X29,X6,X4,X5] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(X4,X5,X3) != c_Divides_Odiv__class_Omod(X29,X5,X3)
| c_Divides_Odiv__class_Omod(X6,X5,X3) != c_Divides_Odiv__class_Omod(X31,X5,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,X6,X3),X5,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X29,X31,X3),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__cong_0) ).
fof(f29129,plain,
spl0_1155,
inference(avatar_split_clause,[],[f173,f29127]) ).
fof(f29127,plain,
( spl0_1155
<=> ! [X6,X4,X5] : c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X6),X5,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),c_Divides_Odiv__class_Odiv(X6,X5,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),c_Divides_Odiv__class_Omod(X6,X5,tc_nat)),X5,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f173,axiom,
! [X6,X4,X5] : c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X6),X5,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),c_Divides_Odiv__class_Odiv(X6,X5,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),c_Divides_Odiv__class_Omod(X6,X5,tc_nat)),X5,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult1__eq_0) ).
fof(f29125,plain,
spl0_1154,
inference(avatar_split_clause,[],[f61,f29123]) ).
fof(f29123,plain,
( spl0_1154
<=> ! [X5,X4,X7,X6,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X7)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f61,axiom,
! [X3,X6,X7,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X7)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(f28881,plain,
( ~ spl0_39
| spl0_1152
| ~ spl0_1153
| ~ spl0_544
| ~ spl0_1051 ),
inference(avatar_split_clause,[],[f25164,f24503,f7478,f28878,f28874,f1877]) ).
fof(f1877,plain,
( spl0_39
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f28874,plain,
( spl0_1152
<=> c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).
fof(f24503,plain,
( spl0_1051
<=> c_HOL_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint)),v_ka____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
fof(f25164,plain,
( c_HOL_Ozero__class_Ozero(tc_Int_Oint) != c_HOL_Oone__class_Oone(tc_Int_Oint)
| c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint)
| ~ spl0_544
| ~ spl0_1051 ),
inference(inner_rewriting,[],[f25127]) ).
fof(f25127,plain,
( c_HOL_Ozero__class_Ozero(tc_Int_Oint) != c_HOL_Oone__class_Oone(tc_Int_Oint)
| c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint)
| ~ spl0_544
| ~ spl0_1051 ),
inference(superposition,[],[f7479,f24505]) ).
fof(f24505,plain,
( c_HOL_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint)),v_ka____)
| ~ spl0_1051 ),
inference(avatar_component_clause,[],[f24503]) ).
fof(f28310,plain,
spl0_1151,
inference(avatar_split_clause,[],[f1432,f28308]) ).
fof(f28308,plain,
( spl0_1151
<=> ! [X2,X9,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f1432,axiom,
! [X2,X3,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I36_J_0) ).
fof(f28306,plain,
spl0_1150,
inference(avatar_split_clause,[],[f1400,f28304]) ).
fof(f28304,plain,
( spl0_1150
<=> ! [X5,X34,X6,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| ~ class_Int_Onumber(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Int_Onumber__class_Onumber__of(X34,X3)),c_HOL_Ominus__class_Ominus(X6,X5,X3)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Int_Onumber__class_Onumber__of(X34,X3)),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Int_Onumber__class_Onumber__of(X34,X3)),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f1400,axiom,
! [X3,X6,X34,X5] :
( ~ class_Ring__and__Field_Oring(X3)
| ~ class_Int_Onumber(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Int_Onumber__class_Onumber__of(X34,X3)),c_HOL_Ominus__class_Ominus(X6,X5,X3)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Int_Onumber__class_Onumber__of(X34,X3)),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Int_Onumber__class_Onumber__of(X34,X3)),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__diff__distrib__number__of_0) ).
fof(f28302,plain,
spl0_1149,
inference(avatar_split_clause,[],[f1309,f28300]) ).
fof(f28300,plain,
( spl0_1149
<=> ! [X4,X34,X6,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| ~ class_Int_Onumber(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X4,X6,X3)),c_Int_Onumber__class_Onumber__of(X34,X3)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_Int_Onumber__class_Onumber__of(X34,X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),c_Int_Onumber__class_Onumber__of(X34,X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f1309,axiom,
! [X3,X6,X4,X34] :
( ~ class_Ring__and__Field_Oring(X3)
| ~ class_Int_Onumber(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X4,X6,X3)),c_Int_Onumber__class_Onumber__of(X34,X3)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_Int_Onumber__class_Onumber__of(X34,X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),c_Int_Onumber__class_Onumber__of(X34,X3)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__diff__distrib__number__of_0) ).
fof(f28298,plain,
spl0_1148,
inference(avatar_split_clause,[],[f1088,f28296]) ).
fof(f28296,plain,
( spl0_1148
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f1088,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__power2__gt__zero__iff_2) ).
fof(f28294,plain,
spl0_1147,
inference(avatar_split_clause,[],[f1087,f28292]) ).
fof(f28292,plain,
( spl0_1147
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X9
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
fof(f1087,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X9
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__power2__gt__zero__iff_1) ).
fof(f28290,plain,
spl0_1146,
inference(avatar_split_clause,[],[f596,f28288]) ).
fof(f28288,plain,
( spl0_1146
<=> ! [X5,X4,X7,X6,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(X5,X7,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X7),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f596,axiom,
! [X3,X6,X7,X4,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(X5,X7,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X7),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).
fof(f28286,plain,
spl0_1145,
inference(avatar_split_clause,[],[f590,f28284]) ).
fof(f28284,plain,
( spl0_1145
<=> ! [X5,X4,X7,X6,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(X5,X7,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X7),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f590,axiom,
! [X3,X6,X7,X4,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(X5,X7,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X7),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).
fof(f28282,plain,
spl0_1144,
inference(avatar_split_clause,[],[f588,f28280]) ).
fof(f28280,plain,
( spl0_1144
<=> ! [X5,X4,X7,X6,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_lessequals(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(X5,X7,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X7),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f588,axiom,
! [X3,X6,X7,X4,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_lessequals(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(X5,X7,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X7),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).
fof(f28278,plain,
spl0_1143,
inference(avatar_split_clause,[],[f587,f28276]) ).
fof(f28276,plain,
( spl0_1143
<=> ! [X5,X4,X7,X6,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_lessequals(X5,X7,X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X7),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).
fof(f587,axiom,
! [X3,X6,X7,X4,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_lessequals(X5,X7,X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X7),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).
fof(f28274,plain,
spl0_1142,
inference(avatar_split_clause,[],[f505,f28272]) ).
fof(f28272,plain,
( spl0_1142
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).
fof(f505,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__power2__le__zero__iff_1) ).
fof(f28270,plain,
( ~ spl0_42
| spl0_1141
| ~ spl0_330
| ~ spl0_1128 ),
inference(avatar_split_clause,[],[f28162,f27820,f4009,f28268,f1892]) ).
fof(f1892,plain,
( spl0_42
<=> class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f28268,plain,
( spl0_1141
<=> ! [X0] :
( c_lessequals(X0,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint)
| c_HOL_Oabs__class_Oabs(X0,tc_Int_Oint) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f4009,plain,
( spl0_330
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f27820,plain,
( spl0_1128
<=> ! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f28162,plain,
( ! [X0] :
( c_lessequals(X0,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint)
| c_HOL_Oabs__class_Oabs(X0,tc_Int_Oint) = X0 )
| ~ spl0_330
| ~ spl0_1128 ),
inference(resolution,[],[f27821,f4010]) ).
fof(f4010,plain,
( ! [X3,X4] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = X4 )
| ~ spl0_330 ),
inference(avatar_component_clause,[],[f4009]) ).
fof(f27821,plain,
( ! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) )
| ~ spl0_1128 ),
inference(avatar_component_clause,[],[f27820]) ).
fof(f28266,plain,
spl0_1140,
inference(avatar_split_clause,[],[f504,f28264]) ).
fof(f28264,plain,
( spl0_1140
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X9
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f504,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X9
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__power2__le__zero__iff_0) ).
fof(f28262,plain,
spl0_1139,
inference(avatar_split_clause,[],[f495,f28260]) ).
fof(f28260,plain,
( spl0_1139
<=> ! [X4,X3,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ c_lessequals(X2,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(X3) = X4
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
fof(f495,axiom,
! [X2,X3,X1,X4] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ c_lessequals(X2,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(X3) = X4
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__diff_0) ).
fof(f28258,plain,
spl0_1138,
inference(avatar_split_clause,[],[f144,f28256]) ).
fof(f28256,plain,
( spl0_1138
<=> ! [X9,X7,X5,X27,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X5 = X7
| c_HOL_Ozero__class_Ozero(X3) = X27
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X27),X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X27),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f144,axiom,
! [X3,X9,X7,X27,X5] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X5 = X7
| c_HOL_Ozero__class_Ozero(X3) = X27
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X27),X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X27),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
fof(f28254,plain,
spl0_1137,
inference(avatar_split_clause,[],[f87,f28252]) ).
fof(f28252,plain,
( spl0_1137
<=> ! [X3,X10,X11,X8,X6,X7,X4,X5,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X11,hAPP(hAPP(X11,X4),X6)),hAPP(hAPP(X11,X5),X7)) = hAPP(hAPP(X11,hAPP(hAPP(X11,X4),X5)),hAPP(hAPP(X11,X6),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f87,axiom,
! [X3,X10,X11,X8,X6,X7,X4,X5,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X11,hAPP(hAPP(X11,X4),X6)),hAPP(hAPP(X11,X5),X7)) = hAPP(hAPP(X11,hAPP(hAPP(X11,X4),X5)),hAPP(hAPP(X11,X6),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I20_J_0) ).
fof(f28250,plain,
spl0_1136,
inference(avatar_split_clause,[],[f80,f28248]) ).
fof(f28248,plain,
( spl0_1136
<=> ! [X21,X3,X10,X11,X18,X8,X19,X12,X13,X20] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,hAPP(hAPP(X12,X18),X19)),hAPP(hAPP(X12,X20),X21)) = hAPP(hAPP(X12,hAPP(hAPP(X12,X18),X20)),hAPP(hAPP(X12,X19),X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f80,axiom,
! [X21,X3,X10,X11,X18,X8,X19,X12,X13,X20] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,hAPP(hAPP(X12,X18),X19)),hAPP(hAPP(X12,X20),X21)) = hAPP(hAPP(X12,hAPP(hAPP(X12,X18),X20)),hAPP(hAPP(X12,X19),X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I13_J_0) ).
fof(f28246,plain,
spl0_1135,
inference(avatar_split_clause,[],[f5,f28244]) ).
fof(f28244,plain,
( spl0_1135
<=> ! [X5,X4,X7,X6,X3] :
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| ~ c_lessequals(X4,X6,X3)
| ~ c_lessequals(X5,X7,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X7),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f5,axiom,
! [X3,X6,X7,X4,X5] :
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| ~ c_lessequals(X4,X6,X3)
| ~ c_lessequals(X5,X7,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X7),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_0) ).
fof(f28242,plain,
spl0_1134,
inference(avatar_split_clause,[],[f4,f28240]) ).
fof(f28240,plain,
( spl0_1134
<=> ! [X5,X4,X7,X6,X3] :
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| ~ c_lessequals(X4,X6,X3)
| ~ c_lessequals(X5,X7,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X7),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f4,axiom,
! [X3,X6,X7,X4,X5] :
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| ~ c_lessequals(X4,X6,X3)
| ~ c_lessequals(X5,X7,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X7),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
fof(f28134,plain,
spl0_1133,
inference(avatar_split_clause,[],[f1299,f28132]) ).
fof(f28132,plain,
( spl0_1133
<=> ! [X2,X4,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f1299,axiom,
! [X2,X3,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__even__eq_0) ).
fof(f28130,plain,
spl0_1132,
inference(avatar_split_clause,[],[f928,f28128]) ).
fof(f28128,plain,
( spl0_1132
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(X9,X17,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X17,X3)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f928,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(X9,X17,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X17,X3)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power2__le__imp__le_0) ).
fof(f28126,plain,
spl0_1131,
inference(avatar_split_clause,[],[f927,f28124]) ).
fof(f28124,plain,
( spl0_1131
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f927,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__power2__eq__zero__iff_1) ).
fof(f28122,plain,
spl0_1130,
inference(avatar_split_clause,[],[f926,f28120]) ).
fof(f28120,plain,
( spl0_1130
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X9
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f926,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X9
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__power2__eq__zero__iff_0) ).
fof(f28118,plain,
spl0_1129,
inference(avatar_split_clause,[],[f419,f28116]) ).
fof(f28116,plain,
( spl0_1129
<=> ! [X3,X4,X6,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| X4 = X6
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X6),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f419,axiom,
! [X2,X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| X4 = X6
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X6),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).
fof(f27822,plain,
( ~ spl0_84
| spl0_1128
| ~ spl0_241
| ~ spl0_1090 ),
inference(avatar_split_clause,[],[f26356,f26313,f2906,f27820,f2102]) ).
fof(f2906,plain,
( spl0_241
<=> ! [X9,X17,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X9,X17,X3)
| c_lessequals(X17,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f26313,plain,
( spl0_1090
<=> ! [X0] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),X0,tc_Int_Oint)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f26356,plain,
( ! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint)
| ~ class_Orderings_Olinorder(tc_Int_Oint) )
| ~ spl0_241
| ~ spl0_1090 ),
inference(resolution,[],[f26314,f2907]) ).
fof(f2907,plain,
( ! [X3,X9,X17] :
( c_lessequals(X17,X9,X3)
| c_lessequals(X9,X17,X3)
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_241 ),
inference(avatar_component_clause,[],[f2906]) ).
fof(f26314,plain,
( ! [X0] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),X0,tc_Int_Oint)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint) )
| ~ spl0_1090 ),
inference(avatar_component_clause,[],[f26313]) ).
fof(f27619,plain,
spl0_1127,
inference(avatar_split_clause,[],[f1300,f27617]) ).
fof(f1300,axiom,
! [X16,X4] :
( ~ c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)
| c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X4,X16) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,X4),X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc_Ohyps_0) ).
fof(f27615,plain,
spl0_1126,
inference(avatar_split_clause,[],[f1244,f27613]) ).
fof(f27613,plain,
( spl0_1126
<=> ! [X17,X3,X30,X2] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| ~ c_lessequals(X30,X2,tc_nat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X2),X30,tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_HOL_Ominus__class_Ominus(X2,X30,tc_nat))),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).
fof(f1244,axiom,
! [X2,X3,X17,X30] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| ~ c_lessequals(X30,X2,tc_nat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X2),X30,tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_HOL_Ominus__class_Ominus(X2,X30,tc_nat))),X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lemma__realpow__diff_0) ).
fof(f27605,plain,
spl0_1125,
inference(avatar_split_clause,[],[f1089,f27603]) ).
fof(f27603,plain,
( spl0_1125
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f1089,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__power2__gt__zero__iff_0) ).
fof(f27601,plain,
spl0_1124,
inference(avatar_split_clause,[],[f966,f27599]) ).
fof(f27599,plain,
( spl0_1124
<=> ! [X3,X4,X6,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| X4 = X6
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(c_Suc,X2)) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X6),hAPP(c_Suc,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f966,axiom,
! [X2,X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| X4 = X6
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(c_Suc,X2)) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X6),hAPP(c_Suc,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__base_0) ).
fof(f27597,plain,
spl0_1123,
inference(avatar_split_clause,[],[f813,f27595]) ).
fof(f27595,plain,
( spl0_1123
<=> ! [X17,X3,X9,X22] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X22),X17)),X17,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oinverse__class_Odivide(X9,X17,X3)),X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f813,axiom,
! [X3,X9,X17,X22] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X22),X17)),X17,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oinverse__class_Odivide(X9,X17,X3)),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__frac__num_0) ).
fof(f27593,plain,
spl0_1122,
inference(avatar_split_clause,[],[f812,f27591]) ).
fof(f27591,plain,
( spl0_1122
<=> ! [X17,X3,X9,X22] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X22),c_HOL_Oinverse__class_Odivide(X9,X17,X3)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X22),X17)),X17,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f812,axiom,
! [X3,X9,X17,X22] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X22),c_HOL_Oinverse__class_Odivide(X9,X17,X3)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X22),X17)),X17,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__num__frac_0) ).
fof(f27589,plain,
spl0_1121,
inference(avatar_split_clause,[],[f719,f27587]) ).
fof(f27587,plain,
( spl0_1121
<=> ! [X17,X9,X3,X22,X24] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| c_HOL_Ozero__class_Ozero(X3) = X22
| c_HOL_Oinverse__class_Odivide(X9,X17,X3) = c_HOL_Oinverse__class_Odivide(X24,X22,X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X24),X17) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f719,axiom,
! [X3,X9,X17,X24,X22] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| c_HOL_Ozero__class_Ozero(X3) = X22
| c_HOL_Oinverse__class_Odivide(X9,X17,X3) = c_HOL_Oinverse__class_Odivide(X24,X22,X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X24),X17) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).
fof(f27585,plain,
spl0_1120,
inference(avatar_split_clause,[],[f718,f27583]) ).
fof(f27583,plain,
( spl0_1120
<=> ! [X17,X9,X3,X22,X24] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| c_HOL_Ozero__class_Ozero(X3) = X22
| c_HOL_Oinverse__class_Odivide(X9,X17,X3) != c_HOL_Oinverse__class_Odivide(X24,X22,X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X24),X17) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f718,axiom,
! [X3,X9,X17,X24,X22] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| c_HOL_Ozero__class_Ozero(X3) = X22
| c_HOL_Oinverse__class_Odivide(X9,X17,X3) != c_HOL_Oinverse__class_Odivide(X24,X22,X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X24),X17) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).
fof(f27581,plain,
spl0_1119,
inference(avatar_split_clause,[],[f519,f27579]) ).
fof(f27579,plain,
( spl0_1119
<=> ! [X6,X4,X7,X5,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X6,X3),X7,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_HOL_Oabs__class_Oabs(X6,X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X7),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f519,axiom,
! [X3,X6,X7,X4,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X6,X3),X7,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_HOL_Oabs__class_Oabs(X6,X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X7),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult__less_0) ).
fof(f27577,plain,
spl0_1118,
inference(avatar_split_clause,[],[f503,f27575]) ).
fof(f27575,plain,
( spl0_1118
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f503,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__power2__le__zero__iff_2) ).
fof(f27573,plain,
spl0_1117,
inference(avatar_split_clause,[],[f327,f27571]) ).
fof(f27571,plain,
( spl0_1117
<=> ! [X17,X33,X32,X9,X2] :
( c_Divides_Odiv__class_Omod(X9,X2,tc_nat) = c_Divides_Odiv__class_Omod(X17,X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X32)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X33)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f327,axiom,
! [X2,X9,X17,X32,X33] :
( c_Divides_Odiv__class_Omod(X9,X2,tc_nat) = c_Divides_Odiv__class_Omod(X17,X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X32)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mod__eq__iff_1) ).
fof(f27509,plain,
( ~ spl0_48
| spl0_1116
| ~ spl0_88
| ~ spl0_249
| ~ spl0_481
| ~ spl0_1108 ),
inference(avatar_split_clause,[],[f27232,f27022,f5954,f2938,f2122,f27507,f1922]) ).
fof(f1922,plain,
( spl0_48
<=> class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f27507,plain,
( spl0_1116
<=> ! [X0] : c_lessequals(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint),c_HOL_Oabs__class_Oabs(X0,tc_Int_Oint),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f2122,plain,
( spl0_88
<=> class_Int_Onumber__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f2938,plain,
( spl0_249
<=> ! [X3] :
( ~ class_Int_Onumber__ring(X3)
| c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f5954,plain,
( spl0_481
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X6,X3),X4,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f27022,plain,
( spl0_1108
<=> ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X0,tc_Int_Oint),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f27232,plain,
( ! [X0] :
( c_lessequals(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint),c_HOL_Oabs__class_Oabs(X0,tc_Int_Oint),tc_Int_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) )
| ~ spl0_88
| ~ spl0_249
| ~ spl0_481
| ~ spl0_1108 ),
inference(forward_demodulation,[],[f27224,f3191]) ).
fof(f3191,plain,
( c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint)
| ~ spl0_88
| ~ spl0_249 ),
inference(resolution,[],[f2939,f2124]) ).
fof(f2124,plain,
( class_Int_Onumber__ring(tc_Int_Oint)
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f2122]) ).
fof(f2939,plain,
( ! [X3] :
( ~ class_Int_Onumber__ring(X3)
| c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3) )
| ~ spl0_249 ),
inference(avatar_component_clause,[],[f2938]) ).
fof(f27224,plain,
( ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),c_HOL_Oabs__class_Oabs(X0,tc_Int_Oint),tc_Int_Oint) )
| ~ spl0_481
| ~ spl0_1108 ),
inference(resolution,[],[f27023,f5955]) ).
fof(f5955,plain,
( ! [X3,X6,X4] :
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X6,X3),X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X6,X3) )
| ~ spl0_481 ),
inference(avatar_component_clause,[],[f5954]) ).
fof(f27023,plain,
( ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X0,tc_Int_Oint),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint)
| ~ spl0_1108 ),
inference(avatar_component_clause,[],[f27022]) ).
fof(f27052,plain,
spl0_1115,
inference(avatar_split_clause,[],[f1631,f27050]) ).
fof(f27050,plain,
( spl0_1115
<=> ! [X2,X1] :
( c_Fact_Ofact__class_Ofact(c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X1),X2,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Fact_Ofact__class_Ofact(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)),c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X1),X2,tc_nat))
| ~ c_HOL_Oord__class_Oless(X2,hAPP(c_Suc,X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f1631,plain,
! [X2,X1] :
( c_Fact_Ofact__class_Ofact(c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X1),X2,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Fact_Ofact__class_Ofact(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)),c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X1),X2,tc_nat))
| ~ c_HOL_Oord__class_Oless(X2,hAPP(c_Suc,X1),tc_nat) ),
inference(forward_demodulation,[],[f1249,f1416]) ).
fof(f1416,axiom,
! [X2,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
fof(f1249,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X2,hAPP(c_Suc,X1),tc_nat)
| c_Fact_Ofact__class_Ofact(c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X1),X2,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X1),X2,tc_nat)),c_Fact_Ofact__class_Ofact(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fact__diff__Suc_0) ).
fof(f27048,plain,
spl0_1114,
inference(avatar_split_clause,[],[f1377,f27046]) ).
fof(f27046,plain,
( spl0_1114
<=> ! [X17,X9,X3,X22,X24] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oinverse__class_Odivide(X9,X17,X3)),c_HOL_Oinverse__class_Odivide(X22,X24,X3)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X22),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X24),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).
fof(f1377,axiom,
! [X3,X9,X17,X24,X22] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oinverse__class_Odivide(X9,X17,X3)),c_HOL_Oinverse__class_Odivide(X22,X24,X3)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X22),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X24),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).
fof(f27044,plain,
spl0_1113,
inference(avatar_split_clause,[],[f1107,f27042]) ).
fof(f27042,plain,
( spl0_1113
<=> ! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f1107,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).
fof(f27040,plain,
spl0_1112,
inference(avatar_split_clause,[],[f1018,f27038]) ).
fof(f27038,plain,
( spl0_1112
<=> ! [X2,X1,X23] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = X23
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X23),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),hAPP(c_Suc,X23)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f1018,axiom,
! [X2,X1,X23] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = X23
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X23),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),hAPP(c_Suc,X23)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div__lemma_0) ).
fof(f27036,plain,
spl0_1111,
inference(avatar_split_clause,[],[f929,f27034]) ).
fof(f27034,plain,
( spl0_1111
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).
fof(f929,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__power2__eq__zero__iff_2) ).
fof(f27032,plain,
spl0_1110,
inference(avatar_split_clause,[],[f490,f27030]) ).
fof(f27030,plain,
( spl0_1110
<=> ! [X15,X9,X2,X1] :
( ~ hBOOL(hAPP(X15,X9))
| hBOOL(hAPP(X15,c_Divides_Odiv__class_Odiv(X1,X2,tc_nat)))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X9),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),hAPP(c_Suc,X9)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).
fof(f490,axiom,
! [X2,X1,X9,X15] :
( ~ hBOOL(hAPP(X15,X9))
| hBOOL(hAPP(X15,c_Divides_Odiv__class_Odiv(X1,X2,tc_nat)))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X9),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),hAPP(c_Suc,X9)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div_H_7) ).
fof(f27028,plain,
spl0_1109,
inference(avatar_split_clause,[],[f282,f27026]) ).
fof(f27026,plain,
( spl0_1109
<=> ! [X3,X10,X11,X8,X9,X23,X12,X30,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,hAPP(hAPP(X8,X9),X30)),hAPP(hAPP(X8,X9),X23)) = hAPP(hAPP(X8,X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X30),X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).
fof(f282,axiom,
! [X3,X10,X11,X8,X9,X12,X23,X13,X30] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,hAPP(hAPP(X8,X9),X30)),hAPP(hAPP(X8,X9),X23)) = hAPP(hAPP(X8,X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X30),X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Omul__pwr_0) ).
fof(f27024,plain,
( ~ spl0_42
| spl0_1108
| ~ spl0_290
| ~ spl0_1100 ),
inference(avatar_split_clause,[],[f26879,f26730,f3491,f27022,f1892]) ).
fof(f3491,plain,
( spl0_290
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X4,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f26730,plain,
( spl0_1100
<=> ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f26879,plain,
( ! [X0] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X0,tc_Int_Oint),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint) )
| ~ spl0_290
| ~ spl0_1100 ),
inference(resolution,[],[f26731,f3492]) ).
fof(f3492,plain,
( ! [X3,X4] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X4,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) )
| ~ spl0_290 ),
inference(avatar_component_clause,[],[f3491]) ).
fof(f26731,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) )
| ~ spl0_1100 ),
inference(avatar_component_clause,[],[f26730]) ).
fof(f27020,plain,
spl0_1107,
inference(avatar_split_clause,[],[f262,f27018]) ).
fof(f27018,plain,
( spl0_1107
<=> ! [X5,X4,X6,X3] :
( ~ class_Divides_Osemiring__div(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),c_Divides_Odiv__class_Odiv(X4,X6,X3))),c_Divides_Odiv__class_Omod(X4,X6,X3))),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f262,axiom,
! [X3,X6,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),c_Divides_Odiv__class_Odiv(X4,X6,X3))),c_Divides_Odiv__class_Omod(X4,X6,X3))),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mod__equality2_0) ).
fof(f27016,plain,
spl0_1106,
inference(avatar_split_clause,[],[f261,f27014]) ).
fof(f27014,plain,
( spl0_1106
<=> ! [X5,X4,X6,X3] :
( ~ class_Divides_Osemiring__div(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Divides_Odiv__class_Odiv(X4,X6,X3)),X6)),c_Divides_Odiv__class_Omod(X4,X6,X3))),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).
fof(f261,axiom,
! [X3,X6,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Divides_Odiv__class_Odiv(X4,X6,X3)),X6)),c_Divides_Odiv__class_Omod(X4,X6,X3))),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mod__equality_0) ).
fof(f27012,plain,
spl0_1105,
inference(avatar_split_clause,[],[f177,f27010]) ).
fof(f27010,plain,
( spl0_1105
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_HOL_Oabs__class_Oabs(X6,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).
fof(f177,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_HOL_Oabs__class_Oabs(X6,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__mult_0) ).
fof(f27008,plain,
spl0_1104,
inference(avatar_split_clause,[],[f176,f27006]) ).
fof(f27006,plain,
( spl0_1104
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_HOL_Oabs__class_Oabs(X6,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).
fof(f176,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_HOL_Oabs__class_Oabs(X6,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__mult_1) ).
fof(f27004,plain,
spl0_1103,
inference(avatar_split_clause,[],[f175,f27002]) ).
fof(f27002,plain,
( spl0_1103
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_HOL_Oabs__class_Oabs(X6,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).
fof(f175,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_HOL_Oabs__class_Oabs(X6,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__mult_2) ).
fof(f27000,plain,
spl0_1102,
inference(avatar_split_clause,[],[f174,f26998]) ).
fof(f26998,plain,
( spl0_1102
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_HOL_Oabs__class_Oabs(X6,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f174,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_HOL_Oabs__class_Oabs(X6,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__mult_3) ).
fof(f26996,plain,
spl0_1101,
inference(avatar_split_clause,[],[f151,f26994]) ).
fof(f26994,plain,
( spl0_1101
<=> ! [X5,X23,X6,X27] :
( ~ c_HOL_Oord__class_Oless(X27,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X6),c_Divides_Odiv__class_Omod(X23,X5,tc_nat))),X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X6),X5),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f151,axiom,
! [X6,X27,X5,X23] :
( ~ c_HOL_Oord__class_Oless(X27,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X6),c_Divides_Odiv__class_Omod(X23,X5,tc_nat))),X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X6),X5),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__lemma_0) ).
fof(f26732,plain,
( ~ spl0_83
| spl0_1100
| ~ spl0_473
| ~ spl0_1061 ),
inference(avatar_split_clause,[],[f25586,f25503,f5902,f26730,f2097]) ).
fof(f5902,plain,
( spl0_473
<=> ! [X17,X3,X9,X22] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X9,X17,X3)
| ~ c_lessequals(X17,X22,X3)
| c_lessequals(X9,X22,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f25586,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| ~ class_Orderings_Opreorder(tc_Int_Oint)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) )
| ~ spl0_473
| ~ spl0_1061 ),
inference(resolution,[],[f25505,f5903]) ).
fof(f5903,plain,
( ! [X3,X9,X17,X22] :
( ~ c_lessequals(X17,X22,X3)
| ~ c_lessequals(X9,X17,X3)
| ~ class_Orderings_Opreorder(X3)
| c_lessequals(X9,X22,X3) )
| ~ spl0_473 ),
inference(avatar_component_clause,[],[f5902]) ).
fof(f26351,plain,
spl0_1099,
inference(avatar_split_clause,[],[f1364,f26349]) ).
fof(f26349,plain,
( spl0_1099
<=> ! [X17,X23,X9,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X17)),X23) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X23)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).
fof(f1364,axiom,
! [X3,X9,X17,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X17)),X23) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X23)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
fof(f26347,plain,
spl0_1098,
inference(avatar_split_clause,[],[f1363,f26345]) ).
fof(f26345,plain,
( spl0_1098
<=> ! [X3,X4,X6,X2] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6)),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X6),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).
fof(f1363,axiom,
! [X2,X3,X6,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6)),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X6),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
fof(f26343,plain,
spl0_1097,
inference(avatar_split_clause,[],[f1250,f26341]) ).
fof(f26341,plain,
( spl0_1097
<=> ! [X2,X0,X7] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X7),X2))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X7),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f1250,axiom,
! [X2,X0,X7] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X7),X2))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X7),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__cancel_0) ).
fof(f26339,plain,
spl0_1096,
inference(avatar_split_clause,[],[f1243,f26337]) ).
fof(f26337,plain,
( spl0_1096
<=> ! [X28,X4,X3,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(X2,X28,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X28),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).
fof(f1243,axiom,
! [X2,X3,X28,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(X2,X28,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X28),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).
fof(f26335,plain,
spl0_1095,
inference(avatar_split_clause,[],[f1086,f26333]) ).
fof(f26333,plain,
( spl0_1095
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).
fof(f1086,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__sum__power2__lt__zero_0) ).
fof(f26331,plain,
spl0_1094,
inference(avatar_split_clause,[],[f1069,f26329]) ).
fof(f26329,plain,
( spl0_1094
<=> ! [X2,X4,X3] :
( ~ class_Ring__and__Field_Oring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(X4,X3)),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3)),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
fof(f1069,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Oring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(X4,X3)),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3)),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__minus_0) ).
fof(f26327,plain,
spl0_1093,
inference(avatar_split_clause,[],[f874,f26325]) ).
fof(f26325,plain,
( spl0_1093
<=> ! [X3,X4,X6,X2] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X6
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Oinverse__class_Odivide(X4,X6,X3)),X2) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X6),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).
fof(f874,axiom,
! [X2,X3,X6,X4] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X6
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Oinverse__class_Odivide(X4,X6,X3)),X2) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X6),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).
fof(f26323,plain,
spl0_1092,
inference(avatar_split_clause,[],[f810,f26321]) ).
fof(f26321,plain,
( spl0_1092
<=> ! [X3,X4,X6,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X6),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f810,axiom,
! [X2,X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X6),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
fof(f26319,plain,
spl0_1091,
inference(avatar_split_clause,[],[f708,f26317]) ).
fof(f26317,plain,
( spl0_1091
<=> ! [X9,X23,X30,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X30)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X23)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X30),X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f708,axiom,
! [X3,X9,X23,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X30)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X23)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X30),X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__pwr_0) ).
fof(f26315,plain,
( ~ spl0_86
| spl0_1090
| ~ spl0_474
| ~ spl0_1061 ),
inference(avatar_split_clause,[],[f25585,f25503,f5906,f26313,f2112]) ).
fof(f5906,plain,
( spl0_474
<=> ! [X17,X3,X9,X22] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X17,X9,X3)
| ~ c_lessequals(X22,X17,X3)
| c_lessequals(X22,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f25585,plain,
( ! [X0] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),X0,tc_Int_Oint)
| ~ class_Orderings_Oorder(tc_Int_Oint)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint) )
| ~ spl0_474
| ~ spl0_1061 ),
inference(resolution,[],[f25505,f5907]) ).
fof(f5907,plain,
( ! [X3,X9,X17,X22] :
( ~ c_lessequals(X22,X17,X3)
| ~ c_lessequals(X17,X9,X3)
| ~ class_Orderings_Oorder(X3)
| c_lessequals(X22,X9,X3) )
| ~ spl0_474 ),
inference(avatar_component_clause,[],[f5906]) ).
fof(f26311,plain,
spl0_1089,
inference(avatar_split_clause,[],[f707,f26309]) ).
fof(f26309,plain,
( spl0_1089
<=> ! [X4,X3,X2,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f707,axiom,
! [X2,X3,X1,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__add_0) ).
fof(f26307,plain,
spl0_1088,
inference(avatar_split_clause,[],[f640,f26305]) ).
fof(f26305,plain,
( spl0_1088
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f640,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
fof(f26303,plain,
spl0_1087,
inference(avatar_split_clause,[],[f638,f26301]) ).
fof(f26301,plain,
( spl0_1087
<=> ! [X31,X4,X6,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X31)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X31)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f638,axiom,
! [X31,X3,X6,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X31)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X31)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oadd__right_0) ).
fof(f26299,plain,
spl0_1086,
inference(avatar_split_clause,[],[f636,f26297]) ).
fof(f26297,plain,
( spl0_1086
<=> ! [X3,X4,X6,X29] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X29)),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X29),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f636,axiom,
! [X3,X29,X6,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X29)),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X29),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oadd__left_0) ).
fof(f26295,plain,
spl0_1085,
inference(avatar_split_clause,[],[f635,f26293]) ).
fof(f26293,plain,
( spl0_1085
<=> ! [X17,X3,X9,X22] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X17),X22)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X17)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).
fof(f635,axiom,
! [X3,X9,X17,X22] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X17),X22)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X17)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
fof(f26291,plain,
spl0_1084,
inference(avatar_split_clause,[],[f634,f26289]) ).
fof(f26289,plain,
( spl0_1084
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f634,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
fof(f26287,plain,
spl0_1083,
inference(avatar_split_clause,[],[f502,f26285]) ).
fof(f26285,plain,
( spl0_1083
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).
fof(f502,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__power2__ge__zero_0) ).
fof(f26283,plain,
spl0_1082,
inference(avatar_split_clause,[],[f284,f26281]) ).
fof(f26281,plain,
( spl0_1082
<=> ! [X5,X4,X6,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = X6
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),c_Divides_Odiv__class_Odiv(X4,X6,X3)) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5)),X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).
fof(f284,axiom,
! [X3,X6,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = X6
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),c_Divides_Odiv__class_Odiv(X4,X6,X3)) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5)),X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self2_0) ).
fof(f26279,plain,
spl0_1081,
inference(avatar_split_clause,[],[f283,f26277]) ).
fof(f26277,plain,
( spl0_1081
<=> ! [X5,X4,X6,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = X6
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6)),X6,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),c_Divides_Odiv__class_Odiv(X4,X6,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).
fof(f283,axiom,
! [X3,X6,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = X6
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6)),X6,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),c_Divides_Odiv__class_Odiv(X4,X6,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1_0) ).
fof(f26275,plain,
spl0_1080,
inference(avatar_split_clause,[],[f268,f26273]) ).
fof(f26273,plain,
( spl0_1080
<=> ! [X28,X4,X3,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(X2,X28,tc_nat)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X28),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f268,axiom,
! [X2,X3,X28,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(X2,X28,tc_nat)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X28),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__decreasing_0) ).
fof(f26262,plain,
spl0_1079,
inference(avatar_split_clause,[],[f152,f26260]) ).
fof(f26260,plain,
( spl0_1079
<=> ! [X6,X4,X5] : c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X6),X5),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X6),c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(X4,X6,tc_nat),X5,tc_nat))),c_Divides_Odiv__class_Omod(X4,X6,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f152,axiom,
! [X6,X4,X5] : c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X6),X5),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X6),c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(X4,X6,tc_nat),X5,tc_nat))),c_Divides_Odiv__class_Omod(X4,X6,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult2__eq_0) ).
fof(f26258,plain,
spl0_1078,
inference(avatar_split_clause,[],[f145,f26256]) ).
fof(f26256,plain,
( spl0_1078
<=> ! [X5,X7,X9,X27] :
( X5 = X7
| c_HOL_Ozero__class_Ozero(tc_nat) = X27
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X27),X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X27),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).
fof(f145,axiom,
! [X9,X7,X27,X5] :
( X5 = X7
| c_HOL_Ozero__class_Ozero(tc_nat) = X27
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X27),X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X27),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__scale__eq__noteq_0) ).
fof(f26254,plain,
spl0_1077,
inference(avatar_split_clause,[],[f101,f26252]) ).
fof(f26252,plain,
( spl0_1077
<=> ! [X3,X10,X11,X8,X9,X17,X12,X23,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X8,hAPP(hAPP(X12,X9),X17)),X23) = hAPP(hAPP(X12,hAPP(hAPP(X8,X9),X23)),hAPP(hAPP(X8,X17),X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).
fof(f101,axiom,
! [X3,X10,X11,X8,X9,X17,X12,X23,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X8,hAPP(hAPP(X12,X9),X17)),X23) = hAPP(hAPP(X12,hAPP(hAPP(X8,X9),X23)),hAPP(hAPP(X8,X17),X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__mul_0) ).
fof(f26250,plain,
spl0_1076,
inference(avatar_split_clause,[],[f100,f26248]) ).
fof(f26248,plain,
( spl0_1076
<=> ! [X3,X10,X11,X8,X9,X17,X22,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,X9),hAPP(hAPP(X11,X17),X22)) = hAPP(hAPP(X11,hAPP(hAPP(X12,X9),X17)),hAPP(hAPP(X12,X9),X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
fof(f100,axiom,
! [X3,X10,X11,X8,X9,X17,X22,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,X9),hAPP(hAPP(X11,X17),X22)) = hAPP(hAPP(X11,hAPP(hAPP(X12,X9),X17)),hAPP(hAPP(X12,X9),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Omul__d_0) ).
fof(f26246,plain,
spl0_1075,
inference(avatar_split_clause,[],[f75,f26244]) ).
fof(f26244,plain,
( spl0_1075
<=> ! [X3,X10,X11,X8,X6,X4,X5,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,hAPP(hAPP(X11,X4),X6)),X5) = hAPP(hAPP(X11,hAPP(hAPP(X12,X4),X5)),hAPP(hAPP(X12,X6),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f75,axiom,
! [X3,X10,X11,X8,X6,X4,X5,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,hAPP(hAPP(X11,X4),X6)),X5) = hAPP(hAPP(X11,hAPP(hAPP(X12,X4),X5)),hAPP(hAPP(X12,X6),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I8_J_0) ).
fof(f26141,plain,
spl0_1074,
inference(avatar_split_clause,[],[f965,f26139]) ).
fof(f26139,plain,
( spl0_1074
<=> ! [X3,X4,X6,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(c_Suc,X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X6),hAPP(c_Suc,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f965,axiom,
! [X2,X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(c_Suc,X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X6),hAPP(c_Suc,X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).
fof(f26137,plain,
spl0_1073,
inference(avatar_split_clause,[],[f780,f26135]) ).
fof(f26135,plain,
( spl0_1073
<=> ! [X5,X4,X7,X6,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X7),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ominus__class_Ominus(X4,X6,X3)),c_HOL_Ominus__class_Ominus(X5,X7,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f780,axiom,
! [X3,X6,X7,X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X7),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ominus__class_Ominus(X4,X6,X3)),c_HOL_Ominus__class_Ominus(X5,X7,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).
fof(f26133,plain,
( ~ spl0_66
| ~ spl0_951
| ~ spl0_1072
| ~ spl0_537
| ~ spl0_1051 ),
inference(avatar_split_clause,[],[f25126,f24503,f7450,f26130,f21188,f2012]) ).
fof(f2012,plain,
( spl0_66
<=> class_Ring__and__Field_Oordered__idom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f21188,plain,
( spl0_951
<=> c_Parity_Oeven__odd__class_Oeven(v_ka____,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f26130,plain,
( spl0_1072
<=> c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f7450,plain,
( spl0_537
<=> ! [X2,X9,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f25126,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| ~ c_Parity_Oeven__odd__class_Oeven(v_ka____,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(tc_Int_Oint)
| ~ spl0_537
| ~ spl0_1051 ),
inference(superposition,[],[f7451,f24505]) ).
fof(f7451,plain,
( ! [X2,X3,X9] :
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X3) )
| ~ spl0_537 ),
inference(avatar_component_clause,[],[f7450]) ).
fof(f26128,plain,
spl0_1071,
inference(avatar_split_clause,[],[f292,f26126]) ).
fof(f26126,plain,
( spl0_1071
<=> ! [X0,X14,X16,X15] :
( ~ c_HOL_Oord__class_Oless(X14,X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| hBOOL(hAPP(X15,X16))
| ~ hBOOL(hAPP(X15,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X16)),X14),X0,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f292,axiom,
! [X0,X16,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X14,X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| hBOOL(hAPP(X15,X16))
| ~ hBOOL(hAPP(X15,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X16)),X14),X0,tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div_1) ).
fof(f26083,plain,
( spl0_1070
| ~ spl0_436
| ~ spl0_701
| ~ spl0_1069 ),
inference(avatar_split_clause,[],[f26079,f26076,f12064,f4888,f26081]) ).
fof(f26081,plain,
( spl0_1070
<=> ! [X0,X14,X15] :
( ~ hBOOL(hAPP(X15,c_Divides_Odiv__class_Omod(X14,X0,tc_nat)))
| ~ c_HOL_Oord__class_Oless(X14,X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| hBOOL(hAPP(X15,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f4888,plain,
( spl0_436
<=> ! [X2,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f12064,plain,
( spl0_701
<=> ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2)),X1),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f26076,plain,
( spl0_1069
<=> ! [X0,X14,X16,X15] :
( ~ c_HOL_Oord__class_Oless(X14,X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| hBOOL(hAPP(X15,X14))
| ~ hBOOL(hAPP(X15,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X16)),X14),X0,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f26079,plain,
( ! [X0,X14,X15] :
( ~ hBOOL(hAPP(X15,c_Divides_Odiv__class_Omod(X14,X0,tc_nat)))
| ~ c_HOL_Oord__class_Oless(X14,X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| hBOOL(hAPP(X15,X14)) )
| ~ spl0_436
| ~ spl0_701
| ~ spl0_1069 ),
inference(forward_demodulation,[],[f26077,f12286]) ).
fof(f12286,plain,
( ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(X2,X1,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0)),X2),X1,tc_nat)
| ~ spl0_436
| ~ spl0_701 ),
inference(superposition,[],[f12065,f4889]) ).
fof(f4889,plain,
( ! [X2,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X1)
| ~ spl0_436 ),
inference(avatar_component_clause,[],[f4888]) ).
fof(f12065,plain,
( ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2)),X1),X2,tc_nat)
| ~ spl0_701 ),
inference(avatar_component_clause,[],[f12064]) ).
fof(f26077,plain,
( ! [X0,X16,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X14,X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| hBOOL(hAPP(X15,X14))
| ~ hBOOL(hAPP(X15,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X16)),X14),X0,tc_nat))) )
| ~ spl0_1069 ),
inference(avatar_component_clause,[],[f26076]) ).
fof(f26078,plain,
spl0_1069,
inference(avatar_split_clause,[],[f15,f26076]) ).
fof(f15,axiom,
! [X0,X16,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X14,X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| hBOOL(hAPP(X15,X14))
| ~ hBOOL(hAPP(X15,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X16)),X14),X0,tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mod_1) ).
fof(f25539,plain,
spl0_1068,
inference(avatar_split_clause,[],[f1390,f25537]) ).
fof(f25537,plain,
( spl0_1068
<=> ! [X3,X4,X6,X2] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Oinverse__class_Odivide(X4,X6,X3)),X2) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X6),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f1390,axiom,
! [X2,X3,X6,X4] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Oinverse__class_Odivide(X4,X6,X3)),X2) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X6),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__divide_0) ).
fof(f25535,plain,
spl0_1067,
inference(avatar_split_clause,[],[f1294,f25533]) ).
fof(f25533,plain,
( spl0_1067
<=> ! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2))),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f1294,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2))),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__power__less__zero_0) ).
fof(f25531,plain,
spl0_1066,
inference(avatar_split_clause,[],[f1152,f25529]) ).
fof(f25529,plain,
( spl0_1066
<=> ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f1152,axiom,
! [X2,X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mult__distrib2_0) ).
fof(f25527,plain,
spl0_1065,
inference(avatar_split_clause,[],[f1151,f25525]) ).
fof(f25525,plain,
( spl0_1065
<=> ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f1151,axiom,
! [X2,X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mult__distrib_0) ).
fof(f25523,plain,
spl0_1064,
inference(avatar_split_clause,[],[f1106,f25521]) ).
fof(f25521,plain,
( spl0_1064
<=> ! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f1106,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2))),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__0__le__power__imp__0__le_0) ).
fof(f25519,plain,
spl0_1063,
inference(avatar_split_clause,[],[f1081,f25517]) ).
fof(f25517,plain,
( spl0_1063
<=> ! [X5,X24,X6,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Oinverse__class_Odivide(X6,X5,X3) != c_Int_Onumber__class_Onumber__of(X24,X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Int_Onumber__class_Onumber__of(X24,X3)),X5) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f1081,axiom,
! [X3,X6,X24,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Oinverse__class_Odivide(X6,X5,X3) != c_Int_Onumber__class_Onumber__of(X24,X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Int_Onumber__class_Onumber__of(X24,X3)),X5) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_0) ).
fof(f25515,plain,
spl0_1062,
inference(avatar_split_clause,[],[f131,f25513]) ).
fof(f25513,plain,
( spl0_1062
<=> ! [X3,X17,X9,X25,X22] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X22) = X25
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X17),X22)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X17),X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).
fof(f131,axiom,
! [X3,X9,X17,X22,X25] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X22) = X25
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X17),X22)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X17),X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
fof(f25506,plain,
( ~ spl0_66
| ~ spl0_951
| spl0_1061
| ~ spl0_530
| ~ spl0_1051 ),
inference(avatar_split_clause,[],[f25125,f24503,f7421,f25503,f21188,f2012]) ).
fof(f7421,plain,
( spl0_530
<=> ! [X2,X9,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f25125,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint)
| ~ c_Parity_Oeven__odd__class_Oeven(v_ka____,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(tc_Int_Oint)
| ~ spl0_530
| ~ spl0_1051 ),
inference(superposition,[],[f7422,f24505]) ).
fof(f7422,plain,
( ! [X2,X3,X9] :
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X3) )
| ~ spl0_530 ),
inference(avatar_component_clause,[],[f7421]) ).
fof(f25396,plain,
spl0_1060,
inference(avatar_split_clause,[],[f1297,f25394]) ).
fof(f25394,plain,
( spl0_1060
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3)),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f1297,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3)),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__minus1__odd_0) ).
fof(f25392,plain,
spl0_1059,
inference(avatar_split_clause,[],[f1148,f25390]) ).
fof(f25390,plain,
( spl0_1059
<=> ! [X3,X10,X11,X8,X9,X23,X12,X30,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X8,hAPP(hAPP(X8,X9),X30)),X23) = hAPP(hAPP(X8,X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X30),X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f1148,axiom,
! [X3,X10,X11,X8,X9,X12,X23,X13,X30] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X8,hAPP(hAPP(X8,X9),X30)),X23) = hAPP(hAPP(X8,X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X30),X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__pwr_0) ).
fof(f25388,plain,
spl0_1058,
inference(avatar_split_clause,[],[f710,f25386]) ).
fof(f25386,plain,
( spl0_1058
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Oinverse__class_Odivide(X4,X6,X3) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).
fof(f710,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Oinverse__class_Odivide(X4,X6,X3) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).
fof(f25384,plain,
spl0_1057,
inference(avatar_split_clause,[],[f709,f25382]) ).
fof(f25382,plain,
( spl0_1057
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Oinverse__class_Odivide(X4,X6,X3) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f709,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Oinverse__class_Odivide(X4,X6,X3) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).
fof(f25335,plain,
spl0_1056,
inference(avatar_split_clause,[],[f626,f25333]) ).
fof(f25333,plain,
( spl0_1056
<=> ! [X5,X4,X6,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X5,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Divides_Odiv__class_Omod(X4,X5,X3)),c_Divides_Odiv__class_Omod(X6,X5,X3)),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f626,axiom,
! [X3,X6,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X5,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Divides_Odiv__class_Omod(X4,X5,X3)),c_Divides_Odiv__class_Omod(X6,X5,X3)),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__eq_0) ).
fof(f25331,plain,
spl0_1055,
inference(avatar_split_clause,[],[f607,f25329]) ).
fof(f25329,plain,
( spl0_1055
<=> ! [X4,X9,X27,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X27,X3),X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X27),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X9,X4,X3),X3),X27,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f607,axiom,
! [X3,X9,X27,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X27,X3),X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X27),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X9,X4,X3),X3),X27,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__diff__less__iff_2) ).
fof(f25327,plain,
spl0_1054,
inference(avatar_split_clause,[],[f360,f25325]) ).
fof(f25325,plain,
( spl0_1054
<=> ! [X5,X4,X6,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X5,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Omod(X4,X5,X3)),c_Divides_Odiv__class_Omod(X6,X5,X3)),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f360,axiom,
! [X3,X6,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X5,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Omod(X4,X5,X3)),c_Divides_Odiv__class_Omod(X6,X5,X3)),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).
fof(f25323,plain,
spl0_1053,
inference(avatar_split_clause,[],[f187,f25321]) ).
fof(f25321,plain,
( spl0_1053
<=> ! [X17,X3,X9,X2] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X9,X3),c_HOL_Oabs__class_Oabs(X17,X3),X3)
| c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f187,axiom,
! [X2,X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X9,X3),c_HOL_Oabs__class_Oabs(X17,X3),X3)
| c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono__even_0) ).
fof(f24746,plain,
( spl0_1052
| ~ spl0_121
| ~ spl0_1034 ),
inference(avatar_split_clause,[],[f24396,f24351,f2287,f24743]) ).
fof(f2287,plain,
( spl0_121
<=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f24351,plain,
( spl0_1034
<=> ! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0)),v_ka____) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f24396,plain,
( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Complex_Ocomplex)),v_ka____)
| ~ spl0_121
| ~ spl0_1034 ),
inference(resolution,[],[f24352,f2289]) ).
fof(f2289,plain,
( class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f2287]) ).
fof(f24352,plain,
( ! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0)),v_ka____) )
| ~ spl0_1034 ),
inference(avatar_component_clause,[],[f24351]) ).
fof(f24506,plain,
( spl0_1051
| ~ spl0_88
| ~ spl0_1034 ),
inference(avatar_split_clause,[],[f24395,f24351,f2122,f24503]) ).
fof(f24395,plain,
( c_HOL_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint)),v_ka____)
| ~ spl0_88
| ~ spl0_1034 ),
inference(resolution,[],[f24352,f2124]) ).
fof(f24494,plain,
spl0_1050,
inference(avatar_split_clause,[],[f1677,f24492]) ).
fof(f24492,plain,
( spl0_1050
<=> ! [X2,X1] :
( c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f1677,plain,
! [X2,X1] :
( c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2,tc_nat) ),
inference(forward_demodulation,[],[f1676,f421]) ).
fof(f1676,plain,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat) ),
inference(forward_demodulation,[],[f1675,f421]) ).
fof(f1675,plain,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat) ),
inference(forward_demodulation,[],[f1096,f421]) ).
fof(f1096,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__mult_0) ).
fof(f24490,plain,
spl0_1049,
inference(avatar_split_clause,[],[f1670,f24488]) ).
fof(f24488,plain,
( spl0_1049
<=> ! [X2,X1] :
( c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat)
| ~ c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2,tc_nat)
| ~ c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f1670,plain,
! [X2,X1] :
( c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat)
| ~ c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2,tc_nat)
| ~ c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat) ),
inference(forward_demodulation,[],[f1669,f421]) ).
fof(f1669,plain,
! [X2,X1] :
( ~ c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2,tc_nat)
| ~ c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat)
| c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat) ),
inference(forward_demodulation,[],[f1668,f421]) ).
fof(f1668,plain,
! [X2,X1] :
( ~ c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat)
| ~ c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat) ),
inference(forward_demodulation,[],[f1019,f421]) ).
fof(f1019,axiom,
! [X2,X1] :
( ~ c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__mult__iff_2) ).
fof(f24486,plain,
spl0_1048,
inference(avatar_split_clause,[],[f1430,f24484]) ).
fof(f24484,plain,
( spl0_1048
<=> ! [X17,X36,X9,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X9,X17,X3)),X36) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X36),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X36),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f1430,axiom,
! [X3,X36,X9,X17] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X9,X17,X3)),X36) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X36),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X36),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Odiff_0) ).
fof(f24482,plain,
spl0_1047,
inference(avatar_split_clause,[],[f1426,f24480]) ).
fof(f24480,plain,
( spl0_1047
<=> ! [X31,X4,X6,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_HOL_Ominus__class_Ominus(X6,X31,X3)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X31),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f1426,axiom,
! [X31,X3,X6,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_HOL_Ominus__class_Ominus(X6,X31,X3)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X31),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Odiff__right_0) ).
fof(f24478,plain,
spl0_1046,
inference(avatar_split_clause,[],[f1373,f24476]) ).
fof(f24476,plain,
( spl0_1046
<=> ! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f1373,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).
fof(f24400,plain,
( spl0_1045
| ~ spl0_121
| ~ spl0_249
| ~ spl0_1044 ),
inference(avatar_split_clause,[],[f24394,f24391,f2938,f2287,f24398]) ).
fof(f24398,plain,
( spl0_1045
<=> ! [X2] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2))),X2) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Complex_Ocomplex)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f24391,plain,
( spl0_1044
<=> ! [X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f24394,plain,
( ! [X2] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2))),X2) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Complex_Ocomplex)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) )
| ~ spl0_121
| ~ spl0_249
| ~ spl0_1044 ),
inference(forward_demodulation,[],[f24392,f3192]) ).
fof(f3192,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Complex_Ocomplex)
| ~ spl0_121
| ~ spl0_249 ),
inference(resolution,[],[f2939,f2289]) ).
fof(f24392,plain,
( ! [X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2))),X2) )
| ~ spl0_1044 ),
inference(avatar_component_clause,[],[f24391]) ).
fof(f24393,plain,
spl0_1044,
inference(avatar_split_clause,[],[f1251,f24391]) ).
fof(f1251,axiom,
! [X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2))),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__cancel2_0) ).
fof(f24389,plain,
spl0_1043,
inference(avatar_split_clause,[],[f762,f24387]) ).
fof(f24387,plain,
( spl0_1043
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(X17,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X17,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X9),X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).
fof(f762,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(X17,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X17,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X9),X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).
fof(f24385,plain,
spl0_1042,
inference(avatar_split_clause,[],[f761,f24383]) ).
fof(f24383,plain,
( spl0_1042
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(X17,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X17,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X17),X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).
fof(f761,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(X17,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X17,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X17),X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).
fof(f24381,plain,
spl0_1041,
inference(avatar_split_clause,[],[f654,f24379]) ).
fof(f24379,plain,
( spl0_1041
<=> ! [X4,X1,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),c_HOL_Oone__class_Oone(X3))),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).
fof(f654,axiom,
! [X3,X1,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),c_HOL_Oone__class_Oone(X3))),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
fof(f24377,plain,
spl0_1040,
inference(avatar_split_clause,[],[f653,f24375]) ).
fof(f24375,plain,
( spl0_1040
<=> ! [X4,X1,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1)),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),c_HOL_Oone__class_Oone(X3))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f653,axiom,
! [X3,X1,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X1)),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),c_HOL_Oone__class_Oone(X3))),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
fof(f24373,plain,
spl0_1039,
inference(avatar_split_clause,[],[f609,f24371]) ).
fof(f24371,plain,
( spl0_1039
<=> ! [X5,X4,X6,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),c_Divides_Odiv__class_Omod(X4,X6,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f609,axiom,
! [X3,X6,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),c_Divides_Odiv__class_Omod(X4,X6,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult1_0) ).
fof(f24369,plain,
spl0_1038,
inference(avatar_split_clause,[],[f608,f24367]) ).
fof(f24367,plain,
( spl0_1038
<=> ! [X5,X4,X6,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Divides_Odiv__class_Omod(X4,X6,X3)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f608,axiom,
! [X3,X6,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Divides_Odiv__class_Omod(X4,X6,X3)),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult2_0) ).
fof(f24365,plain,
spl0_1037,
inference(avatar_split_clause,[],[f604,f24363]) ).
fof(f24363,plain,
( spl0_1037
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Ozero__class_Ozero(X3) = X9
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X17)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f604,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Ozero__class_Ozero(X3) = X9
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X17)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
fof(f24361,plain,
spl0_1036,
inference(avatar_split_clause,[],[f603,f24359]) ).
fof(f24359,plain,
( spl0_1036
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X17)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f603,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X17)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
fof(f24357,plain,
spl0_1035,
inference(avatar_split_clause,[],[f589,f24355]) ).
fof(f24355,plain,
( spl0_1035
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
fof(f589,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
fof(f24353,plain,
( spl0_1034
| ~ spl0_569
| ~ spl0_951 ),
inference(avatar_split_clause,[],[f21891,f21188,f8136,f24351]) ).
fof(f8136,plain,
( spl0_569
<=> ! [X9,X3] :
( ~ class_Int_Onumber__ring(X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Oone__class_Oone(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3)),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f21891,plain,
( ! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0)),v_ka____) )
| ~ spl0_569
| ~ spl0_951 ),
inference(resolution,[],[f21190,f8137]) ).
fof(f8137,plain,
( ! [X3,X9] :
( ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oone__class_Oone(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3)),X9) )
| ~ spl0_569 ),
inference(avatar_component_clause,[],[f8136]) ).
fof(f21190,plain,
( c_Parity_Oeven__odd__class_Oeven(v_ka____,tc_nat)
| ~ spl0_951 ),
inference(avatar_component_clause,[],[f21188]) ).
fof(f24349,plain,
spl0_1033,
inference(avatar_split_clause,[],[f528,f24347]) ).
fof(f24347,plain,
( spl0_1033
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f528,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
fof(f24345,plain,
spl0_1032,
inference(avatar_split_clause,[],[f527,f24343]) ).
fof(f24343,plain,
( spl0_1032
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f527,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
fof(f24341,plain,
spl0_1031,
inference(avatar_split_clause,[],[f403,f24339]) ).
fof(f24339,plain,
( spl0_1031
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Ozero__class_Ozero(X3) = X9
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X17)),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f403,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Ozero__class_Ozero(X3) = X9
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X17)),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
fof(f24337,plain,
spl0_1030,
inference(avatar_split_clause,[],[f402,f24335]) ).
fof(f24335,plain,
( spl0_1030
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X17)),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).
fof(f402,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X17)),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
fof(f24333,plain,
spl0_1029,
inference(avatar_split_clause,[],[f203,f24331]) ).
fof(f24331,plain,
( spl0_1029
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f203,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
fof(f24329,plain,
spl0_1028,
inference(avatar_split_clause,[],[f98,f24327]) ).
fof(f24327,plain,
( spl0_1028
<=> ! [X3,X10,X11,X8,X9,X17,X22,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,X9),hAPP(hAPP(X12,X17),X22)) = hAPP(hAPP(X12,hAPP(hAPP(X12,X9),X17)),X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f98,axiom,
! [X3,X10,X11,X8,X9,X17,X22,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,X9),hAPP(hAPP(X12,X17),X22)) = hAPP(hAPP(X12,hAPP(hAPP(X12,X9),X17)),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Omul__a_0) ).
fof(f24325,plain,
spl0_1027,
inference(avatar_split_clause,[],[f92,f24323]) ).
fof(f24323,plain,
( spl0_1027
<=> ! [X3,X10,X11,X8,X7,X4,X5,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X11,X4),hAPP(hAPP(X11,X5),X7)) = hAPP(hAPP(X11,hAPP(hAPP(X11,X4),X5)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f92,axiom,
! [X3,X10,X11,X8,X7,X4,X5,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X11,X4),hAPP(hAPP(X11,X5),X7)) = hAPP(hAPP(X11,hAPP(hAPP(X11,X4),X5)),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I25_J_0) ).
fof(f24321,plain,
spl0_1026,
inference(avatar_split_clause,[],[f90,f24319]) ).
fof(f24319,plain,
( spl0_1026
<=> ! [X3,X10,X11,X8,X6,X4,X5,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X11,hAPP(hAPP(X11,X4),X6)),X5) = hAPP(hAPP(X11,hAPP(hAPP(X11,X4),X5)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f90,axiom,
! [X3,X10,X11,X8,X6,X4,X5,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X11,hAPP(hAPP(X11,X4),X6)),X5) = hAPP(hAPP(X11,hAPP(hAPP(X11,X4),X5)),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I23_J_0) ).
fof(f24317,plain,
spl0_1025,
inference(avatar_split_clause,[],[f89,f24315]) ).
fof(f24315,plain,
( spl0_1025
<=> ! [X3,X10,X11,X8,X7,X4,X5,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X11,X4),hAPP(hAPP(X11,X5),X7)) = hAPP(hAPP(X11,X5),hAPP(hAPP(X11,X4),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f89,axiom,
! [X3,X10,X11,X8,X7,X4,X5,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X11,X4),hAPP(hAPP(X11,X5),X7)) = hAPP(hAPP(X11,X5),hAPP(hAPP(X11,X4),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I22_J_0) ).
fof(f24313,plain,
spl0_1024,
inference(avatar_split_clause,[],[f86,f24311]) ).
fof(f24311,plain,
( spl0_1024
<=> ! [X21,X3,X10,X11,X18,X8,X12,X13,X20] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,X18),hAPP(hAPP(X12,X20),X21)) = hAPP(hAPP(X12,X20),hAPP(hAPP(X12,X18),X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f86,axiom,
! [X21,X3,X10,X11,X18,X8,X12,X13,X20] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,X18),hAPP(hAPP(X12,X20),X21)) = hAPP(hAPP(X12,X20),hAPP(hAPP(X12,X18),X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I19_J_0) ).
fof(f24308,plain,
( ~ spl0_951
| ~ spl0_603
| ~ spl0_985 ),
inference(avatar_split_clause,[],[f24263,f21846,f8306,f21188]) ).
fof(f8306,plain,
( spl0_603
<=> ! [X9] :
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_Divides_Odiv__class_Omod(X9,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f21846,plain,
( spl0_985
<=> c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(v_ka____,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f24263,plain,
( ~ c_Parity_Oeven__odd__class_Oeven(v_ka____,tc_nat)
| ~ spl0_603
| ~ spl0_985 ),
inference(trivial_inequality_removal,[],[f24253]) ).
fof(f24253,plain,
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(v_ka____,tc_nat)
| ~ spl0_603
| ~ spl0_985 ),
inference(superposition,[],[f8307,f21848]) ).
fof(f21848,plain,
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(v_ka____,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
| ~ spl0_985 ),
inference(avatar_component_clause,[],[f21846]) ).
fof(f8307,plain,
( ! [X9] :
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_Divides_Odiv__class_Omod(X9,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) )
| ~ spl0_603 ),
inference(avatar_component_clause,[],[f8306]) ).
fof(f24307,plain,
spl0_1023,
inference(avatar_split_clause,[],[f83,f24305]) ).
fof(f24305,plain,
( spl0_1023
<=> ! [X3,X10,X11,X18,X8,X19,X12,X13,X20] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,hAPP(hAPP(X12,X18),X19)),X20) = hAPP(hAPP(X12,hAPP(hAPP(X12,X18),X20)),X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f83,axiom,
! [X3,X10,X11,X18,X8,X19,X12,X13,X20] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,hAPP(hAPP(X12,X18),X19)),X20) = hAPP(hAPP(X12,hAPP(hAPP(X12,X18),X20)),X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I16_J_0) ).
fof(f24303,plain,
spl0_1022,
inference(avatar_split_clause,[],[f70,f24301]) ).
fof(f24301,plain,
( spl0_1022
<=> ! [X10,X11,X13,X4,X12,X3,X8,X1] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,hAPP(hAPP(X11,X4),X10)),X1) = hAPP(hAPP(X11,X1),hAPP(hAPP(X12,X4),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f70,axiom,
! [X3,X10,X11,X1,X8,X4,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,hAPP(hAPP(X11,X4),X10)),X1) = hAPP(hAPP(X11,X1),hAPP(hAPP(X12,X4),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I3_J_0) ).
fof(f24299,plain,
spl0_1021,
inference(avatar_split_clause,[],[f69,f24297]) ).
fof(f24297,plain,
( spl0_1021
<=> ! [X10,X11,X13,X4,X12,X3,X8,X1] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X11,hAPP(hAPP(X12,X4),X1)),X1) = hAPP(hAPP(X12,hAPP(hAPP(X11,X4),X10)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f69,axiom,
! [X3,X10,X11,X1,X8,X4,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X11,hAPP(hAPP(X12,X4),X1)),X1) = hAPP(hAPP(X12,hAPP(hAPP(X11,X4),X10)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I2_J_0) ).
fof(f24295,plain,
spl0_1020,
inference(avatar_split_clause,[],[f7,f24293]) ).
fof(f24293,plain,
( spl0_1020
<=> ! [X6,X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = X6
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X4,X6,X3)),c_HOL_Oone__class_Oone(X3)) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X4),X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f7,axiom,
! [X3,X6,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = X6
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X4,X6,X3)),c_HOL_Oone__class_Oone(X3)) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X4),X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self1_0) ).
fof(f24291,plain,
spl0_1019,
inference(avatar_split_clause,[],[f6,f24289]) ).
fof(f24289,plain,
( spl0_1019
<=> ! [X6,X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = X6
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X6,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X4,X6,X3)),c_HOL_Oone__class_Oone(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f6,axiom,
! [X3,X6,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = X6
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X6,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X4,X6,X3)),c_HOL_Oone__class_Oone(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self2_0) ).
fof(f22493,plain,
( spl0_1018
| ~ spl0_650
| ~ spl0_946
| spl0_951
| ~ spl0_985 ),
inference(avatar_split_clause,[],[f21942,f21846,f21188,f20741,f9578,f22490]) ).
fof(f22490,plain,
( spl0_1018
<=> v_ka____ = hAPP(c_Suc,c_HOL_Ominus__class_Ominus(v_ka____,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f9578,plain,
( spl0_650
<=> ! [X2,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),c_Divides_Odiv__class_Odiv(X1,X2,tc_nat)) = c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f20741,plain,
( spl0_946
<=> ! [X9] :
( hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),c_Divides_Odiv__class_Odiv(X9,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat))) = X9
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f21942,plain,
( v_ka____ = hAPP(c_Suc,c_HOL_Ominus__class_Ominus(v_ka____,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat))
| ~ spl0_650
| ~ spl0_946
| spl0_951
| ~ spl0_985 ),
inference(forward_demodulation,[],[f21720,f21848]) ).
fof(f21720,plain,
( v_ka____ = hAPP(c_Suc,c_HOL_Ominus__class_Ominus(v_ka____,c_Divides_Odiv__class_Omod(v_ka____,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat))
| ~ spl0_650
| ~ spl0_946
| spl0_951 ),
inference(forward_demodulation,[],[f21717,f9579]) ).
fof(f9579,plain,
( ! [X2,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),c_Divides_Odiv__class_Odiv(X1,X2,tc_nat)) = c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat)
| ~ spl0_650 ),
inference(avatar_component_clause,[],[f9578]) ).
fof(f21717,plain,
( v_ka____ = hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),c_Divides_Odiv__class_Odiv(v_ka____,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)))
| ~ spl0_946
| spl0_951 ),
inference(resolution,[],[f21189,f20742]) ).
fof(f20742,plain,
( ! [X9] :
( c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),c_Divides_Odiv__class_Odiv(X9,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat))) = X9 )
| ~ spl0_946 ),
inference(avatar_component_clause,[],[f20741]) ).
fof(f21189,plain,
( ~ c_Parity_Oeven__odd__class_Oeven(v_ka____,tc_nat)
| spl0_951 ),
inference(avatar_component_clause,[],[f21188]) ).
fof(f21993,plain,
spl0_1017,
inference(avatar_split_clause,[],[f1410,f21991]) ).
fof(f21991,plain,
( spl0_1017
<=> ! [X9,X23,X30,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X30)),X23) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X30),X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f1410,axiom,
! [X3,X9,X23,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X30)),X23) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X30),X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__pwr_0) ).
fof(f21984,plain,
spl0_1016,
inference(avatar_split_clause,[],[f1408,f21982]) ).
fof(f21982,plain,
( spl0_1016
<=> ! [X2,X4,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X4,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f1408,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X4,X3)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__over_0) ).
fof(f21980,plain,
spl0_1015,
inference(avatar_split_clause,[],[f1360,f21978]) ).
fof(f21978,plain,
( spl0_1015
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6)),X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f1360,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6)),X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(f21976,plain,
spl0_1014,
inference(avatar_split_clause,[],[f1359,f21974]) ).
fof(f21974,plain,
( spl0_1014
<=> ! [X18,X20,X3,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X18),X19)),X20) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X18),X20)),X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f1359,axiom,
! [X3,X18,X19,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X18),X19)),X20) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X18),X20)),X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(f21972,plain,
spl0_1013,
inference(avatar_split_clause,[],[f1357,f21970]) ).
fof(f21970,plain,
( spl0_1013
<=> ! [X18,X20,X3,X21] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X20),X21)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X18),X20)),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f1357,axiom,
! [X21,X3,X18,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X20),X21)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X18),X20)),X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
fof(f21968,plain,
spl0_1012,
inference(avatar_split_clause,[],[f1356,f21966]) ).
fof(f21966,plain,
( spl0_1012
<=> ! [X18,X20,X3,X21] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X20),X21)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X20),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X18),X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).
fof(f1356,axiom,
! [X21,X3,X18,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X20),X21)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X20),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X18),X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(f21964,plain,
spl0_1011,
inference(avatar_split_clause,[],[f1338,f21962]) ).
fof(f21962,plain,
( spl0_1011
<=> ! [X4,X3,X2,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
fof(f1338,axiom,
! [X2,X3,X1,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult_0) ).
fof(f21960,plain,
spl0_1010,
inference(avatar_split_clause,[],[f1334,f21958]) ).
fof(f21958,plain,
( spl0_1010
<=> ! [X28,X4,X3,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(X2,X28,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X28),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
fof(f1334,axiom,
! [X2,X3,X28,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(X2,X28,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X28),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).
fof(f21956,plain,
spl0_1009,
inference(avatar_split_clause,[],[f1333,f21954]) ).
fof(f21954,plain,
( spl0_1009
<=> ! [X4,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
fof(f1333,axiom,
! [X2,X3,X1,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).
fof(f21952,plain,
spl0_1008,
inference(avatar_split_clause,[],[f1314,f21950]) ).
fof(f21950,plain,
( spl0_1008
<=> ! [X4,X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
fof(f1314,axiom,
! [X2,X3,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__commutes_0) ).
fof(f21948,plain,
spl0_1007,
inference(avatar_split_clause,[],[f1296,f21946]) ).
fof(f21946,plain,
( spl0_1007
<=> ! [X2,X3] :
( ~ class_Int_Onumber__ring(X3)
| c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3)),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f1296,axiom,
! [X2,X3] :
( ~ class_Int_Onumber__ring(X3)
| c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3)),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__m1__odd_0) ).
fof(f21941,plain,
( spl0_1006
| ~ spl0_514
| ~ spl0_951 ),
inference(avatar_split_clause,[],[f21890,f21188,f6092,f21938]) ).
fof(f21938,plain,
( spl0_1006
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(v_ka____,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f6092,plain,
( spl0_514
<=> ! [X9] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X9,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f21890,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(v_ka____,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
| ~ spl0_514
| ~ spl0_951 ),
inference(resolution,[],[f21190,f6093]) ).
fof(f6093,plain,
( ! [X9] :
( ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X9,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) )
| ~ spl0_514 ),
inference(avatar_component_clause,[],[f6092]) ).
fof(f21936,plain,
spl0_1005,
inference(avatar_split_clause,[],[f1267,f21934]) ).
fof(f21934,plain,
( spl0_1005
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f1267,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power2__abs_0) ).
fof(f21932,plain,
spl0_1004,
inference(avatar_split_clause,[],[f1266,f21930]) ).
fof(f21930,plain,
( spl0_1004
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(X4,X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f1266,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(X4,X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power2__minus_0) ).
fof(f21928,plain,
spl0_1003,
inference(avatar_split_clause,[],[f1265,f21926]) ).
fof(f21926,plain,
( spl0_1003
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f1265,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__power2_0) ).
fof(f21924,plain,
spl0_1002,
inference(avatar_split_clause,[],[f1230,f21922]) ).
fof(f21922,plain,
( spl0_1002
<=> ! [X4,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
fof(f1230,axiom,
! [X2,X3,X1,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__imp__le__exp_0) ).
fof(f21920,plain,
spl0_1001,
inference(avatar_split_clause,[],[f1228,f21918]) ).
fof(f21918,plain,
( spl0_1001
<=> ! [X17,X9,X6,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(X9,X17,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X6,X3)
| c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X6),X9),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X6),X17),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f1228,axiom,
! [X3,X6,X9,X17] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(X9,X17,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X6,X3)
| c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X6),X9),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X6),X17),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing__iff_1) ).
fof(f21916,plain,
spl0_1000,
inference(avatar_split_clause,[],[f1094,f21914]) ).
fof(f21914,plain,
( spl0_1000
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X0)),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f1094,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X0)),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__power__le__0__imp__0_0) ).
fof(f21912,plain,
spl0_999,
inference(avatar_split_clause,[],[f1035,f21910]) ).
fof(f21910,plain,
( spl0_999
<=> ! [X0,X1,X14] :
( ~ c_lessequals(X0,X14,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X14,X0,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),hAPP(c_Suc,X14),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f1035,axiom,
! [X0,X1,X14] :
( ~ c_lessequals(X0,X14,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X14,X0,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),hAPP(c_Suc,X14),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq1_0) ).
fof(f21908,plain,
spl0_998,
inference(avatar_split_clause,[],[f822,f21906]) ).
fof(f21906,plain,
( spl0_998
<=> ! [X28,X4,X3,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(X2,X28,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),X4,X3)
| c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X28),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
fof(f822,axiom,
! [X2,X3,X28,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(X2,X28,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),X4,X3)
| c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X28),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing_0) ).
fof(f21904,plain,
spl0_997,
inference(avatar_split_clause,[],[f787,f21902]) ).
fof(f21902,plain,
( spl0_997
<=> ! [X3,X4,X6,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X6),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f787,axiom,
! [X2,X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X6),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
fof(f21900,plain,
spl0_996,
inference(avatar_split_clause,[],[f602,f21898]) ).
fof(f21898,plain,
( spl0_996
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X6,X4,X3)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
fof(f602,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X6,X4,X3)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
fof(f21889,plain,
spl0_995,
inference(avatar_split_clause,[],[f601,f21887]) ).
fof(f21887,plain,
( spl0_995
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(X6,X4,X3)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
fof(f601,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(X6,X4,X3)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
fof(f21885,plain,
spl0_994,
inference(avatar_split_clause,[],[f600,f21883]) ).
fof(f21883,plain,
( spl0_994
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f600,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
fof(f21881,plain,
spl0_993,
inference(avatar_split_clause,[],[f599,f21879]) ).
fof(f21879,plain,
( spl0_993
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
fof(f599,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
fof(f21877,plain,
spl0_992,
inference(avatar_split_clause,[],[f598,f21875]) ).
fof(f21875,plain,
( spl0_992
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_lessequals(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f598,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_lessequals(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
fof(f21873,plain,
spl0_991,
inference(avatar_split_clause,[],[f597,f21871]) ).
fof(f21871,plain,
( spl0_991
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_lessequals(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f597,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_lessequals(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
fof(f21869,plain,
spl0_990,
inference(avatar_split_clause,[],[f595,f21867]) ).
fof(f21867,plain,
( spl0_990
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__semiring(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
fof(f595,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__semiring(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
fof(f21865,plain,
spl0_989,
inference(avatar_split_clause,[],[f594,f21863]) ).
fof(f21863,plain,
( spl0_989
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__semiring(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f594,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__semiring(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
fof(f21861,plain,
spl0_988,
inference(avatar_split_clause,[],[f593,f21859]) ).
fof(f21859,plain,
( spl0_988
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f593,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
fof(f21857,plain,
spl0_987,
inference(avatar_split_clause,[],[f592,f21855]) ).
fof(f21855,plain,
( spl0_987
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f592,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
fof(f21853,plain,
spl0_986,
inference(avatar_split_clause,[],[f533,f21851]) ).
fof(f21851,plain,
( spl0_986
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f533,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
fof(f21849,plain,
( spl0_985
| ~ spl0_604
| spl0_951 ),
inference(avatar_split_clause,[],[f21719,f21188,f8310,f21846]) ).
fof(f8310,plain,
( spl0_604
<=> ! [X9] :
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(X9,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f21719,plain,
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(v_ka____,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
| ~ spl0_604
| spl0_951 ),
inference(resolution,[],[f21189,f8311]) ).
fof(f8311,plain,
( ! [X9] :
( c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(X9,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) )
| ~ spl0_604 ),
inference(avatar_component_clause,[],[f8310]) ).
fof(f21844,plain,
spl0_984,
inference(avatar_split_clause,[],[f532,f21842]) ).
fof(f21842,plain,
( spl0_984
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X6,X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f532,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X6,X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
fof(f21840,plain,
spl0_983,
inference(avatar_split_clause,[],[f531,f21838]) ).
fof(f21838,plain,
( spl0_983
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f531,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
fof(f21836,plain,
spl0_982,
inference(avatar_split_clause,[],[f530,f21834]) ).
fof(f21834,plain,
( spl0_982
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X6,X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f530,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X6,X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
fof(f21832,plain,
spl0_981,
inference(avatar_split_clause,[],[f518,f21830]) ).
fof(f21830,plain,
( spl0_981
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f518,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
fof(f21828,plain,
spl0_980,
inference(avatar_split_clause,[],[f516,f21826]) ).
fof(f21826,plain,
( spl0_980
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f516,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
fof(f21824,plain,
spl0_979,
inference(avatar_split_clause,[],[f515,f21822]) ).
fof(f21822,plain,
( spl0_979
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f515,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
fof(f21820,plain,
spl0_978,
inference(avatar_split_clause,[],[f514,f21818]) ).
fof(f21818,plain,
( spl0_978
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X6,X4,X3)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f514,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X6,X4,X3)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
fof(f21816,plain,
spl0_977,
inference(avatar_split_clause,[],[f512,f21814]) ).
fof(f21814,plain,
( spl0_977
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f512,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
fof(f21812,plain,
spl0_976,
inference(avatar_split_clause,[],[f511,f21810]) ).
fof(f21810,plain,
( spl0_976
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f511,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
fof(f21808,plain,
spl0_975,
inference(avatar_split_clause,[],[f508,f21806]) ).
fof(f21806,plain,
( spl0_975
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f508,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
fof(f21800,plain,
spl0_974,
inference(avatar_split_clause,[],[f507,f21798]) ).
fof(f21798,plain,
( spl0_974
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X6,X4,X3)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f507,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X6,X4,X3)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).
fof(f21796,plain,
spl0_973,
inference(avatar_split_clause,[],[f506,f21794]) ).
fof(f21794,plain,
( spl0_973
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X6,X4,X3)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f506,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X6,X4,X3)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
fof(f21792,plain,
spl0_972,
inference(avatar_split_clause,[],[f462,f21790]) ).
fof(f21790,plain,
( spl0_972
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f462,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
fof(f21788,plain,
spl0_971,
inference(avatar_split_clause,[],[f391,f21786]) ).
fof(f21786,plain,
( spl0_971
<=> ! [X3,X4,X6,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X6),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f391,axiom,
! [X2,X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X6),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono_0) ).
fof(f21784,plain,
spl0_970,
inference(avatar_split_clause,[],[f371,f21782]) ).
fof(f21782,plain,
( spl0_970
<=> ! [X4,X7,X5,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X7)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f371,axiom,
! [X3,X7,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X7)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(f21780,plain,
spl0_969,
inference(avatar_split_clause,[],[f370,f21778]) ).
fof(f21778,plain,
( spl0_969
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
fof(f370,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5)),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(f21776,plain,
spl0_968,
inference(avatar_split_clause,[],[f368,f21774]) ).
fof(f21774,plain,
( spl0_968
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).
fof(f368,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6)),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(f21772,plain,
spl0_967,
inference(avatar_split_clause,[],[f365,f21770]) ).
fof(f21770,plain,
( spl0_967
<=> ! [X17,X3,X9,X22] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X17),X22)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X17),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f365,axiom,
! [X3,X9,X17,X22] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X17),X22)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X17),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
fof(f21768,plain,
spl0_966,
inference(avatar_split_clause,[],[f364,f21766]) ).
fof(f21766,plain,
( spl0_966
<=> ! [X17,X3,X9,X22] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X17),X22)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X17)),X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f364,axiom,
! [X3,X9,X17,X22] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X17),X22)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X17)),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
fof(f21764,plain,
spl0_965,
inference(avatar_split_clause,[],[f363,f21762]) ).
fof(f21762,plain,
( spl0_965
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f363,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6)),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
fof(f21760,plain,
spl0_964,
inference(avatar_split_clause,[],[f362,f21758]) ).
fof(f21758,plain,
( spl0_964
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f362,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(f21756,plain,
spl0_963,
inference(avatar_split_clause,[],[f342,f21754]) ).
fof(f21754,plain,
( spl0_963
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_HOL_Oabs__class_Oabs(X6,X3)) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_HOL_Oabs__class_Oabs(X6,X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f342,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_HOL_Oabs__class_Oabs(X6,X3)) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_HOL_Oabs__class_Oabs(X6,X3)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__add__abs_0) ).
fof(f21752,plain,
spl0_962,
inference(avatar_split_clause,[],[f217,f21750]) ).
fof(f21750,plain,
( spl0_962
<=> ! [X9,X17,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X9
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X17,X3)
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f217,axiom,
! [X3,X9,X17] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X9
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X17,X3)
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
fof(f21748,plain,
spl0_961,
inference(avatar_split_clause,[],[f216,f21746]) ).
fof(f21746,plain,
( spl0_961
<=> ! [X9,X17,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X17,X3)
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f216,axiom,
! [X3,X9,X17] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X17,X3)
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
fof(f21744,plain,
spl0_960,
inference(avatar_split_clause,[],[f150,f21742]) ).
fof(f21742,plain,
( spl0_960
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Omult__mono1(X3)
| ~ c_lessequals(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f150,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Omult__mono1(X3)
| ~ c_lessequals(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
fof(f21740,plain,
spl0_959,
inference(avatar_split_clause,[],[f149,f21738]) ).
fof(f21738,plain,
( spl0_959
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Omult__mono(X3)
| ~ c_lessequals(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f149,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Omult__mono(X3)
| ~ c_lessequals(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
fof(f21736,plain,
spl0_958,
inference(avatar_split_clause,[],[f148,f21734]) ).
fof(f21734,plain,
( spl0_958
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Omult__mono(X3)
| ~ c_lessequals(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f148,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Omult__mono(X3)
| ~ c_lessequals(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
fof(f21732,plain,
spl0_957,
inference(avatar_split_clause,[],[f147,f21730]) ).
fof(f21730,plain,
( spl0_957
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(X6,X4,X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f147,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(X6,X4,X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
fof(f21728,plain,
spl0_956,
inference(avatar_split_clause,[],[f146,f21726]) ).
fof(f21726,plain,
( spl0_956
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(X6,X4,X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f146,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(X6,X4,X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
fof(f21724,plain,
spl0_955,
inference(avatar_split_clause,[],[f143,f21722]) ).
fof(f21722,plain,
( spl0_955
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Ozero__class_Ozero(X3) = X9
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f143,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Ozero__class_Ozero(X3) = X9
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
fof(f21716,plain,
spl0_954,
inference(avatar_split_clause,[],[f42,f21714]) ).
fof(f21714,plain,
( spl0_954
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f42,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Ozero__class_Ozero(X3) = X17
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
fof(f21712,plain,
spl0_953,
inference(avatar_split_clause,[],[f3,f21710]) ).
fof(f21710,plain,
( spl0_953
<=> ! [X5,X4,X6,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_Divides_Odiv__class_Odiv(X4,X6,X3) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f3,axiom,
! [X3,X6,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_Divides_Odiv__class_Odiv(X4,X6,X3) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult1_0) ).
fof(f21708,plain,
spl0_952,
inference(avatar_split_clause,[],[f2,f21706]) ).
fof(f21706,plain,
( spl0_952
<=> ! [X5,X4,X6,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) = c_Divides_Odiv__class_Odiv(X4,X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f2,axiom,
! [X3,X6,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) = c_Divides_Odiv__class_Odiv(X4,X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult2_0) ).
fof(f21191,plain,
( ~ spl0_948
| ~ spl0_949
| spl0_950
| spl0_951
| spl0_608
| ~ spl0_919 ),
inference(avatar_split_clause,[],[f20748,f20600,f9094,f21188,f21184,f21180,f21176]) ).
fof(f21176,plain,
( spl0_948
<=> class_Ring__and__Field_Oordered__idom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f21180,plain,
( spl0_949
<=> c_lessequals(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f21184,plain,
( spl0_950
<=> c_HOL_Ozero__class_Ozero(tc_nat) = v_ka____ ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f9094,plain,
( spl0_608
<=> c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f20600,plain,
( spl0_919
<=> ! [X2,X9,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f20748,plain,
( c_Parity_Oeven__odd__class_Oeven(v_ka____,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = v_ka____
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(tc_nat)
| spl0_608
| ~ spl0_919 ),
inference(resolution,[],[f20601,f9096]) ).
fof(f9096,plain,
( ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| spl0_608 ),
inference(avatar_component_clause,[],[f9094]) ).
fof(f20601,plain,
( ! [X2,X3,X9] :
( c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),c_HOL_Ozero__class_Ozero(X3),X3)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) )
| ~ spl0_919 ),
inference(avatar_component_clause,[],[f20600]) ).
fof(f20747,plain,
( spl0_947
| ~ spl0_174
| ~ spl0_926 ),
inference(avatar_split_clause,[],[f20675,f20628,f2522,f20745]) ).
fof(f20745,plain,
( spl0_947
<=> ! [X0] :
( c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0,tc_nat)
| c_lessequals(X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f2522,plain,
( spl0_174
<=> ! [X2,X1] :
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f20628,plain,
( spl0_926
<=> ! [X0] :
( ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X0,tc_nat)
| c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f20675,plain,
( ! [X0] :
( c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0,tc_nat)
| c_lessequals(X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat) )
| ~ spl0_174
| ~ spl0_926 ),
inference(resolution,[],[f20629,f2523]) ).
fof(f2523,plain,
( ! [X2,X1] :
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) )
| ~ spl0_174 ),
inference(avatar_component_clause,[],[f2522]) ).
fof(f20629,plain,
( ! [X0] :
( ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X0,tc_nat)
| c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0,tc_nat) )
| ~ spl0_926 ),
inference(avatar_component_clause,[],[f20628]) ).
fof(f20743,plain,
spl0_946,
inference(avatar_split_clause,[],[f1616,f20741]) ).
fof(f1616,plain,
! [X9] :
( hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),c_Divides_Odiv__class_Odiv(X9,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat))) = X9
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ),
inference(forward_demodulation,[],[f1615,f1583]) ).
fof(f1583,plain,
c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) = hAPP(c_Suc,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
inference(forward_demodulation,[],[f1259,f421]) ).
fof(f1259,axiom,
hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__arith_I115_J_0) ).
fof(f1615,plain,
! [X9] :
( hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))),c_Divides_Odiv__class_Odiv(X9,hAPP(c_Suc,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),tc_nat))) = X9
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ),
inference(forward_demodulation,[],[f132,f421]) ).
fof(f132,axiom,
! [X9] :
( c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),c_Divides_Odiv__class_Odiv(X9,hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat))) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__nat__div__two__times__two__plus__one_0) ).
fof(f20739,plain,
spl0_945,
inference(avatar_split_clause,[],[f1614,f20737]) ).
fof(f20737,plain,
( spl0_945
<=> ! [X9] :
( c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(X9,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat))
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f1614,plain,
! [X9] :
( c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(X9,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat))
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ),
inference(forward_demodulation,[],[f1613,f1583]) ).
fof(f1613,plain,
! [X9] :
( c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X9),hAPP(c_Suc,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(X9,hAPP(c_Suc,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),tc_nat))
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ),
inference(forward_demodulation,[],[f56,f421]) ).
fof(f56,axiom,
! [X9] :
( c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X9),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(X9,hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__nat__plus__one__div__two_0) ).
fof(f20735,plain,
spl0_944,
inference(avatar_split_clause,[],[f1428,f20733]) ).
fof(f20733,plain,
( spl0_944
<=> ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f1428,axiom,
! [X2,X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__mult__distrib2_0) ).
fof(f20731,plain,
spl0_943,
inference(avatar_split_clause,[],[f1427,f20729]) ).
fof(f20729,plain,
( spl0_943
<=> ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)),X0) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f1427,axiom,
! [X2,X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)),X0) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__mult__distrib_0) ).
fof(f20727,plain,
spl0_942,
inference(avatar_split_clause,[],[f1423,f20725]) ).
fof(f20725,plain,
( spl0_942
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X4)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f1423,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X4)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power3__eq__cube_0) ).
fof(f20723,plain,
spl0_941,
inference(avatar_split_clause,[],[f1347,f20721]) ).
fof(f20721,plain,
( spl0_941
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| c_HOL_Oord__class_Oless(X6,X4,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f1347,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| c_HOL_Oord__class_Oless(X6,X4,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
fof(f20719,plain,
spl0_940,
inference(avatar_split_clause,[],[f1346,f20717]) ).
fof(f20717,plain,
( spl0_940
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| c_HOL_Oord__class_Oless(X6,X4,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f1346,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| c_HOL_Oord__class_Oless(X6,X4,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
fof(f20715,plain,
spl0_939,
inference(avatar_split_clause,[],[f1165,f20713]) ).
fof(f20713,plain,
( spl0_939
<=> ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f1165,axiom,
! [X2,X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__distrib2_0) ).
fof(f20711,plain,
spl0_938,
inference(avatar_split_clause,[],[f1164,f20709]) ).
fof(f20709,plain,
( spl0_938
<=> ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f1164,axiom,
! [X2,X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),X0) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__distrib_0) ).
fof(f20707,plain,
spl0_937,
inference(avatar_split_clause,[],[f1141,f20705]) ).
fof(f20705,plain,
( spl0_937
<=> ! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(c_Suc,X2)),c_HOL_Oone__class_Oone(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f1141,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(c_Suc,X2)),c_HOL_Oone__class_Oone(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).
fof(f20670,plain,
spl0_936,
inference(avatar_split_clause,[],[f1017,f20668]) ).
fof(f20668,plain,
( spl0_936
<=> ! [X17,X36,X9,X3] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X17),X36,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oinverse__class_Odivide(X9,X36,X3)),c_HOL_Oinverse__class_Odivide(X17,X36,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f1017,axiom,
! [X3,X36,X9,X17] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X17),X36,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oinverse__class_Odivide(X9,X36,X3)),c_HOL_Oinverse__class_Odivide(X17,X36,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Oadd_0) ).
fof(f20666,plain,
spl0_935,
inference(avatar_split_clause,[],[f1016,f20664]) ).
fof(f20664,plain,
( spl0_935
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X5,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3)),c_HOL_Oinverse__class_Odivide(X6,X5,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f1016,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X5,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3)),c_HOL_Oinverse__class_Odivide(X6,X5,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).
fof(f20662,plain,
spl0_934,
inference(avatar_split_clause,[],[f951,f20660]) ).
fof(f20660,plain,
( spl0_934
<=> ! [X10,X11,X9,X13,X12,X3,X8,X23] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X8,X9),hAPP(c_Suc,X23)) = hAPP(hAPP(X12,hAPP(hAPP(X8,X9),X23)),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f951,axiom,
! [X3,X10,X11,X8,X9,X12,X23,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X8,X9),hAPP(c_Suc,X23)) = hAPP(hAPP(X12,hAPP(hAPP(X8,X9),X23)),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I28_J_0) ).
fof(f20658,plain,
spl0_933,
inference(avatar_split_clause,[],[f949,f20656]) ).
fof(f20656,plain,
( spl0_933
<=> ! [X2,X10,X11,X9,X13,X12,X3,X8] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X8,X9),hAPP(c_Suc,X2)) = hAPP(hAPP(X12,X9),hAPP(hAPP(X8,X9),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f949,axiom,
! [X2,X3,X10,X11,X8,X9,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X8,X9),hAPP(c_Suc,X2)) = hAPP(hAPP(X12,X9),hAPP(hAPP(X8,X9),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__Suc_0) ).
fof(f20654,plain,
spl0_932,
inference(avatar_split_clause,[],[f752,f20652]) ).
fof(f20652,plain,
( spl0_932
<=> ! [X5,X4,X6,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X5,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_Divides_Odiv__class_Omod(X6,X5,X3)),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f752,axiom,
! [X3,X6,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X5,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_Divides_Odiv__class_Omod(X6,X5,X3)),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__right__eq_0) ).
fof(f20650,plain,
spl0_931,
inference(avatar_split_clause,[],[f748,f20648]) ).
fof(f20648,plain,
( spl0_931
<=> ! [X5,X4,X6,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X5,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Divides_Odiv__class_Omod(X4,X5,X3)),X6),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f748,axiom,
! [X3,X6,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X5,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Divides_Odiv__class_Omod(X4,X5,X3)),X6),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I4_J_0) ).
fof(f20646,plain,
spl0_930,
inference(avatar_split_clause,[],[f562,f20644]) ).
fof(f20644,plain,
( spl0_930
<=> ! [X5,X4,X7,X6,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(X5,X7,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X7),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f562,axiom,
! [X3,X6,X7,X4,X5] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(X5,X7,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X7),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
fof(f20642,plain,
spl0_929,
inference(avatar_split_clause,[],[f545,f20640]) ).
fof(f20640,plain,
( spl0_929
<=> ! [X5,X4,X7,X6,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(X5,X7,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X7),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f545,axiom,
! [X3,X6,X7,X4,X5] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(X5,X7,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X7),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
fof(f20638,plain,
spl0_928,
inference(avatar_split_clause,[],[f544,f20636]) ).
fof(f20636,plain,
( spl0_928
<=> ! [X5,X4,X7,X6,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_lessequals(X5,X7,X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X7),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f544,axiom,
! [X3,X6,X7,X4,X5] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_lessequals(X5,X7,X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X7),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
fof(f20634,plain,
spl0_927,
inference(avatar_split_clause,[],[f453,f20632]) ).
fof(f20632,plain,
( spl0_927
<=> ! [X5,X4,X7,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X5,X7,X3)
| ~ c_lessequals(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X5),X3)
| c_lessequals(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X7),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f453,axiom,
! [X3,X6,X7,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X5,X7,X3)
| ~ c_lessequals(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X5),X3)
| c_lessequals(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X7),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
fof(f20630,plain,
( spl0_926
| ~ spl0_346
| ~ spl0_780 ),
inference(avatar_split_clause,[],[f13922,f13301,f4082,f20628]) ).
fof(f4082,plain,
( spl0_346
<=> ! [X16,X0,X14] :
( ~ c_lessequals(X16,X14,tc_nat)
| ~ c_lessequals(X14,X0,tc_nat)
| c_lessequals(X16,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f13301,plain,
( spl0_780
<=> c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f13922,plain,
( ! [X0] :
( ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X0,tc_nat)
| c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0,tc_nat) )
| ~ spl0_346
| ~ spl0_780 ),
inference(resolution,[],[f13303,f4083]) ).
fof(f4083,plain,
( ! [X0,X16,X14] :
( ~ c_lessequals(X16,X14,tc_nat)
| ~ c_lessequals(X14,X0,tc_nat)
| c_lessequals(X16,X0,tc_nat) )
| ~ spl0_346 ),
inference(avatar_component_clause,[],[f4082]) ).
fof(f13303,plain,
( c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)
| ~ spl0_780 ),
inference(avatar_component_clause,[],[f13301]) ).
fof(f20626,plain,
spl0_925,
inference(avatar_split_clause,[],[f384,f20624]) ).
fof(f20624,plain,
( spl0_925
<=> ! [X5,X4,X6,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Omod(X4,X5,X3)),X6),X5,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f384,axiom,
! [X3,X6,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Omod(X4,X5,X3)),X6),X5,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__left__eq_0) ).
fof(f20622,plain,
spl0_924,
inference(avatar_split_clause,[],[f383,f20620]) ).
fof(f20620,plain,
( spl0_924
<=> ! [X5,X4,X6,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X5,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),c_Divides_Odiv__class_Omod(X6,X5,X3)),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f383,axiom,
! [X3,X6,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X5,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),c_Divides_Odiv__class_Omod(X6,X5,X3)),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__right__eq_0) ).
fof(f20618,plain,
spl0_923,
inference(avatar_split_clause,[],[f347,f20616]) ).
fof(f20616,plain,
( spl0_923
<=> ! [X2,X9,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f347,axiom,
! [X2,X3,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_0) ).
fof(f20614,plain,
spl0_922,
inference(avatar_split_clause,[],[f301,f20612]) ).
fof(f20612,plain,
( spl0_922
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oabs__class_Oabs(X17,X3)),X9) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X9),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f301,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oabs__class_Oabs(X17,X3)),X9) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X9),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult__pos_0) ).
fof(f20610,plain,
spl0_921,
inference(avatar_split_clause,[],[f281,f20608]) ).
fof(f20608,plain,
( spl0_921
<=> ! [X3,X4,X6,X29] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(X4,X6,X3) != c_Divides_Odiv__class_Omod(X29,X6,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X4,X3),X6,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X29,X3),X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f281,axiom,
! [X3,X29,X6,X4] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(X4,X6,X3) != c_Divides_Odiv__class_Omod(X29,X6,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X4,X3),X6,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X29,X3),X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__minus__cong_0) ).
fof(f20606,plain,
spl0_920,
inference(avatar_split_clause,[],[f137,f20604]) ).
fof(f20604,plain,
( spl0_920
<=> ! [X5,X4,X7,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X6,X3)
| ~ c_lessequals(X5,X7,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X7),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f137,axiom,
! [X3,X6,X7,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X6,X3)
| ~ c_lessequals(X5,X7,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X7),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).
fof(f20602,plain,
spl0_919,
inference(avatar_split_clause,[],[f40,f20600]) ).
fof(f40,axiom,
! [X2,X3,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_4) ).
fof(f18254,plain,
spl0_918,
inference(avatar_split_clause,[],[f1674,f18252]) ).
fof(f18252,plain,
( spl0_918
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f1674,plain,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat) ),
inference(forward_demodulation,[],[f1673,f421]) ).
fof(f1673,plain,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat) ),
inference(forward_demodulation,[],[f1098,f421]) ).
fof(f1098,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__m__mult__n_0) ).
fof(f18250,plain,
spl0_917,
inference(avatar_split_clause,[],[f1672,f18248]) ).
fof(f18248,plain,
( spl0_917
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f1672,plain,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X1),tc_nat) ),
inference(forward_demodulation,[],[f1671,f421]) ).
fof(f1671,plain,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X1),tc_nat) ),
inference(forward_demodulation,[],[f1097,f421]) ).
fof(f1097,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__n__mult__m_0) ).
fof(f18246,plain,
spl0_916,
inference(avatar_split_clause,[],[f1664,f18244]) ).
fof(f18244,plain,
( spl0_916
<=> ! [X2,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X2
| c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f1664,plain,
! [X2,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X2
| c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1 ),
inference(forward_demodulation,[],[f1663,f421]) ).
fof(f1663,plain,
! [X2,X1] :
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X2
| c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
inference(forward_demodulation,[],[f1662,f421]) ).
fof(f1662,plain,
! [X2,X1] :
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X2
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
inference(forward_demodulation,[],[f289,f421]) ).
fof(f289,axiom,
! [X2,X1] :
( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X2
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_1) ).
fof(f18242,plain,
spl0_915,
inference(avatar_split_clause,[],[f1619,f18240]) ).
fof(f18240,plain,
( spl0_915
<=> ! [X0,X1,X14] :
( c_HOL_Ominus__class_Ominus(hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X14,X0,tc_nat)),X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X14),X0,tc_nat),X1,tc_nat)
| ~ c_lessequals(X0,X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f1619,plain,
! [X0,X1,X14] :
( c_HOL_Ominus__class_Ominus(hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X14,X0,tc_nat)),X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X14),X0,tc_nat),X1,tc_nat)
| ~ c_lessequals(X0,X14,tc_nat) ),
inference(forward_demodulation,[],[f1036,f1191]) ).
fof(f1036,axiom,
! [X0,X1,X14] :
( ~ c_lessequals(X0,X14,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X14,X0,tc_nat)),X1,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq2_0) ).
fof(f18232,plain,
spl0_914,
inference(avatar_split_clause,[],[f1437,f18230]) ).
fof(f18230,plain,
( spl0_914
<=> ! [X17,X3,X9,X22] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oinverse__class_Odivide(X9,X17,X3)),X22) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X22),X17,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f1437,axiom,
! [X3,X9,X17,X22] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oinverse__class_Odivide(X9,X17,X3)),X22) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X22),X17,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).
fof(f18228,plain,
spl0_913,
inference(avatar_split_clause,[],[f1355,f18226]) ).
fof(f18226,plain,
( spl0_913
<=> ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f1355,axiom,
! [X2,X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).
fof(f18224,plain,
spl0_912,
inference(avatar_split_clause,[],[f1330,f18222]) ).
fof(f18222,plain,
( spl0_912
<=> ! [X4,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f1330,axiom,
! [X2,X3,X1,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
fof(f18220,plain,
spl0_911,
inference(avatar_split_clause,[],[f1289,f18218]) ).
fof(f18218,plain,
( spl0_911
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_HOL_Oone__class_Oone(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f1289,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_HOL_Oone__class_Oone(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__minus1__even_0) ).
fof(f18216,plain,
spl0_910,
inference(avatar_split_clause,[],[f1263,f18214]) ).
fof(f18214,plain,
( spl0_910
<=> ! [X1] : c_Divides_Odiv__class_Odiv(hAPP(c_Suc,hAPP(c_Suc,X1)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f1263,axiom,
! [X1] : c_Divides_Odiv__class_Odiv(hAPP(c_Suc,hAPP(c_Suc,X1)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div2__Suc__Suc_0) ).
fof(f18212,plain,
spl0_909,
inference(avatar_split_clause,[],[f1197,f18210]) ).
fof(f18210,plain,
( spl0_909
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X0,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ominus__class_Ominus(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_909])]) ).
fof(f1197,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X0,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).
fof(f18208,plain,
spl0_908,
inference(avatar_split_clause,[],[f1084,f18206]) ).
fof(f18206,plain,
( spl0_908
<=> ! [X24,X3] :
( ~ class_Int_Onumber__ring(X3)
| c_Int_Onumber__class_Onumber__of(c_Int_OBit1(X24),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_Int_Onumber__class_Onumber__of(X24,X3))),c_Int_Onumber__class_Onumber__of(X24,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f1084,axiom,
! [X3,X24] :
( ~ class_Int_Onumber__ring(X3)
| c_Int_Onumber__class_Onumber__of(c_Int_OBit1(X24),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_Int_Onumber__class_Onumber__of(X24,X3))),c_Int_Onumber__class_Onumber__of(X24,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_number__of__Bit1_0) ).
fof(f18204,plain,
spl0_907,
inference(avatar_split_clause,[],[f1034,f18202]) ).
fof(f18202,plain,
( spl0_907
<=> ! [X2,X1] :
( ~ c_lessequals(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f1034,axiom,
! [X2,X1] :
( ~ c_lessequals(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__div__geq_0) ).
fof(f18200,plain,
spl0_906,
inference(avatar_split_clause,[],[f1033,f18198]) ).
fof(f18198,plain,
( spl0_906
<=> ! [X2,X0,X1] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f1033,axiom,
! [X2,X0,X1] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel2_0) ).
fof(f18196,plain,
spl0_905,
inference(avatar_split_clause,[],[f1032,f18194]) ).
fof(f18194,plain,
( spl0_905
<=> ! [X2,X0,X1] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f1032,axiom,
! [X2,X0,X1] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel1_0) ).
fof(f18192,plain,
( spl0_904
| ~ spl0_180
| ~ spl0_812 ),
inference(avatar_split_clause,[],[f15813,f15327,f2546,f18190]) ).
fof(f18190,plain,
( spl0_904
<=> ! [X0] :
( ~ c_lessequals(hAPP(c_Suc,X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_lessequals(X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f2546,plain,
( spl0_180
<=> ! [X9,X17] :
( ~ c_HOL_Oord__class_Oless(X9,X17,tc_nat)
| c_lessequals(X9,X17,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f15327,plain,
( spl0_812
<=> ! [X0] :
( ~ c_lessequals(hAPP(c_Suc,X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f15813,plain,
( ! [X0] :
( ~ c_lessequals(hAPP(c_Suc,X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_lessequals(X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat) )
| ~ spl0_180
| ~ spl0_812 ),
inference(resolution,[],[f15328,f2547]) ).
fof(f2547,plain,
( ! [X9,X17] :
( ~ c_HOL_Oord__class_Oless(X9,X17,tc_nat)
| c_lessequals(X9,X17,tc_nat) )
| ~ spl0_180 ),
inference(avatar_component_clause,[],[f2546]) ).
fof(f15328,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)
| ~ c_lessequals(hAPP(c_Suc,X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
| ~ spl0_812 ),
inference(avatar_component_clause,[],[f15327]) ).
fof(f18188,plain,
spl0_903,
inference(avatar_split_clause,[],[f1020,f18186]) ).
fof(f18186,plain,
( spl0_903
<=> ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(hAPP(c_Suc,X1),X2,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2)),X1)),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f1020,axiom,
! [X2,X0,X1] : c_Divides_Odiv__class_Omod(hAPP(c_Suc,X1),X2,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2)),X1)),X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self4_0) ).
fof(f18184,plain,
spl0_902,
inference(avatar_split_clause,[],[f919,f18182]) ).
fof(f18182,plain,
( spl0_902
<=> ! [X2,X16,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X16),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X16),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f919,axiom,
! [X2,X1,X16] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X16),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X16),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__power__less__imp__less_0) ).
fof(f18180,plain,
spl0_901,
inference(avatar_split_clause,[],[f889,f18178]) ).
fof(f18178,plain,
( spl0_901
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f889,axiom,
! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_2) ).
fof(f18176,plain,
spl0_900,
inference(avatar_split_clause,[],[f888,f18174]) ).
fof(f18174,plain,
( spl0_900
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f888,axiom,
! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_2) ).
fof(f18172,plain,
spl0_899,
inference(avatar_split_clause,[],[f819,f18170]) ).
fof(f18170,plain,
( spl0_899
<=> ! [X24,X3] :
( ~ class_Int_Onumber__ring(X3)
| c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X24),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),c_Int_Onumber__class_Onumber__of(X24,X3))),c_Int_Onumber__class_Onumber__of(X24,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f819,axiom,
! [X3,X24] :
( ~ class_Int_Onumber__ring(X3)
| c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X24),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),c_Int_Onumber__class_Onumber__of(X24,X3))),c_Int_Onumber__class_Onumber__of(X24,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_number__of__Bit0_0) ).
fof(f18168,plain,
spl0_898,
inference(avatar_split_clause,[],[f789,f18166]) ).
fof(f18166,plain,
( spl0_898
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f789,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_2) ).
fof(f18164,plain,
spl0_897,
inference(avatar_split_clause,[],[f767,f18162]) ).
fof(f18162,plain,
( spl0_897
<=> ! [X5,X4,X6,X3] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,X6,X3),X5,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X4,X5,X3),c_Divides_Odiv__class_Omod(X6,X5,X3),X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f767,axiom,
! [X3,X6,X4,X5] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,X6,X3),X5,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X4,X5,X3),c_Divides_Odiv__class_Omod(X6,X5,X3),X3),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__eq_0) ).
fof(f18160,plain,
spl0_896,
inference(avatar_split_clause,[],[f747,f18158]) ).
fof(f18158,plain,
( spl0_896
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| X4 = X6
| c_HOL_Ouminus__class_Ouminus(X6,X3) = X4
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X4) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f747,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oidom(X3)
| X4 = X6
| c_HOL_Ouminus__class_Ouminus(X6,X3) = X4
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X4) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
fof(f18156,plain,
spl0_895,
inference(avatar_split_clause,[],[f494,f18154]) ).
fof(f18154,plain,
( spl0_895
<=> ! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f494,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = hAPP(c_Suc,c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__if_1) ).
fof(f18152,plain,
spl0_894,
inference(avatar_split_clause,[],[f367,f18150]) ).
fof(f18150,plain,
( spl0_894
<=> ! [X22,X9,X17] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X22)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f367,axiom,
! [X9,X17,X22] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X22)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X22)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
fof(f18148,plain,
( spl0_893
| ~ spl0_279
| ~ spl0_832 ),
inference(avatar_split_clause,[],[f15684,f15630,f3058,f18146]) ).
fof(f18146,plain,
( spl0_893
<=> ! [X0] :
( ~ c_lessequals(hAPP(c_Suc,X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f3058,plain,
( spl0_279
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,hAPP(c_Suc,X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f15630,plain,
( spl0_832
<=> ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f15684,plain,
( ! [X0] :
( ~ c_lessequals(hAPP(c_Suc,X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X0,tc_nat) )
| ~ spl0_279
| ~ spl0_832 ),
inference(resolution,[],[f15631,f3059]) ).
fof(f3059,plain,
( ! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,hAPP(c_Suc,X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
| ~ spl0_279 ),
inference(avatar_component_clause,[],[f3058]) ).
fof(f15631,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X0,tc_nat)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
| ~ spl0_832 ),
inference(avatar_component_clause,[],[f15630]) ).
fof(f18144,plain,
spl0_892,
inference(avatar_split_clause,[],[f366,f18142]) ).
fof(f18142,plain,
( spl0_892
<=> ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f366,axiom,
! [X2,X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
fof(f18140,plain,
spl0_891,
inference(avatar_split_clause,[],[f325,f18138]) ).
fof(f18138,plain,
( spl0_891
<=> ! [X0,X16,X14] :
( ~ c_lessequals(X0,X14,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14),X0,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Ominus__class_Ominus(X14,X0,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f325,axiom,
! [X0,X16,X14] :
( ~ c_lessequals(X0,X14,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14),X0,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Ominus__class_Ominus(X14,X0,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__assoc_0) ).
fof(f18136,plain,
spl0_890,
inference(avatar_split_clause,[],[f324,f18134]) ).
fof(f18134,plain,
( spl0_890
<=> ! [X0,X16,X14] :
( ~ c_lessequals(X0,X14,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X16),X0,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X14,X0,tc_nat)),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f324,axiom,
! [X0,X16,X14] :
( ~ c_lessequals(X0,X14,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X16),X0,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X14,X0,tc_nat)),X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__assoc2_0) ).
fof(f18132,plain,
spl0_889,
inference(avatar_split_clause,[],[f38,f18130]) ).
fof(f18130,plain,
( spl0_889
<=> ! [X17,X3,X9,X2] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_lessequals(X9,X17,X3)
| c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f38,axiom,
! [X2,X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_lessequals(X9,X17,X3)
| c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X17),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono__odd_0) ).
fof(f18128,plain,
spl0_888,
inference(avatar_split_clause,[],[f1,f18126]) ).
fof(f18126,plain,
( spl0_888
<=> ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2),tc_nat) = c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2),tc_nat) = c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__div__cancel__disj_1) ).
fof(f17901,plain,
( spl0_887
| ~ spl0_253
| ~ spl0_813 ),
inference(avatar_split_clause,[],[f15573,f15503,f2954,f17899]) ).
fof(f17899,plain,
( spl0_887
<=> ! [X0] :
( ~ c_lessequals(hAPP(c_Suc,X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f2954,plain,
( spl0_253
<=> ! [X2,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,hAPP(c_Suc,X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f15503,plain,
( spl0_813
<=> ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f15573,plain,
( ! [X0] :
( ~ c_lessequals(hAPP(c_Suc,X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X0,tc_nat) )
| ~ spl0_253
| ~ spl0_813 ),
inference(resolution,[],[f15504,f2955]) ).
fof(f2955,plain,
( ! [X2,X1] :
( c_lessequals(X1,hAPP(c_Suc,X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) )
| ~ spl0_253 ),
inference(avatar_component_clause,[],[f2954]) ).
fof(f15504,plain,
( ! [X0] :
( ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X0,tc_nat)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
| ~ spl0_813 ),
inference(avatar_component_clause,[],[f15503]) ).
fof(f17383,plain,
( ~ spl0_30
| ~ spl0_886
| ~ spl0_272
| ~ spl0_748 ),
inference(avatar_split_clause,[],[f13205,f13149,f3030,f17380,f1832]) ).
fof(f1832,plain,
( spl0_30
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f17380,plain,
( spl0_886
<=> c_HOL_Oord__class_Oless(hAPP(c_Suc,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f3030,plain,
( spl0_272
<=> ! [X9,X17,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X9,X17,X3)
| ~ c_HOL_Oord__class_Oless(X17,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f13149,plain,
( spl0_748
<=> c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Suc,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f13205,plain,
( ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| ~ spl0_272
| ~ spl0_748 ),
inference(resolution,[],[f13151,f3031]) ).
fof(f3031,plain,
( ! [X3,X9,X17] :
( ~ c_HOL_Oord__class_Oless(X17,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X17,X3)
| ~ class_Orderings_Opreorder(X3) )
| ~ spl0_272 ),
inference(avatar_component_clause,[],[f3030]) ).
fof(f13151,plain,
( c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Suc,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat)
| ~ spl0_748 ),
inference(avatar_component_clause,[],[f13149]) ).
fof(f16568,plain,
( ~ spl0_30
| ~ spl0_885
| ~ spl0_245
| ~ spl0_748 ),
inference(avatar_split_clause,[],[f13203,f13149,f2922,f16565,f1832]) ).
fof(f16565,plain,
( spl0_885
<=> c_lessequals(hAPP(c_Suc,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f13203,plain,
( ~ c_lessequals(hAPP(c_Suc,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| ~ spl0_245
| ~ spl0_748 ),
inference(resolution,[],[f13151,f2923]) ).
fof(f16236,plain,
( ~ spl0_884
| ~ spl0_663
| ~ spl0_689 ),
inference(avatar_split_clause,[],[f11859,f11029,f10071,f16233]) ).
fof(f16233,plain,
( spl0_884
<=> c_lessequals(hAPP(c_Suc,hAPP(c_Suc,hAPP(c_Suc,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)))),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f10071,plain,
( spl0_663
<=> ! [X0] : ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f11029,plain,
( spl0_689
<=> ! [X2] : hAPP(c_Suc,hAPP(c_Suc,hAPP(c_Suc,X2))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f11859,plain,
( ~ c_lessequals(hAPP(c_Suc,hAPP(c_Suc,hAPP(c_Suc,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)))),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_663
| ~ spl0_689 ),
inference(superposition,[],[f10072,f11030]) ).
fof(f11030,plain,
( ! [X2] : hAPP(c_Suc,hAPP(c_Suc,hAPP(c_Suc,X2))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2)
| ~ spl0_689 ),
inference(avatar_component_clause,[],[f11029]) ).
fof(f10072,plain,
( ! [X0] : ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_663 ),
inference(avatar_component_clause,[],[f10071]) ).
fof(f15934,plain,
spl0_883,
inference(avatar_split_clause,[],[f1633,f15932]) ).
fof(f15932,plain,
( spl0_883
<=> ! [X2,X1] :
( c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X1),X2,tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),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_883])]) ).
fof(f1633,plain,
! [X2,X1] :
( c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X1),X2,tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(forward_demodulation,[],[f1632,f1577]) ).
fof(f1577,plain,
c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),
inference(forward_demodulation,[],[f1247,f421]) ).
fof(f1247,axiom,
hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_numeral__1__eq__Suc__0_0) ).
fof(f1632,plain,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X1),X2,tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f1344,f875]) ).
fof(f875,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__number__of__Pls_0) ).
fof(f1344,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat),X2,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X1),X2,tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__eq__diff__pred_0) ).
fof(f15930,plain,
spl0_882,
inference(avatar_split_clause,[],[f1629,f15928]) ).
fof(f15928,plain,
( spl0_882
<=> ! [X2,X0,X1] :
( c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),X0,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f1629,plain,
! [X2,X0,X1] :
( c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),X0,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
inference(forward_demodulation,[],[f1027,f1038]) ).
fof(f1038,axiom,
! [X6,X4,X5] : c_Divides_Odiv__class_Odiv(X4,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X6),X5),tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X4,X6,tc_nat),X5,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult2__eq_0) ).
fof(f1027,axiom,
! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2),tc_nat) = c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__div__cancel1_0) ).
fof(f15926,plain,
spl0_881,
inference(avatar_split_clause,[],[f1608,f15924]) ).
fof(f15924,plain,
( spl0_881
<=> ! [X9] :
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),c_Divides_Odiv__class_Odiv(X9,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)) = X9
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f1608,plain,
! [X9] :
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),c_Divides_Odiv__class_Odiv(X9,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)) = X9
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ),
inference(forward_demodulation,[],[f1607,f1583]) ).
fof(f1607,plain,
! [X9] :
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))),c_Divides_Odiv__class_Odiv(X9,hAPP(c_Suc,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),tc_nat)) = X9
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ),
inference(forward_demodulation,[],[f240,f421]) ).
fof(f240,axiom,
! [X9] :
( ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),c_Divides_Odiv__class_Odiv(X9,hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__nat__div__two__times__two_0) ).
fof(f15922,plain,
spl0_880,
inference(avatar_split_clause,[],[f1606,f15920]) ).
fof(f15920,plain,
( spl0_880
<=> ! [X9] :
( c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X9,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f1606,plain,
! [X9] :
( c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X9,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ),
inference(forward_demodulation,[],[f1605,f1583]) ).
fof(f1605,plain,
! [X9] :
( c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X9),hAPP(c_Suc,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),tc_nat) = c_Divides_Odiv__class_Odiv(X9,hAPP(c_Suc,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ),
inference(forward_demodulation,[],[f336,f421]) ).
fof(f336,axiom,
! [X9] :
( ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_Divides_Odiv__class_Odiv(hAPP(c_Suc,X9),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_Divides_Odiv__class_Odiv(X9,hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__nat__plus__one__div__two_0) ).
fof(f15918,plain,
spl0_879,
inference(avatar_split_clause,[],[f1439,f15916]) ).
fof(f15916,plain,
( spl0_879
<=> ! [X2,X1,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f1439,axiom,
! [X2,X3,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X1),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
fof(f15914,plain,
spl0_878,
inference(avatar_split_clause,[],[f1434,f15912]) ).
fof(f15912,plain,
( spl0_878
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X0)),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X0)),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f1434,axiom,
! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X0)),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X0)),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).
fof(f15910,plain,
spl0_877,
inference(avatar_split_clause,[],[f1413,f15908]) ).
fof(f15908,plain,
( spl0_877
<=> ! [X2,X4,X3] :
( ~ class_Power_Opower(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(c_Suc,X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f1413,axiom,
! [X2,X3,X4] :
( ~ class_Power_Opower(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(c_Suc,X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc_0) ).
fof(f15906,plain,
spl0_876,
inference(avatar_split_clause,[],[f1412,f15904]) ).
fof(f15904,plain,
( spl0_876
<=> ! [X4,X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(c_Suc,X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f1412,axiom,
! [X2,X3,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(c_Suc,X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc2_0) ).
fof(f15902,plain,
spl0_875,
inference(avatar_split_clause,[],[f1411,f15900]) ).
fof(f1411,axiom,
! [X2,X3,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),hAPP(c_Suc,X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__Suc_0) ).
fof(f15898,plain,
spl0_874,
inference(avatar_split_clause,[],[f1389,f15896]) ).
fof(f15896,plain,
( spl0_874
<=> ! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f1389,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).
fof(f15894,plain,
( ~ spl0_873
| spl0_437
| ~ spl0_812 ),
inference(avatar_split_clause,[],[f15826,f15327,f4892,f15891]) ).
fof(f15891,plain,
( spl0_873
<=> c_lessequals(hAPP(c_Suc,v_i____),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f4892,plain,
( spl0_437
<=> c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f15826,plain,
( ~ c_lessequals(hAPP(c_Suc,v_i____),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| spl0_437
| ~ spl0_812 ),
inference(resolution,[],[f15328,f4894]) ).
fof(f4894,plain,
( ~ c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)
| spl0_437 ),
inference(avatar_component_clause,[],[f4892]) ).
fof(f15889,plain,
spl0_872,
inference(avatar_split_clause,[],[f1332,f15887]) ).
fof(f15887,plain,
( spl0_872
<=> ! [X9,X23,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),hAPP(c_Suc,X23)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X23)),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f1332,axiom,
! [X3,X9,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),hAPP(c_Suc,X23)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X23)),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I28_J_0) ).
fof(f15885,plain,
spl0_871,
inference(avatar_split_clause,[],[f1295,f15883]) ).
fof(f15883,plain,
( spl0_871
<=> ! [X2,X3] :
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Oone__class_Oone(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f1295,axiom,
! [X2,X3] :
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Oone__class_Oone(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__m1__even_0) ).
fof(f15881,plain,
spl0_870,
inference(avatar_split_clause,[],[f1248,f15879]) ).
fof(f15879,plain,
( spl0_870
<=> ! [X10,X11,X9,X13,X12,X3,X8] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,X9),X9) = hAPP(hAPP(X8,X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f1248,axiom,
! [X3,X10,X11,X8,X9,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,X9),X9) = hAPP(hAPP(X8,X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I29_J_0) ).
fof(f15877,plain,
spl0_869,
inference(avatar_split_clause,[],[f1187,f15875]) ).
fof(f15875,plain,
( spl0_869
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X0,X2,tc_nat)
| c_lessequals(X1,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_869])]) ).
fof(f1187,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X0,X2,tc_nat)
| c_lessequals(X1,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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).
fof(f15873,plain,
spl0_868,
inference(avatar_split_clause,[],[f1150,f15871]) ).
fof(f15871,plain,
( spl0_868
<=> ! [X0,X14,X16,X26] :
( ~ c_lessequals(X16,X14,tc_nat)
| ~ c_lessequals(X0,X26,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X26),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f1150,axiom,
! [X0,X26,X16,X14] :
( ~ c_lessequals(X16,X14,tc_nat)
| ~ c_lessequals(X0,X26,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X16),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X26),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__mono_0) ).
fof(f15869,plain,
spl0_867,
inference(avatar_split_clause,[],[f1142,f15867]) ).
fof(f15867,plain,
( spl0_867
<=> ! [X2,X4,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f1142,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__power_0) ).
fof(f15865,plain,
spl0_866,
inference(avatar_split_clause,[],[f1140,f15863]) ).
fof(f15863,plain,
( spl0_866
<=> ! [X24,X3] :
( ~ class_Int_Onumber__ring(X3)
| c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X24),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_HOL_Oone__class_Oone(X3))),c_Int_Onumber__class_Onumber__of(X24,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f1140,axiom,
! [X3,X24] :
( ~ class_Int_Onumber__ring(X3)
| c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X24),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_HOL_Oone__class_Oone(X3))),c_Int_Onumber__class_Onumber__of(X24,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__number__of__Bit0_0) ).
fof(f15861,plain,
spl0_865,
inference(avatar_split_clause,[],[f998,f15859]) ).
fof(f15859,plain,
( spl0_865
<=> ! [X34,X35] :
( ~ c_HOL_Oord__class_Oless(X35,c_Int_OPls,tc_Int_Oint)
| c_HOL_Oord__class_Oless(X34,c_Int_OPls,tc_Int_Oint)
| c_Int_Onumber__class_Onumber__of(X34,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat)),c_Int_Onumber__class_Onumber__of(X35,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f998,axiom,
! [X34,X35] :
( ~ c_HOL_Oord__class_Oless(X35,c_Int_OPls,tc_Int_Oint)
| c_HOL_Oord__class_Oless(X34,c_Int_OPls,tc_Int_Oint)
| c_Int_Onumber__class_Onumber__of(X34,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat)),c_Int_Onumber__class_Onumber__of(X35,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nat__number__of_1) ).
fof(f15857,plain,
spl0_864,
inference(avatar_split_clause,[],[f979,f15855]) ).
fof(f15855,plain,
( spl0_864
<=> ! [X0,X14,X16,X26] :
( ~ c_HOL_Oord__class_Oless(X16,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X26,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X26),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f979,axiom,
! [X0,X26,X16,X14] :
( ~ c_HOL_Oord__class_Oless(X16,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X26,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X26),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
fof(f15853,plain,
spl0_863,
inference(avatar_split_clause,[],[f907,f15851]) ).
fof(f15851,plain,
( spl0_863
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X0,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(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_863])]) ).
fof(f907,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X0,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).
fof(f15808,plain,
spl0_862,
inference(avatar_split_clause,[],[f881,f15806]) ).
fof(f15806,plain,
( spl0_862
<=> ! [X2,X0,X1] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X0)),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X0)),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f881,axiom,
! [X2,X0,X1] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X0)),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X0)),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__le__cancel1_0) ).
fof(f15804,plain,
spl0_861,
inference(avatar_split_clause,[],[f652,f15802]) ).
fof(f15802,plain,
( spl0_861
<=> ! [X1,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_HOL_Oone__class_Oone(X3))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f652,axiom,
! [X3,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_HOL_Oone__class_Oone(X3))),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
fof(f15800,plain,
spl0_860,
inference(avatar_split_clause,[],[f591,f15798]) ).
fof(f15798,plain,
( spl0_860
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X17)),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f591,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X17)),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
fof(f15796,plain,
spl0_859,
inference(avatar_split_clause,[],[f525,f15794]) ).
fof(f15794,plain,
( spl0_859
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f525,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
fof(f15792,plain,
spl0_858,
inference(avatar_split_clause,[],[f524,f15790]) ).
fof(f15790,plain,
( spl0_858
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f524,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).
fof(f15788,plain,
spl0_857,
inference(avatar_split_clause,[],[f523,f15786]) ).
fof(f15786,plain,
( spl0_857
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f523,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X4),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
fof(f15784,plain,
spl0_856,
inference(avatar_split_clause,[],[f522,f15782]) ).
fof(f15782,plain,
( spl0_856
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f522,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
fof(f15780,plain,
spl0_855,
inference(avatar_split_clause,[],[f521,f15778]) ).
fof(f15778,plain,
( spl0_855
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f521,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
fof(f15776,plain,
spl0_854,
inference(avatar_split_clause,[],[f520,f15774]) ).
fof(f15774,plain,
( spl0_854
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f520,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
fof(f15772,plain,
spl0_853,
inference(avatar_split_clause,[],[f492,f15770]) ).
fof(f15770,plain,
( spl0_853
<=> ! [X34,X0,X35] :
( ~ c_HOL_Oord__class_Oless(X34,c_Int_OPls,tc_Int_Oint)
| c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(X35,tc_nat)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f492,axiom,
! [X0,X34,X35] :
( ~ c_HOL_Oord__class_Oless(X34,c_Int_OPls,tc_Int_Oint)
| c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(X35,tc_nat)),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__number__of__mult__left_0) ).
fof(f15739,plain,
spl0_852,
inference(avatar_split_clause,[],[f455,f15737]) ).
fof(f15737,plain,
( spl0_852
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f455,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
fof(f15735,plain,
spl0_851,
inference(avatar_split_clause,[],[f401,f15733]) ).
fof(f15733,plain,
( spl0_851
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f401,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
fof(f15731,plain,
spl0_850,
inference(avatar_split_clause,[],[f389,f15729]) ).
fof(f15729,plain,
( spl0_850
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| ~ c_HOL_Oord__class_Oless(X6,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f389,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| ~ c_HOL_Oord__class_Oless(X6,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
fof(f15727,plain,
spl0_849,
inference(avatar_split_clause,[],[f376,f15725]) ).
fof(f15725,plain,
( spl0_849
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_HOL_Oabs__class_Oabs(X6,X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f376,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_HOL_Oabs__class_Oabs(X6,X3)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__triangle__ineq_0) ).
fof(f15723,plain,
spl0_848,
inference(avatar_split_clause,[],[f350,f15721]) ).
fof(f15721,plain,
( spl0_848
<=> ! [X9,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X9,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_Int_Onumber__class_Onumber__of(X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f350,axiom,
! [X3,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X9,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_Int_Onumber__class_Onumber__of(X9,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__number__of_0) ).
fof(f15719,plain,
spl0_847,
inference(avatar_split_clause,[],[f343,f15717]) ).
fof(f15717,plain,
( spl0_847
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Olordered__ring(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_HOL_Oabs__class_Oabs(X6,X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f343,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Olordered__ring(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_HOL_Oabs__class_Oabs(X6,X3)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__mult_0) ).
fof(f15715,plain,
spl0_846,
inference(avatar_split_clause,[],[f332,f15713]) ).
fof(f15713,plain,
( spl0_846
<=> ! [X2,X9,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(X9,X3)),X2) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f332,axiom,
! [X2,X3,X9] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(X9,X3)),X2) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__power__if_1) ).
fof(f15711,plain,
spl0_845,
inference(avatar_split_clause,[],[f305,f15709]) ).
fof(f15709,plain,
( spl0_845
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f305,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
fof(f15707,plain,
spl0_844,
inference(avatar_split_clause,[],[f246,f15705]) ).
fof(f15705,plain,
( spl0_844
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| ~ c_lessequals(X6,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f246,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| ~ c_lessequals(X6,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
fof(f15703,plain,
spl0_843,
inference(avatar_split_clause,[],[f236,f15701]) ).
fof(f15701,plain,
( spl0_843
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| ~ c_lessequals(X6,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f236,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| ~ c_lessequals(X6,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).
fof(f15672,plain,
spl0_842,
inference(avatar_split_clause,[],[f235,f15670]) ).
fof(f15670,plain,
( spl0_842
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| ~ c_lessequals(X6,X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f235,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| ~ c_lessequals(X6,X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
fof(f15668,plain,
spl0_841,
inference(avatar_split_clause,[],[f232,f15666]) ).
fof(f15666,plain,
( spl0_841
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X17)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f232,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X17),X17)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
fof(f15664,plain,
spl0_840,
inference(avatar_split_clause,[],[f207,f15662]) ).
fof(f15662,plain,
( spl0_840
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f207,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
fof(f15660,plain,
spl0_839,
inference(avatar_split_clause,[],[f206,f15658]) ).
fof(f15658,plain,
( spl0_839
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f206,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
fof(f15656,plain,
spl0_838,
inference(avatar_split_clause,[],[f197,f15654]) ).
fof(f15654,plain,
( spl0_838
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X5,X3)
| c_lessequals(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),c_HOL_Oabs__class_Oabs(X6,X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f197,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X5,X3)
| c_lessequals(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),c_HOL_Oabs__class_Oabs(X6,X3)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_estimate__by__abs_0) ).
fof(f15652,plain,
spl0_837,
inference(avatar_split_clause,[],[f168,f15650]) ).
fof(f15650,plain,
( spl0_837
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Power_Opower(X3)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f168,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Power_Opower(X3)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
fof(f15648,plain,
spl0_836,
inference(avatar_split_clause,[],[f159,f15646]) ).
fof(f15646,plain,
( spl0_836
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f159,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
fof(f15644,plain,
spl0_835,
inference(avatar_split_clause,[],[f158,f15642]) ).
fof(f15642,plain,
( spl0_835
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f158,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
fof(f15640,plain,
spl0_834,
inference(avatar_split_clause,[],[f157,f15638]) ).
fof(f15638,plain,
( spl0_834
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f157,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
fof(f15636,plain,
spl0_833,
inference(avatar_split_clause,[],[f156,f15634]) ).
fof(f15634,plain,
( spl0_833
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f156,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
fof(f15632,plain,
( ~ spl0_30
| spl0_832
| ~ spl0_272
| ~ spl0_614 ),
inference(avatar_split_clause,[],[f9463,f9394,f3030,f15630,f1832]) ).
fof(f9394,plain,
( spl0_614
<=> ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f9463,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X0,tc_nat)
| ~ class_Orderings_Opreorder(tc_nat) )
| ~ spl0_272
| ~ spl0_614 ),
inference(resolution,[],[f9395,f3031]) ).
fof(f9395,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
| ~ spl0_614 ),
inference(avatar_component_clause,[],[f9394]) ).
fof(f15628,plain,
spl0_831,
inference(avatar_split_clause,[],[f136,f15626]) ).
fof(f15626,plain,
( spl0_831
<=> ! [X0,X14,X16,X26] :
( ~ c_lessequals(X16,X14,tc_nat)
| ~ c_lessequals(X0,X26,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X26),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f136,axiom,
! [X0,X26,X16,X14] :
( ~ c_lessequals(X16,X14,tc_nat)
| ~ c_lessequals(X0,X26,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X26),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono_0) ).
fof(f15624,plain,
spl0_830,
inference(avatar_split_clause,[],[f135,f15622]) ).
fof(f15622,plain,
( spl0_830
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f135,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
fof(f15620,plain,
spl0_829,
inference(avatar_split_clause,[],[f121,f15618]) ).
fof(f15618,plain,
( spl0_829
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f121,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
fof(f15616,plain,
spl0_828,
inference(avatar_split_clause,[],[f120,f15614]) ).
fof(f15614,plain,
( spl0_828
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f120,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
fof(f15612,plain,
spl0_827,
inference(avatar_split_clause,[],[f117,f15610]) ).
fof(f15610,plain,
( spl0_827
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f117,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).
fof(f15608,plain,
spl0_826,
inference(avatar_split_clause,[],[f116,f15606]) ).
fof(f15606,plain,
( spl0_826
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f116,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).
fof(f15604,plain,
spl0_825,
inference(avatar_split_clause,[],[f113,f15602]) ).
fof(f15602,plain,
( spl0_825
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f113,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
fof(f15600,plain,
spl0_824,
inference(avatar_split_clause,[],[f112,f15598]) ).
fof(f15598,plain,
( spl0_824
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f112,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
fof(f15596,plain,
spl0_823,
inference(avatar_split_clause,[],[f71,f15594]) ).
fof(f15594,plain,
( spl0_823
<=> ! [X10,X11,X13,X12,X3,X8,X1] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X11,X1),X1) = hAPP(hAPP(X12,hAPP(hAPP(X11,X10),X10)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f71,axiom,
! [X3,X10,X11,X1,X8,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X11,X1),X1) = hAPP(hAPP(X12,hAPP(hAPP(X11,X10),X10)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I4_J_0) ).
fof(f15592,plain,
spl0_822,
inference(avatar_split_clause,[],[f28,f15590]) ).
fof(f15590,plain,
( spl0_822
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f28,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).
fof(f15563,plain,
spl0_821,
inference(avatar_split_clause,[],[f27,f15561]) ).
fof(f15561,plain,
( spl0_821
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f27,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).
fof(f15559,plain,
spl0_820,
inference(avatar_split_clause,[],[f24,f15557]) ).
fof(f15557,plain,
( spl0_820
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f24,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
fof(f15555,plain,
spl0_819,
inference(avatar_split_clause,[],[f23,f15553]) ).
fof(f15553,plain,
( spl0_819
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f23,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).
fof(f15551,plain,
spl0_818,
inference(avatar_split_clause,[],[f22,f15549]) ).
fof(f15549,plain,
( spl0_818
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f22,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
fof(f15547,plain,
spl0_817,
inference(avatar_split_clause,[],[f14,f15545]) ).
fof(f15545,plain,
( spl0_817
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f14,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
fof(f15543,plain,
spl0_816,
inference(avatar_split_clause,[],[f13,f15541]) ).
fof(f15541,plain,
( spl0_816
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f13,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
fof(f15539,plain,
spl0_815,
inference(avatar_split_clause,[],[f12,f15537]) ).
fof(f15537,plain,
( spl0_815
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f12,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
fof(f15535,plain,
spl0_814,
inference(avatar_split_clause,[],[f11,f15533]) ).
fof(f15533,plain,
( spl0_814
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f11,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X6,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
fof(f15505,plain,
( ~ spl0_30
| spl0_813
| ~ spl0_245
| ~ spl0_614 ),
inference(avatar_split_clause,[],[f9461,f9394,f2922,f15503,f1832]) ).
fof(f9461,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X0,tc_nat)
| ~ class_Orderings_Opreorder(tc_nat) )
| ~ spl0_245
| ~ spl0_614 ),
inference(resolution,[],[f9395,f2923]) ).
fof(f15329,plain,
( spl0_812
| ~ spl0_278
| ~ spl0_614 ),
inference(avatar_split_clause,[],[f9446,f9394,f3054,f15327]) ).
fof(f3054,plain,
( spl0_278
<=> ! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X1),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f9446,plain,
( ! [X0] :
( ~ c_lessequals(hAPP(c_Suc,X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat) )
| ~ spl0_278
| ~ spl0_614 ),
inference(resolution,[],[f9395,f3055]) ).
fof(f3055,plain,
( ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X1),X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
| ~ spl0_278 ),
inference(avatar_component_clause,[],[f3054]) ).
fof(f15147,plain,
( spl0_811
| ~ spl0_263
| ~ spl0_614 ),
inference(avatar_split_clause,[],[f9440,f9394,f2994,f15145]) ).
fof(f15145,plain,
( spl0_811
<=> ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_Divides_Odiv__class_Omod(X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f2994,plain,
( spl0_263
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f9440,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_Divides_Odiv__class_Omod(X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat) = X0 )
| ~ spl0_263
| ~ spl0_614 ),
inference(resolution,[],[f9395,f2995]) ).
fof(f2995,plain,
( ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1 )
| ~ spl0_263 ),
inference(avatar_component_clause,[],[f2994]) ).
fof(f15143,plain,
spl0_810,
inference(avatar_split_clause,[],[f1657,f15141]) ).
fof(f15141,plain,
( spl0_810
<=> ! [X2,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f1657,plain,
! [X2,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X2 ),
inference(forward_demodulation,[],[f1656,f421]) ).
fof(f1656,plain,
! [X2,X1] :
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
inference(forward_demodulation,[],[f123,f421]) ).
fof(f123,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X2
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_3) ).
fof(f15139,plain,
spl0_809,
inference(avatar_split_clause,[],[f1655,f15137]) ).
fof(f15137,plain,
( spl0_809
<=> ! [X2,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f1655,plain,
! [X2,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 ),
inference(forward_demodulation,[],[f1654,f421]) ).
fof(f1654,plain,
! [X2,X1] :
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) = X1
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
inference(forward_demodulation,[],[f124,f421]) ).
fof(f124,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_0) ).
fof(f15135,plain,
spl0_808,
inference(avatar_split_clause,[],[f1653,f15133]) ).
fof(f15133,plain,
( spl0_808
<=> ! [X9,X1] :
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X9),X1)
| c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X9
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f1653,plain,
! [X1,X9] :
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X9),X1)
| c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X9
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 ),
inference(forward_demodulation,[],[f1652,f421]) ).
fof(f1652,plain,
! [X1,X9] :
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X9
| c_HOL_Ozero__class_Ozero(tc_nat) = X1
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X9),X1) ),
inference(forward_demodulation,[],[f918,f421]) ).
fof(f918,axiom,
! [X1,X9] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X9
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X9),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__power__eq__Suc__0__iff_0) ).
fof(f15131,plain,
spl0_807,
inference(avatar_split_clause,[],[f1260,f15129]) ).
fof(f15129,plain,
( spl0_807
<=> ! [X1] : c_Divides_Odiv__class_Omod(hAPP(c_Suc,hAPP(c_Suc,X1)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f1260,axiom,
! [X1] : c_Divides_Odiv__class_Omod(hAPP(c_Suc,hAPP(c_Suc,X1)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod2__Suc__Suc_0) ).
fof(f15127,plain,
spl0_806,
inference(avatar_split_clause,[],[f1095,f15125]) ).
fof(f15125,plain,
( spl0_806
<=> ! [X2,X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f1095,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__even__power_H_0) ).
fof(f15123,plain,
spl0_805,
inference(avatar_split_clause,[],[f980,f15121]) ).
fof(f15121,plain,
( spl0_805
<=> ! [X26,X0,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X26,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f980,axiom,
! [X2,X0,X1,X26] :
( ~ c_HOL_Oord__class_Oless(X0,X26,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
fof(f15119,plain,
spl0_804,
inference(avatar_split_clause,[],[f968,f15117]) ).
fof(f15117,plain,
( spl0_804
<=> ! [X4,X2,X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Power_Opower(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f968,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Power_Opower(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
fof(f15115,plain,
spl0_803,
inference(avatar_split_clause,[],[f956,f15113]) ).
fof(f15113,plain,
( spl0_803
<=> ! [X2,X1] :
( hAPP(c_Suc,c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = X2
| hAPP(c_Suc,c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,X1),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f956,axiom,
! [X2,X1] :
( hAPP(c_Suc,c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = X2
| hAPP(c_Suc,c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,X1),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_1) ).
fof(f15111,plain,
spl0_802,
inference(avatar_split_clause,[],[f898,f15109]) ).
fof(f15109,plain,
( spl0_802
<=> ! [X2,X0,X1] :
( X1 = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f898,axiom,
! [X2,X0,X1] :
( X1 = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).
fof(f15107,plain,
spl0_801,
inference(avatar_split_clause,[],[f743,f15105]) ).
fof(f15105,plain,
( spl0_801
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_HOL_Oabs__class_Oabs(X6,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f743,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_HOL_Oabs__class_Oabs(X6,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult_0) ).
fof(f15053,plain,
spl0_800,
inference(avatar_split_clause,[],[f730,f15051]) ).
fof(f15051,plain,
( spl0_800
<=> ! [X6,X24,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Int_Onumber__class_Onumber__of(X24,X3)
| c_Int_Onumber__class_Onumber__of(X24,X3) != c_HOL_Oinverse__class_Odivide(X6,c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f730,axiom,
! [X3,X6,X24] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Int_Onumber__class_Onumber__of(X24,X3)
| c_Int_Onumber__class_Onumber__of(X24,X3) != c_HOL_Oinverse__class_Odivide(X6,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_1) ).
fof(f15049,plain,
spl0_799,
inference(avatar_split_clause,[],[f475,f15047]) ).
fof(f15047,plain,
( spl0_799
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X4,X3)),c_HOL_Ouminus__class_Ouminus(X6,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f475,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X4,X3)),c_HOL_Ouminus__class_Ouminus(X6,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
fof(f15045,plain,
spl0_798,
inference(avatar_split_clause,[],[f474,f15043]) ).
fof(f15043,plain,
( spl0_798
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X6,X3)),c_HOL_Ouminus__class_Ouminus(X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f474,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X6,X3)),c_HOL_Ouminus__class_Ouminus(X4,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add_0) ).
fof(f15041,plain,
spl0_797,
inference(avatar_split_clause,[],[f461,f15039]) ).
fof(f15039,plain,
( spl0_797
<=> ! [X6,X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Omod(X4,X6,X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Divides_Odiv__class_Odiv(X4,X6,X3)),X6)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f461,axiom,
! [X3,X6,X4] :
( ~ class_Divides_Osemiring__div(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Omod(X4,X6,X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Divides_Odiv__class_Odiv(X4,X6,X3)),X6)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_semiring__div__class_Omod__div__equality_H_0) ).
fof(f15037,plain,
spl0_796,
inference(avatar_split_clause,[],[f425,f15035]) ).
fof(f15035,plain,
( spl0_796
<=> ! [X5,X4,X6,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,X6,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6)),X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f425,axiom,
! [X3,X6,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,X6,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X5),X6)),X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1_0) ).
fof(f15033,plain,
spl0_795,
inference(avatar_split_clause,[],[f424,f15031]) ).
fof(f15031,plain,
( spl0_795
<=> ! [X5,X4,X6,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,X6,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5)),X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f424,axiom,
! [X3,X6,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,X6,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X5)),X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2_0) ).
fof(f15029,plain,
spl0_794,
inference(avatar_split_clause,[],[f393,f15027]) ).
fof(f15027,plain,
( spl0_794
<=> ! [X9,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X9
| c_lessequals(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f393,axiom,
! [X2,X3,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X9
| c_lessequals(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_3) ).
fof(f15025,plain,
spl0_793,
inference(avatar_split_clause,[],[f298,f15023]) ).
fof(f15023,plain,
( spl0_793
<=> ! [X0,X16,X14] :
( ~ c_lessequals(X0,X14,tc_nat)
| c_HOL_Ominus__class_Ominus(X16,c_HOL_Ominus__class_Ominus(X14,X0,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X0),X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f298,axiom,
! [X0,X16,X14] :
( ~ c_lessequals(X0,X14,tc_nat)
| c_HOL_Ominus__class_Ominus(X16,c_HOL_Ominus__class_Ominus(X14,X0,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X0),X14,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__right_0) ).
fof(f15021,plain,
spl0_792,
inference(avatar_split_clause,[],[f297,f15019]) ).
fof(f15019,plain,
( spl0_792
<=> ! [X2,X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(X4,X3)),X2),X3) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f297,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(X4,X3)),X2),X3) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__power__minus_0) ).
fof(f15017,plain,
spl0_791,
inference(avatar_split_clause,[],[f163,f15015]) ).
fof(f15015,plain,
( spl0_791
<=> ! [X6,X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f163,axiom,
! [X3,X6,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult1__if_0) ).
fof(f15013,plain,
( spl0_790
| ~ spl0_291
| ~ spl0_780 ),
inference(avatar_split_clause,[],[f13920,f13301,f3495,f15010]) ).
fof(f15010,plain,
( spl0_790
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f3495,plain,
( spl0_291
<=> ! [X2,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f13920,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)
| ~ spl0_291
| ~ spl0_780 ),
inference(resolution,[],[f13303,f3496]) ).
fof(f3496,plain,
( ! [X2,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) )
| ~ spl0_291 ),
inference(avatar_component_clause,[],[f3495]) ).
fof(f15008,plain,
spl0_789,
inference(avatar_split_clause,[],[f32,f15006]) ).
fof(f15006,plain,
( spl0_789
<=> ! [X6,X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Divides_Odiv__class_Odiv(X4,X6,X3)),X6)),c_Divides_Odiv__class_Omod(X4,X6,X3)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f32,axiom,
! [X3,X6,X4] :
( ~ class_Divides_Osemiring__div(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Divides_Odiv__class_Odiv(X4,X6,X3)),X6)),c_Divides_Odiv__class_Omod(X4,X6,X3)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__equality_0) ).
fof(f15004,plain,
spl0_788,
inference(avatar_split_clause,[],[f31,f15002]) ).
fof(f15002,plain,
( spl0_788
<=> ! [X6,X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),c_Divides_Odiv__class_Odiv(X4,X6,X3))),c_Divides_Odiv__class_Omod(X4,X6,X3)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f31,axiom,
! [X3,X6,X4] :
( ~ class_Divides_Osemiring__div(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),c_Divides_Odiv__class_Odiv(X4,X6,X3))),c_Divides_Odiv__class_Omod(X4,X6,X3)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__equality2_0) ).
fof(f14288,plain,
( spl0_787
| ~ spl0_180
| ~ spl0_748 ),
inference(avatar_split_clause,[],[f13200,f13149,f2546,f14285]) ).
fof(f14285,plain,
( spl0_787
<=> c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Suc,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f13200,plain,
( c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Suc,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat)
| ~ spl0_180
| ~ spl0_748 ),
inference(resolution,[],[f13151,f2547]) ).
fof(f13328,plain,
spl0_786,
inference(avatar_split_clause,[],[f1397,f13326]) ).
fof(f13326,plain,
( spl0_786
<=> ! [X17,X36,X9,X3] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X9,X17,X3),X36,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X9,X36,X3),c_HOL_Oinverse__class_Odivide(X17,X36,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f1397,axiom,
! [X3,X36,X9,X17] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X9,X17,X3),X36,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X9,X36,X3),c_HOL_Oinverse__class_Odivide(X17,X36,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Odiff_0) ).
fof(f13324,plain,
spl0_785,
inference(avatar_split_clause,[],[f1396,f13322]) ).
fof(f13322,plain,
( spl0_785
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X4,X6,X3),X5,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Oinverse__class_Odivide(X6,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f1396,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X4,X6,X3),X5,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Oinverse__class_Odivide(X6,X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).
fof(f13320,plain,
spl0_784,
inference(avatar_split_clause,[],[f1367,f13318]) ).
fof(f13318,plain,
( spl0_784
<=> ! [X2,X0,X1] :
( X1 = X2
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X0)),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f1367,axiom,
! [X2,X0,X1] :
( X1 = X2
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X0)),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X0)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__cancel1_0) ).
fof(f13316,plain,
spl0_783,
inference(avatar_split_clause,[],[f1280,f13314]) ).
fof(f13314,plain,
( spl0_783
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f1280,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power2_1) ).
fof(f13312,plain,
spl0_782,
inference(avatar_split_clause,[],[f1192,f13310]) ).
fof(f13310,plain,
( spl0_782
<=> ! [X2,X0,X1] :
( X1 = X2
| ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X0,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) != c_HOL_Ominus__class_Ominus(X2,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f1192,axiom,
! [X2,X0,X1] :
( X1 = X2
| ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X0,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) != c_HOL_Ominus__class_Ominus(X2,X0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).
fof(f13308,plain,
spl0_781,
inference(avatar_split_clause,[],[f1145,f13306]) ).
fof(f13306,plain,
( spl0_781
<=> ! [X2,X0,X1] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f1145,axiom,
! [X2,X0,X1] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel2_0) ).
fof(f13304,plain,
( spl0_780
| ~ spl0_259
| ~ spl0_748 ),
inference(avatar_split_clause,[],[f13196,f13149,f2978,f13301]) ).
fof(f2978,plain,
( spl0_259
<=> ! [X2,X1] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(c_Suc,X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f13196,plain,
( c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)
| ~ spl0_259
| ~ spl0_748 ),
inference(resolution,[],[f13151,f2979]) ).
fof(f2979,plain,
( ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,hAPP(c_Suc,X2),tc_nat)
| c_lessequals(X1,X2,tc_nat) )
| ~ spl0_259 ),
inference(avatar_component_clause,[],[f2978]) ).
fof(f13299,plain,
spl0_779,
inference(avatar_split_clause,[],[f1143,f13297]) ).
fof(f13297,plain,
( spl0_779
<=> ! [X2,X0,X1] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f1143,axiom,
! [X2,X0,X1] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel__disj_0) ).
fof(f13295,plain,
spl0_778,
inference(avatar_split_clause,[],[f899,f13293]) ).
fof(f13293,plain,
( spl0_778
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f899,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_2) ).
fof(f13291,plain,
spl0_777,
inference(avatar_split_clause,[],[f885,f13289]) ).
fof(f13289,plain,
( spl0_777
<=> ! [X2,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),hAPP(c_Suc,X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f885,axiom,
! [X2,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),hAPP(c_Suc,X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc__right_0) ).
fof(f13287,plain,
spl0_776,
inference(avatar_split_clause,[],[f884,f13285]) ).
fof(f13285,plain,
( spl0_776
<=> ! [X2,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X1)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f884,axiom,
! [X2,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X1)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc_0) ).
fof(f13283,plain,
spl0_775,
inference(avatar_split_clause,[],[f786,f13281]) ).
fof(f13281,plain,
( spl0_775
<=> ! [X2,X9,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f786,axiom,
! [X2,X3,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__zero__eq_2) ).
fof(f13279,plain,
spl0_774,
inference(avatar_split_clause,[],[f784,f13277]) ).
fof(f13277,plain,
( spl0_774
<=> ! [X2,X9,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f784,axiom,
! [X2,X3,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_5) ).
fof(f13275,plain,
spl0_773,
inference(avatar_split_clause,[],[f766,f13273]) ).
fof(f13273,plain,
( spl0_773
<=> ! [X5,X4,X6,X3] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,X6,X3),X5,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X4,X5,X3),X6,X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f766,axiom,
! [X3,X6,X4,X5] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,X6,X3),X5,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X4,X5,X3),X6,X3),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__left__eq_0) ).
fof(f13271,plain,
spl0_772,
inference(avatar_split_clause,[],[f765,f13269]) ).
fof(f13269,plain,
( spl0_772
<=> ! [X5,X4,X6,X3] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,X6,X3),X5,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,c_Divides_Odiv__class_Omod(X6,X5,X3),X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f765,axiom,
! [X3,X6,X4,X5] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,X6,X3),X5,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,c_Divides_Odiv__class_Omod(X6,X5,X3),X3),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__right__eq_0) ).
fof(f13267,plain,
spl0_771,
inference(avatar_split_clause,[],[f606,f13265]) ).
fof(f13265,plain,
( spl0_771
<=> ! [X4,X9,X27,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X9,X4,X3),X3),X27,X3)
| c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X27),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f606,axiom,
! [X3,X9,X27,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X9,X4,X3),X3),X27,X3)
| c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X27),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__diff__less__iff_1) ).
fof(f13263,plain,
spl0_770,
inference(avatar_split_clause,[],[f605,f13261]) ).
fof(f13261,plain,
( spl0_770
<=> ! [X9,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_Int_Onumber__class_Onumber__of(X9,X3) = c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f605,axiom,
! [X3,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_Int_Onumber__class_Onumber__of(X9,X3) = c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X9,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__number__of_1) ).
fof(f13259,plain,
( ~ spl0_769
| ~ spl0_277
| ~ spl0_748 ),
inference(avatar_split_clause,[],[f13195,f13149,f3050,f13256]) ).
fof(f13256,plain,
( spl0_769
<=> c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f3050,plain,
( spl0_277
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,hAPP(c_Suc,X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f13195,plain,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)
| ~ spl0_277
| ~ spl0_748 ),
inference(resolution,[],[f13151,f3051]) ).
fof(f3051,plain,
( ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X2,hAPP(c_Suc,X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
| ~ spl0_277 ),
inference(avatar_component_clause,[],[f3050]) ).
fof(f13254,plain,
spl0_768,
inference(avatar_split_clause,[],[f559,f13252]) ).
fof(f13252,plain,
( spl0_768
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f559,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
fof(f13250,plain,
spl0_767,
inference(avatar_split_clause,[],[f558,f13248]) ).
fof(f13248,plain,
( spl0_767
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f558,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
fof(f13246,plain,
spl0_766,
inference(avatar_split_clause,[],[f557,f13244]) ).
fof(f13244,plain,
( spl0_766
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f557,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
fof(f13242,plain,
spl0_765,
inference(avatar_split_clause,[],[f556,f13240]) ).
fof(f13240,plain,
( spl0_765
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f556,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
fof(f13238,plain,
spl0_764,
inference(avatar_split_clause,[],[f555,f13236]) ).
fof(f13236,plain,
( spl0_764
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f555,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
fof(f13234,plain,
spl0_763,
inference(avatar_split_clause,[],[f554,f13232]) ).
fof(f13232,plain,
( spl0_763
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f554,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
fof(f13230,plain,
spl0_762,
inference(avatar_split_clause,[],[f486,f13228]) ).
fof(f13228,plain,
( spl0_762
<=> ! [X9,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3),X9,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f486,axiom,
! [X3,X9] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3),X9,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X9,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus1__divide_0) ).
fof(f13226,plain,
spl0_761,
inference(avatar_split_clause,[],[f465,f13224]) ).
fof(f13224,plain,
( spl0_761
<=> ! [X2,X9,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f465,axiom,
! [X2,X3,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__odd__power_0) ).
fof(f13222,plain,
spl0_760,
inference(avatar_split_clause,[],[f420,f13220]) ).
fof(f13220,plain,
( spl0_760
<=> ! [X17,X3,X9,X22] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(X22,X3) = X9
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X17),X22)) != X17 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f420,axiom,
! [X3,X9,X17,X22] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(X22,X3) = X9
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X17),X22)) != X17 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
fof(f13218,plain,
spl0_759,
inference(avatar_split_clause,[],[f406,f13216]) ).
fof(f13216,plain,
( spl0_759
<=> ! [X2,X9,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Oabs__class_Oabs(X9,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f406,axiom,
! [X2,X3,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Oabs__class_Oabs(X9,X3)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__even__abs_0) ).
fof(f13192,plain,
spl0_758,
inference(avatar_split_clause,[],[f392,f13190]) ).
fof(f13190,plain,
( spl0_758
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),X2),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f392,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),X2),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_5) ).
fof(f13188,plain,
spl0_757,
inference(avatar_split_clause,[],[f373,f13186]) ).
fof(f13186,plain,
( spl0_757
<=> ! [X2,X1] :
( c_HOL_Oord__class_Oless(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)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f373,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(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)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
fof(f13184,plain,
spl0_756,
inference(avatar_split_clause,[],[f356,f13182]) ).
fof(f13182,plain,
( spl0_756
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X6,X3),X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X6,X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f356,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X6,X3),X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X6,X3),X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__triangle__ineq3_0) ).
fof(f13180,plain,
spl0_755,
inference(avatar_split_clause,[],[f331,f13178]) ).
fof(f13178,plain,
( spl0_755
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X6,X3),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_HOL_Oabs__class_Oabs(X6,X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f331,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X6,X3),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_HOL_Oabs__class_Oabs(X6,X3)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__triangle__ineq4_0) ).
fof(f13176,plain,
spl0_754,
inference(avatar_split_clause,[],[f319,f13174]) ).
fof(f13174,plain,
( spl0_754
<=> ! [X2,X9,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_lessequals(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f319,axiom,
! [X2,X3,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_lessequals(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_2) ).
fof(f13172,plain,
spl0_753,
inference(avatar_split_clause,[],[f259,f13170]) ).
fof(f13170,plain,
( spl0_753
<=> ! [X2,X9,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(X9,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f259,axiom,
! [X2,X3,X9] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(X9,X3)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__power__if_0) ).
fof(f13168,plain,
spl0_752,
inference(avatar_split_clause,[],[f238,f13166]) ).
fof(f13166,plain,
( spl0_752
<=> ! [X0,X16,X14] :
( ~ c_lessequals(X0,X14,tc_nat)
| ~ c_lessequals(X16,c_HOL_Ominus__class_Ominus(X14,X0,tc_nat),tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X0),X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f238,axiom,
! [X0,X16,X14] :
( ~ c_lessequals(X0,X14,tc_nat)
| ~ c_lessequals(X16,c_HOL_Ominus__class_Ominus(X14,X0,tc_nat),tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X0),X14,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv2_0) ).
fof(f13164,plain,
spl0_751,
inference(avatar_split_clause,[],[f183,f13162]) ).
fof(f13162,plain,
( spl0_751
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X6,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f183,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X6,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
fof(f13160,plain,
spl0_750,
inference(avatar_split_clause,[],[f182,f13158]) ).
fof(f13158,plain,
( spl0_750
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X6,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f182,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X6,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
fof(f13156,plain,
spl0_749,
inference(avatar_split_clause,[],[f181,f13154]) ).
fof(f13154,plain,
( spl0_749
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X4,X6,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f181,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X4,X6,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
fof(f13152,plain,
( spl0_748
| ~ spl0_154
| ~ spl0_741 ),
inference(avatar_split_clause,[],[f13044,f12794,f2436,f13149]) ).
fof(f2436,plain,
( spl0_154
<=> ! [X2] : c_HOL_Oord__class_Oless(X2,hAPP(c_Suc,X2),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f12794,plain,
( spl0_741
<=> ! [X0] :
( c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f13044,plain,
( c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Suc,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat)
| ~ spl0_154
| ~ spl0_741 ),
inference(resolution,[],[f12795,f2437]) ).
fof(f2437,plain,
( ! [X2] : c_HOL_Oord__class_Oless(X2,hAPP(c_Suc,X2),tc_nat)
| ~ spl0_154 ),
inference(avatar_component_clause,[],[f2436]) ).
fof(f12795,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X0,tc_nat)
| c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0,tc_nat) )
| ~ spl0_741 ),
inference(avatar_component_clause,[],[f12794]) ).
fof(f13147,plain,
spl0_747,
inference(avatar_split_clause,[],[f180,f13145]) ).
fof(f13145,plain,
( spl0_747
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X4,X6,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f180,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X4,X6,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
fof(f13143,plain,
spl0_746,
inference(avatar_split_clause,[],[f179,f13141]) ).
fof(f13141,plain,
( spl0_746
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X4,X6,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f179,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X4,X6,X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
fof(f13139,plain,
spl0_745,
inference(avatar_split_clause,[],[f178,f13137]) ).
fof(f13137,plain,
( spl0_745
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X4,X6,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f178,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X4,X6,X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
fof(f13135,plain,
spl0_744,
inference(avatar_split_clause,[],[f153,f13133]) ).
fof(f13133,plain,
( spl0_744
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(X6,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f153,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(X6,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
fof(f13131,plain,
spl0_743,
inference(avatar_split_clause,[],[f108,f13129]) ).
fof(f13129,plain,
( spl0_743
<=> ! [X17,X3,X9,X22] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X17 = X22
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X17) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f108,axiom,
! [X3,X9,X17,X22] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X17 = X22
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X17) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
fof(f13127,plain,
spl0_742,
inference(avatar_split_clause,[],[f20,f13125]) ).
fof(f13125,plain,
( spl0_742
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f20,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_1) ).
fof(f12796,plain,
( spl0_741
| ~ spl0_200
| ~ spl0_506
| ~ spl0_606 ),
inference(avatar_split_clause,[],[f8809,f8336,f6059,f2654,f12794]) ).
fof(f2654,plain,
( spl0_200
<=> hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f6059,plain,
( spl0_506
<=> ! [X16,X0,X14] :
( ~ c_HOL_Oord__class_Oless(X16,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X0,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(c_Suc,X16),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f8336,plain,
( spl0_606
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f8809,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X0,tc_nat) )
| ~ spl0_200
| ~ spl0_506
| ~ spl0_606 ),
inference(forward_demodulation,[],[f8791,f2656]) ).
fof(f2656,plain,
( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_200 ),
inference(avatar_component_clause,[],[f2654]) ).
fof(f8791,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X0,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat) )
| ~ spl0_506
| ~ spl0_606 ),
inference(resolution,[],[f8338,f6060]) ).
fof(f6060,plain,
( ! [X0,X16,X14] :
( ~ c_HOL_Oord__class_Oless(X16,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X0,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(c_Suc,X16),X0,tc_nat) )
| ~ spl0_506 ),
inference(avatar_component_clause,[],[f6059]) ).
fof(f8338,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)
| ~ spl0_606 ),
inference(avatar_component_clause,[],[f8336]) ).
fof(f12252,plain,
spl0_740,
inference(avatar_split_clause,[],[f1646,f12250]) ).
fof(f12250,plain,
( spl0_740
<=> ! [X2,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f1646,plain,
! [X2,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 ),
inference(forward_demodulation,[],[f35,f421]) ).
fof(f35,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X1
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_2) ).
fof(f12248,plain,
spl0_739,
inference(avatar_split_clause,[],[f1643,f12246]) ).
fof(f12246,plain,
( spl0_739
<=> ! [X2,X1] :
( ~ c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat)
| c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f1643,plain,
! [X2,X1] :
( ~ c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat)
| c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2,tc_nat) ),
inference(forward_demodulation,[],[f1642,f421]) ).
fof(f1642,plain,
! [X2,X1] :
( c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2,tc_nat)
| ~ c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat) ),
inference(forward_demodulation,[],[f1022,f421]) ).
fof(f1022,axiom,
! [X2,X1] :
( c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__mult__iff_1) ).
fof(f12244,plain,
spl0_738,
inference(avatar_split_clause,[],[f1641,f12242]) ).
fof(f12242,plain,
( spl0_738
<=> ! [X2,X1] :
( ~ c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat)
| c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f1641,plain,
! [X2,X1] :
( ~ c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat)
| c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat) ),
inference(forward_demodulation,[],[f1640,f421]) ).
fof(f1640,plain,
! [X2,X1] :
( c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat)
| ~ c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat) ),
inference(forward_demodulation,[],[f1021,f421]) ).
fof(f1021,axiom,
! [X2,X1] :
( c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__mult__iff_0) ).
fof(f12240,plain,
( spl0_737
| ~ spl0_193
| ~ spl0_691 ),
inference(avatar_split_clause,[],[f11169,f11037,f2626,f12238]) ).
fof(f12238,plain,
( spl0_737
<=> ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f2626,plain,
( spl0_193
<=> ! [X2,X1] : c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f11037,plain,
( spl0_691
<=> ! [X0] :
( ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f11169,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat)
| ~ spl0_193
| ~ spl0_691 ),
inference(resolution,[],[f11038,f2627]) ).
fof(f2627,plain,
( ! [X2,X1] : c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
| ~ spl0_193 ),
inference(avatar_component_clause,[],[f2626]) ).
fof(f11038,plain,
( ! [X0] :
( ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
| ~ spl0_691 ),
inference(avatar_component_clause,[],[f11037]) ).
fof(f12236,plain,
spl0_736,
inference(avatar_split_clause,[],[f1639,f12234]) ).
fof(f12234,plain,
( spl0_736
<=> ! [X2,X16] :
( c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X16),X2),tc_nat)
| ~ c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f1639,plain,
! [X2,X16] :
( c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X16),X2),tc_nat)
| ~ c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X16,tc_nat) ),
inference(forward_demodulation,[],[f1638,f421]) ).
fof(f1638,plain,
! [X2,X16] :
( ~ c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X16,tc_nat)
| c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X16),X2),tc_nat) ),
inference(forward_demodulation,[],[f1200,f421]) ).
fof(f1200,axiom,
! [X2,X16] :
( ~ c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X16,tc_nat)
| c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X16),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__one__le__power_0) ).
fof(f12232,plain,
spl0_735,
inference(avatar_split_clause,[],[f1576,f12230]) ).
fof(f12230,plain,
( spl0_735
<=> ! [X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f1576,plain,
! [X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)) ),
inference(duplicate_literal_removal,[],[f357]) ).
fof(f357,axiom,
! [X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
fof(f12228,plain,
spl0_734,
inference(avatar_split_clause,[],[f1365,f12226]) ).
fof(f12226,plain,
( spl0_734
<=> ! [X38,X17,X3,X9,X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X9,X17,X3)
| c_HOL_Oord__class_Oless(X38,X39,X3)
| c_HOL_Ominus__class_Ominus(X9,X17,X3) != c_HOL_Ominus__class_Ominus(X38,X39,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f1365,axiom,
! [X38,X3,X39,X9,X17] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X9,X17,X3)
| c_HOL_Oord__class_Oless(X38,X39,X3)
| c_HOL_Ominus__class_Ominus(X9,X17,X3) != c_HOL_Ominus__class_Ominus(X38,X39,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).
fof(f12224,plain,
spl0_733,
inference(avatar_split_clause,[],[f1362,f12222]) ).
fof(f12222,plain,
( spl0_733
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f1362,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power2__eq__square_0) ).
fof(f12220,plain,
spl0_732,
inference(avatar_split_clause,[],[f1343,f12218]) ).
fof(f12218,plain,
( spl0_732
<=> ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X1),X2,tc_nat),hAPP(c_Suc,X0),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f1343,axiom,
! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X1),X2,tc_nat),hAPP(c_Suc,X0),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).
fof(f12216,plain,
spl0_731,
inference(avatar_split_clause,[],[f1337,f12214]) ).
fof(f12214,plain,
( spl0_731
<=> ! [X9,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f1337,axiom,
! [X3,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X9),X9) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I29_J_0) ).
fof(f12212,plain,
spl0_730,
inference(avatar_split_clause,[],[f1328,f12210]) ).
fof(f12210,plain,
( spl0_730
<=> ! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(c_Suc,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f1328,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),hAPP(c_Suc,X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1_0) ).
fof(f12208,plain,
spl0_729,
inference(avatar_split_clause,[],[f1268,f12206]) ).
fof(f12206,plain,
( spl0_729
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f1268,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__eq__power2_0) ).
fof(f12204,plain,
spl0_728,
inference(avatar_split_clause,[],[f1257,f12202]) ).
fof(f12202,plain,
( spl0_728
<=> ! [X22,X3] :
( ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X22),X22) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X3)),X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f1257,axiom,
! [X3,X22] :
( ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X22),X22) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X3)),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__2_0) ).
fof(f12200,plain,
spl0_727,
inference(avatar_split_clause,[],[f1256,f12198]) ).
fof(f12198,plain,
( spl0_727
<=> ! [X22,X3] :
( ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X22),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X22),X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f1256,axiom,
! [X3,X22] :
( ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X22),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X22),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__2__right_0) ).
fof(f12196,plain,
( spl0_726
| ~ spl0_192
| ~ spl0_691 ),
inference(avatar_split_clause,[],[f11168,f11037,f2622,f12194]) ).
fof(f12194,plain,
( spl0_726
<=> ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f2622,plain,
( spl0_192
<=> ! [X9,X1] : c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X9),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f11168,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),X0),tc_nat)
| ~ spl0_192
| ~ spl0_691 ),
inference(resolution,[],[f11038,f2623]) ).
fof(f2623,plain,
( ! [X1,X9] : c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X9),tc_nat)
| ~ spl0_192 ),
inference(avatar_component_clause,[],[f2622]) ).
fof(f12192,plain,
spl0_725,
inference(avatar_split_clause,[],[f1182,f12190]) ).
fof(f12190,plain,
( spl0_725
<=> ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f1182,axiom,
! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).
fof(f12188,plain,
spl0_724,
inference(avatar_split_clause,[],[f1181,f12186]) ).
fof(f12186,plain,
( spl0_724
<=> ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f1181,axiom,
! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel_0) ).
fof(f12184,plain,
spl0_723,
inference(avatar_split_clause,[],[f1029,f12182]) ).
fof(f12182,plain,
( spl0_723
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f1029,axiom,
! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel2_1) ).
fof(f12180,plain,
spl0_722,
inference(avatar_split_clause,[],[f1028,f12178]) ).
fof(f12178,plain,
( spl0_722
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f1028,axiom,
! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel1_1) ).
fof(f12176,plain,
spl0_721,
inference(avatar_split_clause,[],[f969,f12174]) ).
fof(f12174,plain,
( spl0_721
<=> ! [X2,X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Oabs__class_Oabs(X4,X3)),X2) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f969,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Oabs__class_Oabs(X4,X3)),X2) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__abs_0) ).
fof(f12172,plain,
spl0_720,
inference(avatar_split_clause,[],[f921,f12170]) ).
fof(f12170,plain,
( spl0_720
<=> ! [X2,X9] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| 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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X9),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f921,axiom,
! [X2,X9] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| 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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X9),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__zero__less__power__iff_0) ).
fof(f12168,plain,
spl0_719,
inference(avatar_split_clause,[],[f897,f12166]) ).
fof(f12166,plain,
( spl0_719
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f897,axiom,
! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_0) ).
fof(f12164,plain,
spl0_718,
inference(avatar_split_clause,[],[f896,f12162]) ).
fof(f12162,plain,
( spl0_718
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f896,axiom,
! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_0) ).
fof(f12160,plain,
spl0_717,
inference(avatar_split_clause,[],[f820,f12158]) ).
fof(f12158,plain,
( spl0_717
<=> ! [X9,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3)),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f820,axiom,
! [X3,X9] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3)),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__one__odd__power_0) ).
fof(f12156,plain,
spl0_716,
inference(avatar_split_clause,[],[f783,f12154]) ).
fof(f12154,plain,
( spl0_716
<=> ! [X2,X9,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_HOL_Ozero__class_Ozero(X3) = X9
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f783,axiom,
! [X2,X3,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_HOL_Ozero__class_Ozero(X3) = X9
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_4) ).
fof(f12122,plain,
spl0_715,
inference(avatar_split_clause,[],[f769,f12120]) ).
fof(f12120,plain,
( spl0_715
<=> ! [X38,X17,X9,X3,X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X17,X9,X3)
| c_lessequals(X39,X38,X3)
| c_HOL_Ominus__class_Ominus(X9,X17,X3) != c_HOL_Ominus__class_Ominus(X38,X39,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f769,axiom,
! [X38,X3,X39,X9,X17] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X17,X9,X3)
| c_lessequals(X39,X38,X3)
| c_HOL_Ominus__class_Ominus(X9,X17,X3) != c_HOL_Ominus__class_Ominus(X38,X39,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).
fof(f12118,plain,
spl0_714,
inference(avatar_split_clause,[],[f745,f12116]) ).
fof(f12116,plain,
( spl0_714
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) = X6
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f745,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) = X6
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
fof(f12114,plain,
spl0_713,
inference(avatar_split_clause,[],[f744,f12112]) ).
fof(f12112,plain,
( spl0_713
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) = X6
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f744,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) = X6
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
fof(f12110,plain,
spl0_712,
inference(avatar_split_clause,[],[f716,f12108]) ).
fof(f12108,plain,
( spl0_712
<=> ! [X6,X5,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oinverse__class_Odivide(X6,X5,X3)),X5) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f716,axiom,
! [X3,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oinverse__class_Odivide(X6,X5,X3)),X5) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).
fof(f12106,plain,
spl0_711,
inference(avatar_split_clause,[],[f642,f12104]) ).
fof(f12104,plain,
( spl0_711
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(X4,X3)),X6) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f642,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oring(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(X4,X3)),X6) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
fof(f12102,plain,
spl0_710,
inference(avatar_split_clause,[],[f641,f12100]) ).
fof(f12100,plain,
( spl0_710
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_HOL_Ouminus__class_Ouminus(X6,X3)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f641,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oring(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_HOL_Ouminus__class_Ouminus(X6,X3)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
fof(f12098,plain,
spl0_709,
inference(avatar_split_clause,[],[f632,f12096]) ).
fof(f12096,plain,
( spl0_709
<=> ! [X6,X4,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(X4,X3)),X6) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f632,axiom,
! [X3,X6,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(X4,X3)),X6) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).
fof(f12094,plain,
spl0_708,
inference(avatar_split_clause,[],[f630,f12092]) ).
fof(f12092,plain,
( spl0_708
<=> ! [X6,X4,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_HOL_Ouminus__class_Ouminus(X6,X3)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f630,axiom,
! [X3,X6,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_HOL_Ouminus__class_Ouminus(X6,X3)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
fof(f12090,plain,
spl0_707,
inference(avatar_split_clause,[],[f628,f12088]) ).
fof(f12088,plain,
( spl0_707
<=> ! [X6,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(X6,X3)),c_HOL_Ouminus__class_Ouminus(X6,X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f628,axiom,
! [X3,X6] :
( ~ class_Ring__and__Field_Oidom(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(X6,X3)),c_HOL_Ouminus__class_Ouminus(X6,X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
fof(f12086,plain,
spl0_706,
inference(avatar_split_clause,[],[f627,f12084]) ).
fof(f12084,plain,
( spl0_706
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(X4,X3)),c_HOL_Ouminus__class_Ouminus(X6,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f627,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oring(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(X4,X3)),c_HOL_Ouminus__class_Ouminus(X6,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
fof(f12082,plain,
( spl0_705
| ~ spl0_174
| ~ spl0_691 ),
inference(avatar_split_clause,[],[f11162,f11037,f2522,f12080]) ).
fof(f12080,plain,
( spl0_705
<=> ! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_lessequals(X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f11162,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_lessequals(X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat) )
| ~ spl0_174
| ~ spl0_691 ),
inference(resolution,[],[f11038,f2523]) ).
fof(f12078,plain,
spl0_704,
inference(avatar_split_clause,[],[f623,f12076]) ).
fof(f12076,plain,
( spl0_704
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_HOL_Oabs__class_Oabs(X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f623,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oabs__class_Oabs(X4,X3)),c_HOL_Oabs__class_Oabs(X4,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).
fof(f12074,plain,
spl0_703,
inference(avatar_split_clause,[],[f610,f12072]) ).
fof(f12072,plain,
( spl0_703
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(X4,X3)),X6) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_HOL_Ouminus__class_Ouminus(X6,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f610,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oring(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(X4,X3)),X6) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_HOL_Ouminus__class_Ouminus(X6,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
fof(f12070,plain,
spl0_702,
inference(avatar_split_clause,[],[f491,f12068]) ).
fof(f12068,plain,
( spl0_702
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),hAPP(c_Suc,c_Divides_Odiv__class_Odiv(X1,X2,tc_nat))),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f491,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),hAPP(c_Suc,c_Divides_Odiv__class_Odiv(X1,X2,tc_nat))),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div__lemma_2) ).
fof(f12066,plain,
spl0_701,
inference(avatar_split_clause,[],[f426,f12064]) ).
fof(f426,axiom,
! [X2,X0,X1] : c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2)),X1),X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self3_0) ).
fof(f12062,plain,
spl0_700,
inference(avatar_split_clause,[],[f349,f12060]) ).
fof(f12060,plain,
( spl0_700
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X6
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X6,X3),X3) = c_HOL_Oinverse__class_Odivide(X4,c_HOL_Ouminus__class_Ouminus(X6,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f349,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X6
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X6,X3),X3) = c_HOL_Oinverse__class_Odivide(X4,c_HOL_Ouminus__class_Ouminus(X6,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).
fof(f12058,plain,
spl0_699,
inference(avatar_split_clause,[],[f279,f12056]) ).
fof(f12056,plain,
( spl0_699
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Odiv(X0,X2,tc_nat),c_Divides_Odiv__class_Odiv(X0,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f279,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Odiv(X0,X2,tc_nat),c_Divides_Odiv__class_Odiv(X0,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__le__mono2_0) ).
fof(f12054,plain,
spl0_698,
inference(avatar_split_clause,[],[f66,f12052]) ).
fof(f12052,plain,
( spl0_698
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X6
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ouminus__class_Ouminus(X6,X3),X3) = c_HOL_Oinverse__class_Odivide(X4,X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f66,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X6
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ouminus__class_Ouminus(X6,X3),X3) = c_HOL_Oinverse__class_Odivide(X4,X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).
fof(f12050,plain,
spl0_697,
inference(avatar_split_clause,[],[f39,f12048]) ).
fof(f12048,plain,
( spl0_697
<=> ! [X2,X9,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_HOL_Ozero__class_Ozero(X3) = X9
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f39,axiom,
! [X2,X3,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_HOL_Ozero__class_Ozero(X3) = X9
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_1) ).
fof(f11506,plain,
( ~ spl0_695
| spl0_696
| ~ spl0_662
| ~ spl0_676 ),
inference(avatar_split_clause,[],[f11250,f10964,f9887,f11504,f11500]) ).
fof(f11500,plain,
( spl0_695
<=> class_OrderedGroup_Olordered__ab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f11504,plain,
( spl0_696
<=> ! [X0] : ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_HOL_Ouminus__class_Ouminus(X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f9887,plain,
( spl0_662
<=> ! [X0] : ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f10964,plain,
( spl0_676
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X6,X3),X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f11250,plain,
( ! [X0] :
( ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_HOL_Ouminus__class_Ouminus(X0,tc_nat),tc_nat)
| ~ class_OrderedGroup_Olordered__ab__group__add(tc_nat) )
| ~ spl0_662
| ~ spl0_676 ),
inference(resolution,[],[f10965,f9888]) ).
fof(f9888,plain,
( ! [X0] : ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_662 ),
inference(avatar_component_clause,[],[f9887]) ).
fof(f10965,plain,
( ! [X3,X6,X4] :
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X6,X3),X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X3) )
| ~ spl0_676 ),
inference(avatar_component_clause,[],[f10964]) ).
fof(f11051,plain,
spl0_694,
inference(avatar_split_clause,[],[f1648,f11049]) ).
fof(f11049,plain,
( spl0_694
<=> ! [X2] :
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| ~ c_HOL_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f1648,plain,
! [X2] :
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| ~ c_HOL_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f1283,f421]) ).
fof(f1283,axiom,
! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X2
| ~ c_HOL_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__2__cases_0) ).
fof(f11047,plain,
spl0_693,
inference(avatar_split_clause,[],[f1376,f11045]) ).
fof(f11045,plain,
( spl0_693
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f1376,axiom,
! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).
fof(f11043,plain,
spl0_692,
inference(avatar_split_clause,[],[f1375,f11041]) ).
fof(f11041,plain,
( spl0_692
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f1375,axiom,
! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).
fof(f11039,plain,
( ~ spl0_32
| spl0_691
| ~ spl0_484
| ~ spl0_606 ),
inference(avatar_split_clause,[],[f8804,f8336,f5966,f11037,f1842]) ).
fof(f1842,plain,
( spl0_32
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f5966,plain,
( spl0_484
<=> ! [X17,X3,X9,X22] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X17,X9,X3)
| ~ c_HOL_Oord__class_Oless(X22,X17,X3)
| c_HOL_Oord__class_Oless(X22,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f8804,plain,
( ! [X0] :
( ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),X0,tc_nat)
| ~ class_Orderings_Oorder(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
| ~ spl0_484
| ~ spl0_606 ),
inference(resolution,[],[f8338,f5967]) ).
fof(f5967,plain,
( ! [X3,X9,X17,X22] :
( ~ c_HOL_Oord__class_Oless(X22,X17,X3)
| ~ c_lessequals(X17,X9,X3)
| ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X22,X9,X3) )
| ~ spl0_484 ),
inference(avatar_component_clause,[],[f5966]) ).
fof(f11035,plain,
spl0_690,
inference(avatar_split_clause,[],[f1312,f11033]) ).
fof(f11033,plain,
( spl0_690
<=> ! [X2,X1,X26] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X26,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X26,X2,tc_nat),c_HOL_Ominus__class_Ominus(X26,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f1312,axiom,
! [X2,X1,X26] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X26,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X26,X2,tc_nat),c_HOL_Ominus__class_Ominus(X26,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
fof(f11031,plain,
spl0_689,
inference(avatar_split_clause,[],[f1245,f11029]) ).
fof(f1245,axiom,
! [X2] : hAPP(c_Suc,hAPP(c_Suc,hAPP(c_Suc,X2))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc3__eq__add__3_0) ).
fof(f11027,plain,
spl0_688,
inference(avatar_split_clause,[],[f1156,f11025]) ).
fof(f11025,plain,
( spl0_688
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f1156,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel2_2) ).
fof(f11023,plain,
spl0_687,
inference(avatar_split_clause,[],[f1154,f11021]) ).
fof(f11021,plain,
( spl0_687
<=> ! [X16,X0,X14] :
( ~ c_lessequals(X16,X14,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X14),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f1154,axiom,
! [X0,X16,X14] :
( ~ c_lessequals(X16,X14,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X14),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__mono2_0) ).
fof(f11019,plain,
spl0_686,
inference(avatar_split_clause,[],[f999,f11017]) ).
fof(f11017,plain,
( spl0_686
<=> ! [X34,X35] :
( ~ c_HOL_Oord__class_Oless(X34,c_Int_OPls,tc_Int_Oint)
| c_Int_Onumber__class_Onumber__of(X35,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat)),c_Int_Onumber__class_Onumber__of(X35,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f999,axiom,
! [X34,X35] :
( ~ c_HOL_Oord__class_Oless(X34,c_Int_OPls,tc_Int_Oint)
| c_Int_Onumber__class_Onumber__of(X35,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat)),c_Int_Onumber__class_Onumber__of(X35,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nat__number__of_0) ).
fof(f11015,plain,
spl0_685,
inference(avatar_split_clause,[],[f972,f11013]) ).
fof(f11013,plain,
( spl0_685
<=> ! [X16,X0,X14] :
( ~ c_HOL_Oord__class_Oless(X16,X14,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f972,axiom,
! [X0,X16,X14] :
( ~ c_HOL_Oord__class_Oless(X16,X14,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
fof(f11011,plain,
spl0_684,
inference(avatar_split_clause,[],[f971,f11009]) ).
fof(f11009,plain,
( spl0_684
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f971,axiom,
! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
fof(f11007,plain,
spl0_683,
inference(avatar_split_clause,[],[f970,f11005]) ).
fof(f11005,plain,
( spl0_683
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f970,axiom,
! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
fof(f11003,plain,
spl0_682,
inference(avatar_split_clause,[],[f902,f11001]) ).
fof(f11001,plain,
( spl0_682
<=> ! [X6,X4,X5] :
( ~ c_lessequals(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X5,tc_nat),c_HOL_Ominus__class_Ominus(X6,X5,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f902,axiom,
! [X6,X4,X5] :
( ~ c_lessequals(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X5,tc_nat),c_HOL_Ominus__class_Ominus(X6,X5,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).
fof(f10999,plain,
spl0_681,
inference(avatar_split_clause,[],[f538,f10997]) ).
fof(f10997,plain,
( spl0_681
<=> ! [X4,X9,X27,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X27,X3),X9,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X9,X4,X3),X3),X27,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f538,axiom,
! [X3,X9,X27,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X27,X3),X9,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X9,X4,X3),X3),X27,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__diff__less__iff_0) ).
fof(f10982,plain,
spl0_680,
inference(avatar_split_clause,[],[f375,f10980]) ).
fof(f10980,plain,
( spl0_680
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Power_Opower(X3)
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f375,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Power_Opower(X3)
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
fof(f10978,plain,
spl0_679,
inference(avatar_split_clause,[],[f186,f10976]) ).
fof(f10976,plain,
( spl0_679
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f186,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).
fof(f10974,plain,
spl0_678,
inference(avatar_split_clause,[],[f185,f10972]) ).
fof(f10972,plain,
( spl0_678
<=> ! [X2,X0,X1] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f185,axiom,
! [X2,X0,X1] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).
fof(f10970,plain,
spl0_677,
inference(avatar_split_clause,[],[f184,f10968]) ).
fof(f10968,plain,
( spl0_677
<=> ! [X16,X0,X14] :
( ~ c_lessequals(X16,X14,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f184,axiom,
! [X0,X16,X14] :
( ~ c_lessequals(X16,X14,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).
fof(f10966,plain,
spl0_676,
inference(avatar_split_clause,[],[f172,f10964]) ).
fof(f172,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X6,X3),X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__neg_0) ).
fof(f10962,plain,
spl0_675,
inference(avatar_split_clause,[],[f171,f10960]) ).
fof(f10960,plain,
( spl0_675
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X6,X3),X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f171,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X6,X3),X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__neg_1) ).
fof(f10958,plain,
spl0_674,
inference(avatar_split_clause,[],[f167,f10956]) ).
fof(f10956,plain,
( spl0_674
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Osemiring__0(X3)
| ~ class_Power_Opower(X3)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f167,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Osemiring__0(X3)
| ~ class_Power_Opower(X3)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).
fof(f10954,plain,
spl0_673,
inference(avatar_split_clause,[],[f162,f10952]) ).
fof(f10952,plain,
( spl0_673
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X3),X6,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X3),X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f162,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X3),X6,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X3),X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_2) ).
fof(f10950,plain,
spl0_672,
inference(avatar_split_clause,[],[f111,f10948]) ).
fof(f10948,plain,
( spl0_672
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| X5 = X6
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f111,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| X5 = X6
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
fof(f10946,plain,
spl0_671,
inference(avatar_split_clause,[],[f110,f10944]) ).
fof(f10944,plain,
( spl0_671
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| X5 = X6
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f110,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| X5 = X6
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
fof(f10936,plain,
spl0_670,
inference(avatar_split_clause,[],[f109,f10934]) ).
fof(f10934,plain,
( spl0_670
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| X5 = X6
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f109,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| X5 = X6
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
fof(f10932,plain,
spl0_669,
inference(avatar_split_clause,[],[f103,f10930]) ).
fof(f10930,plain,
( spl0_669
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X6,X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f103,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X6,X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__iff_2) ).
fof(f10928,plain,
spl0_668,
inference(avatar_split_clause,[],[f95,f10926]) ).
fof(f10926,plain,
( spl0_668
<=> ! [X17,X10,X11,X9,X13,X12,X3,X8] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X11,X9),X17) = hAPP(hAPP(X11,X17),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f95,axiom,
! [X3,X10,X11,X8,X9,X17,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X11,X9),X17) = hAPP(hAPP(X11,X17),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__c_0) ).
fof(f10924,plain,
spl0_667,
inference(avatar_split_clause,[],[f74,f10922]) ).
fof(f10922,plain,
( spl0_667
<=> ! [X6,X10,X11,X13,X4,X12,X3,X8] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,X4),X6) = hAPP(hAPP(X12,X6),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f74,axiom,
! [X3,X10,X11,X8,X6,X4,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,X4),X6) = hAPP(hAPP(X12,X6),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I7_J_0) ).
fof(f10920,plain,
spl0_666,
inference(avatar_split_clause,[],[f57,f10918]) ).
fof(f10918,plain,
( spl0_666
<=> ! [X6,X4,X3] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X4,X3),X6,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X4,X6,X3),X3),X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f57,axiom,
! [X3,X6,X4] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X4,X3),X6,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X4,X6,X3),X3),X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__minus__eq_0) ).
fof(f10916,plain,
spl0_665,
inference(avatar_split_clause,[],[f21,f10914]) ).
fof(f10914,plain,
( spl0_665
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X6,X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X6,X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f21,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X6,X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X6,X3),X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__triangle__ineq2_0) ).
fof(f10829,plain,
( ~ spl0_664
| ~ spl0_597
| ~ spl0_662 ),
inference(avatar_split_clause,[],[f10394,f9887,f8249,f10826]) ).
fof(f10826,plain,
( spl0_664
<=> c_lessequals(hAPP(c_Suc,hAPP(c_Suc,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f8249,plain,
( spl0_597
<=> ! [X2] : hAPP(c_Suc,hAPP(c_Suc,X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f10394,plain,
( ~ c_lessequals(hAPP(c_Suc,hAPP(c_Suc,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_597
| ~ spl0_662 ),
inference(superposition,[],[f9888,f8250]) ).
fof(f8250,plain,
( ! [X2] : hAPP(c_Suc,hAPP(c_Suc,X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))
| ~ spl0_597 ),
inference(avatar_component_clause,[],[f8249]) ).
fof(f10073,plain,
( spl0_663
| ~ spl0_220
| ~ spl0_614 ),
inference(avatar_split_clause,[],[f9443,f9394,f2736,f10071]) ).
fof(f2736,plain,
( spl0_220
<=> ! [X16,X14] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X16),X16,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f9443,plain,
( ! [X0] : ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_220
| ~ spl0_614 ),
inference(resolution,[],[f9395,f2737]) ).
fof(f2737,plain,
( ! [X16,X14] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X16),X16,tc_nat)
| ~ spl0_220 ),
inference(avatar_component_clause,[],[f2736]) ).
fof(f9889,plain,
( spl0_662
| ~ spl0_219
| ~ spl0_614 ),
inference(avatar_split_clause,[],[f9442,f9394,f2732,f9887]) ).
fof(f2732,plain,
( spl0_219
<=> ! [X16,X14] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14),X16,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f9442,plain,
( ! [X0] : ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_219
| ~ spl0_614 ),
inference(resolution,[],[f9395,f2733]) ).
fof(f2733,plain,
( ! [X16,X14] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14),X16,tc_nat)
| ~ spl0_219 ),
inference(avatar_component_clause,[],[f2732]) ).
fof(f9626,plain,
spl0_661,
inference(avatar_split_clause,[],[f1637,f9624]) ).
fof(f9624,plain,
( spl0_661
<=> ! [X2,X1] :
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)
| c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f1637,plain,
! [X2,X1] :
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)
| c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1 ),
inference(forward_demodulation,[],[f1636,f421]) ).
fof(f1636,plain,
! [X2,X1] :
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) ),
inference(forward_demodulation,[],[f883,f421]) ).
fof(f883,axiom,
! [X2,X1] :
( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_0) ).
fof(f9622,plain,
spl0_660,
inference(avatar_split_clause,[],[f1635,f9620]) ).
fof(f9620,plain,
( spl0_660
<=> ! [X2,X1] :
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)
| c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f1635,plain,
! [X2,X1] :
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)
| c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X2 ),
inference(forward_demodulation,[],[f1634,f421]) ).
fof(f1634,plain,
! [X2,X1] :
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X2
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) ),
inference(forward_demodulation,[],[f882,f421]) ).
fof(f882,axiom,
! [X2,X1] :
( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X2
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_1) ).
fof(f9618,plain,
spl0_659,
inference(avatar_split_clause,[],[f1596,f9616]) ).
fof(f9616,plain,
( spl0_659
<=> ! [X2,X1] : c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),c_Divides_Odiv__class_Odiv(X1,X2,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f1596,plain,
! [X2,X1] : c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),c_Divides_Odiv__class_Odiv(X1,X2,tc_nat)),tc_nat),
inference(forward_demodulation,[],[f1173,f1416]) ).
fof(f1173,axiom,
! [X2,X1] : c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Odiv(X1,X2,tc_nat)),X2),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__div__equality_H_0) ).
fof(f9614,plain,
spl0_658,
inference(avatar_split_clause,[],[f1595,f9611]) ).
fof(f9611,plain,
( spl0_658
<=> c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f1595,plain,
c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
inference(forward_demodulation,[],[f887,f421]) ).
fof(f887,axiom,
hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_2) ).
fof(f9609,plain,
spl0_657,
inference(avatar_split_clause,[],[f1281,f9607]) ).
fof(f9607,plain,
( spl0_657
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f1281,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power2_0) ).
fof(f9605,plain,
( ~ spl0_656
| ~ spl0_333
| ~ spl0_614 ),
inference(avatar_split_clause,[],[f9447,f9394,f4021,f9602]) ).
fof(f9602,plain,
( spl0_656
<=> c_lessequals(hAPP(c_Suc,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f4021,plain,
( spl0_333
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X0),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f9447,plain,
( ~ c_lessequals(hAPP(c_Suc,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_333
| ~ spl0_614 ),
inference(resolution,[],[f9395,f4022]) ).
fof(f4022,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X0),X0,tc_nat)
| ~ spl0_333 ),
inference(avatar_component_clause,[],[f4021]) ).
fof(f9600,plain,
spl0_655,
inference(avatar_split_clause,[],[f1273,f9598]) ).
fof(f9598,plain,
( spl0_655
<=> ! [X22] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X22) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f1273,axiom,
! [X22] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X22) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X22),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__2__right_0) ).
fof(f9596,plain,
spl0_654,
inference(avatar_split_clause,[],[f1272,f9594]) ).
fof(f9594,plain,
( spl0_654
<=> ! [X22] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X22) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X22) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f1272,axiom,
! [X22] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X22) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__2_0) ).
fof(f9592,plain,
spl0_653,
inference(avatar_split_clause,[],[f1191,f9590]) ).
fof(f9590,plain,
( spl0_653
<=> ! [X0,X16,X14] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X16,X14,tc_nat),X0,tc_nat) = c_HOL_Ominus__class_Ominus(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f9588,plain,
spl0_652,
inference(avatar_split_clause,[],[f1184,f9586]) ).
fof(f9586,plain,
( spl0_652
<=> ! [X2,X1] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f1184,axiom,
! [X2,X1] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
fof(f9584,plain,
spl0_651,
inference(avatar_split_clause,[],[f1167,f9582]) ).
fof(f9582,plain,
( spl0_651
<=> ! [X2,X1] : c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Odiv(X1,X2,tc_nat)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f1167,axiom,
! [X2,X1] : c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Odiv(X1,X2,tc_nat)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mod__equality_H_0) ).
fof(f9580,plain,
spl0_650,
inference(avatar_split_clause,[],[f1166,f9578]) ).
fof(f1166,axiom,
! [X2,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),c_Divides_Odiv__class_Odiv(X1,X2,tc_nat)) = c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__div__cancel_0) ).
fof(f9576,plain,
spl0_649,
inference(avatar_split_clause,[],[f1159,f9574]) ).
fof(f9574,plain,
( spl0_649
<=> ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f1159,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_0) ).
fof(f9572,plain,
spl0_648,
inference(avatar_split_clause,[],[f1038,f9570]) ).
fof(f9570,plain,
( spl0_648
<=> ! [X6,X4,X5] : c_Divides_Odiv__class_Odiv(X4,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X6),X5),tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X4,X6,tc_nat),X5,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f9568,plain,
spl0_647,
inference(avatar_split_clause,[],[f1009,f9566]) ).
fof(f9566,plain,
( spl0_647
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ouminus__class_Ouminus(X6,X3),X3) = c_HOL_Oinverse__class_Odivide(X4,X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f1009,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ouminus__class_Ouminus(X6,X3),X3) = c_HOL_Oinverse__class_Odivide(X4,X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).
fof(f9564,plain,
spl0_646,
inference(avatar_split_clause,[],[f1008,f9562]) ).
fof(f9562,plain,
( spl0_646
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X6,X3),X3) = c_HOL_Oinverse__class_Odivide(X4,c_HOL_Ouminus__class_Ouminus(X6,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f1008,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X6,X3),X3) = c_HOL_Oinverse__class_Odivide(X4,c_HOL_Ouminus__class_Ouminus(X6,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).
fof(f9556,plain,
spl0_645,
inference(avatar_split_clause,[],[f946,f9554]) ).
fof(f9554,plain,
( spl0_645
<=> ! [X2,X1] : hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,X1)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f946,axiom,
! [X2,X1] : hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,X1)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc_0) ).
fof(f9552,plain,
spl0_644,
inference(avatar_split_clause,[],[f945,f9550]) ).
fof(f9550,plain,
( spl0_644
<=> ! [X2,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(c_Suc,X2)) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f945,axiom,
! [X2,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(c_Suc,X2)) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
fof(f9548,plain,
spl0_643,
inference(avatar_split_clause,[],[f913,f9546]) ).
fof(f9546,plain,
( spl0_643
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(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)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f913,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(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)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less_0) ).
fof(f9544,plain,
spl0_642,
inference(avatar_split_clause,[],[f900,f9542]) ).
fof(f9542,plain,
( spl0_642
<=> ! [X2,X1] :
( ~ c_lessequals(X2,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X1),X2,tc_nat) = hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f900,axiom,
! [X2,X1] :
( ~ c_lessequals(X2,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X1),X2,tc_nat) = hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).
fof(f9540,plain,
spl0_641,
inference(avatar_split_clause,[],[f823,f9538]) ).
fof(f9538,plain,
( spl0_641
<=> ! [X9,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Oone__class_Oone(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3)),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f823,axiom,
! [X3,X9] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Oone__class_Oone(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3)),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__one__even__power_0) ).
fof(f9536,plain,
spl0_640,
inference(avatar_split_clause,[],[f818,f9534]) ).
fof(f9534,plain,
( spl0_640
<=> ! [X9,X3] :
( ~ class_Int_Onumber__ring(X3)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3)),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f818,axiom,
! [X3,X9] :
( ~ class_Int_Onumber__ring(X3)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3)),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__one__odd__power_0) ).
fof(f9532,plain,
spl0_639,
inference(avatar_split_clause,[],[f763,f9530]) ).
fof(f9530,plain,
( spl0_639
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ouminus__class_Ouminus(X6,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X4,X6,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f763,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ouminus__class_Ouminus(X6,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X4,X6,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).
fof(f9528,plain,
spl0_638,
inference(avatar_split_clause,[],[f727,f9526]) ).
fof(f9526,plain,
( spl0_638
<=> ! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),X4,X3)
| c_lessequals(c_HOL_Oone__class_Oone(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f727,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),X4,X3)
| c_lessequals(c_HOL_Oone__class_Oone(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__power_0) ).
fof(f9524,plain,
spl0_637,
inference(avatar_split_clause,[],[f715,f9522]) ).
fof(f9522,plain,
( spl0_637
<=> ! [X5,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X5),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f715,axiom,
! [X3,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X5),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_4) ).
fof(f9520,plain,
spl0_636,
inference(avatar_split_clause,[],[f713,f9518]) ).
fof(f9518,plain,
( spl0_636
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),X5,X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f713,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X5),X5,X3) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__imp_0) ).
fof(f9516,plain,
( ~ spl0_635
| spl0_437
| ~ spl0_614 ),
inference(avatar_split_clause,[],[f9451,f9394,f4892,f9513]) ).
fof(f9513,plain,
( spl0_635
<=> c_lessequals(v_i____,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f9451,plain,
( ~ c_lessequals(v_i____,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| spl0_437
| ~ spl0_614 ),
inference(resolution,[],[f9395,f4894]) ).
fof(f9511,plain,
spl0_634,
inference(avatar_split_clause,[],[f684,f9509]) ).
fof(f9509,plain,
( spl0_634
<=> ! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f684,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
fof(f9507,plain,
spl0_633,
inference(avatar_split_clause,[],[f683,f9505]) ).
fof(f9505,plain,
( spl0_633
<=> ! [X9,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f683,axiom,
! [X2,X3,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__zero__eq_1) ).
fof(f9503,plain,
spl0_632,
inference(avatar_split_clause,[],[f493,f9501]) ).
fof(f9501,plain,
( spl0_632
<=> ! [X34,X35] :
( ~ c_HOL_Oord__class_Oless(X34,c_Int_OPls,tc_Int_Oint)
| c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat)),c_Int_Onumber__class_Onumber__of(X35,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f493,axiom,
! [X34,X35] :
( ~ c_HOL_Oord__class_Oless(X34,c_Int_OPls,tc_Int_Oint)
| c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat)),c_Int_Onumber__class_Onumber__of(X35,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nat__number__of_0) ).
fof(f9499,plain,
spl0_631,
inference(avatar_split_clause,[],[f478,f9497]) ).
fof(f9497,plain,
( spl0_631
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oone__class_Oone(X3) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3)),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f478,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oone__class_Oone(X3) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3)),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__power__minus__one_0) ).
fof(f9495,plain,
spl0_630,
inference(avatar_split_clause,[],[f470,f9493]) ).
fof(f9493,plain,
( spl0_630
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),c_Divides_Odiv__class_Odiv(X1,X2,tc_nat)),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f470,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),c_Divides_Odiv__class_Odiv(X1,X2,tc_nat)),X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div__lemma_1) ).
fof(f9491,plain,
spl0_629,
inference(avatar_split_clause,[],[f411,f9489]) ).
fof(f9489,plain,
( spl0_629
<=> ! [X2,X1] :
( hAPP(c_Suc,c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) != X2
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,X1),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f411,axiom,
! [X2,X1] :
( hAPP(c_Suc,c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) != X2
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,X1),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_0) ).
fof(f9487,plain,
spl0_628,
inference(avatar_split_clause,[],[f396,f9485]) ).
fof(f9485,plain,
( spl0_628
<=> ! [X2,X9,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ class_OrderedGroup_Omonoid__mult(X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f396,axiom,
! [X2,X3,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ class_OrderedGroup_Omonoid__mult(X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__even__power_0) ).
fof(f9483,plain,
spl0_627,
inference(avatar_split_clause,[],[f338,f9481]) ).
fof(f9481,plain,
( spl0_627
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X4),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f338,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X4),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
fof(f9479,plain,
spl0_626,
inference(avatar_split_clause,[],[f337,f9477]) ).
fof(f9477,plain,
( spl0_626
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X4),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f337,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X4),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
fof(f9475,plain,
spl0_625,
inference(avatar_split_clause,[],[f335,f9473]) ).
fof(f9473,plain,
( spl0_625
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(X1,tc_nat),c_Fact_Ofact__class_Ofact(X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f335,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Fact_Ofact__class_Ofact(X1,tc_nat),c_Fact_Ofact__class_Ofact(X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fact__less__mono__nat_0) ).
fof(f9436,plain,
spl0_624,
inference(avatar_split_clause,[],[f314,f9434]) ).
fof(f9434,plain,
( spl0_624
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X4,X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f314,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X4,X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
fof(f9432,plain,
spl0_623,
inference(avatar_split_clause,[],[f313,f9430]) ).
fof(f9430,plain,
( spl0_623
<=> ! [X22,X17,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X22,X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X17),X22)) = X17 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f313,axiom,
! [X3,X17,X22] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X22,X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X17),X22)) = X17 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
fof(f9428,plain,
spl0_622,
inference(avatar_split_clause,[],[f250,f9426]) ).
fof(f9426,plain,
( spl0_622
<=> ! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f250,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
fof(f9424,plain,
spl0_621,
inference(avatar_split_clause,[],[f249,f9422]) ).
fof(f9422,plain,
( spl0_621
<=> ! [X4,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f249,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power__iff_1) ).
fof(f9420,plain,
spl0_620,
inference(avatar_split_clause,[],[f212,f9418]) ).
fof(f9418,plain,
( spl0_620
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X4),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f212,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X4),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
fof(f9416,plain,
spl0_619,
inference(avatar_split_clause,[],[f211,f9414]) ).
fof(f9414,plain,
( spl0_619
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X4),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f211,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X4),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
fof(f9412,plain,
spl0_618,
inference(avatar_split_clause,[],[f210,f9410]) ).
fof(f9410,plain,
( spl0_618
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X4),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f210,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X4),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(f9408,plain,
spl0_617,
inference(avatar_split_clause,[],[f209,f9406]) ).
fof(f9406,plain,
( spl0_617
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X4),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f209,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X4),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(f9404,plain,
spl0_616,
inference(avatar_split_clause,[],[f205,f9402]) ).
fof(f9402,plain,
( spl0_616
<=> ! [X6,X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = X6
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X4),X6,X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f205,axiom,
! [X3,X6,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = X6
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X4),X6,X3) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1__is__id_0) ).
fof(f9400,plain,
spl0_615,
inference(avatar_split_clause,[],[f204,f9398]) ).
fof(f9398,plain,
( spl0_615
<=> ! [X6,X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = X6
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X6,X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f204,axiom,
! [X3,X6,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = X6
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X6,X3) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self2__is__id_0) ).
fof(f9396,plain,
( ~ spl0_32
| spl0_614
| ~ spl0_483
| ~ spl0_606 ),
inference(avatar_split_clause,[],[f8803,f8336,f5962,f9394,f1842]) ).
fof(f8803,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ class_Orderings_Oorder(tc_nat)
| c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat) )
| ~ spl0_483
| ~ spl0_606 ),
inference(resolution,[],[f8338,f5963]) ).
fof(f9392,plain,
spl0_613,
inference(avatar_split_clause,[],[f154,f9390]) ).
fof(f9390,plain,
( spl0_613
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X4,X3)),X6)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f154,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X4,X3)),X6)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
fof(f9388,plain,
spl0_612,
inference(avatar_split_clause,[],[f140,f9386]) ).
fof(f9386,plain,
( spl0_612
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f140,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X4),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
fof(f9384,plain,
spl0_611,
inference(avatar_split_clause,[],[f139,f9382]) ).
fof(f9382,plain,
( spl0_611
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f139,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X4),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
fof(f9380,plain,
spl0_610,
inference(avatar_split_clause,[],[f17,f9378]) ).
fof(f9378,plain,
( spl0_610
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f17,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X4),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(f9376,plain,
spl0_609,
inference(avatar_split_clause,[],[f16,f9374]) ).
fof(f9374,plain,
( spl0_609
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f16,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X4),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(f9097,plain,
( ~ spl0_30
| ~ spl0_608
| ~ spl0_245
| ~ spl0_606 ),
inference(avatar_split_clause,[],[f8798,f8336,f2922,f9094,f1832]) ).
fof(f8798,plain,
( ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| ~ spl0_245
| ~ spl0_606 ),
inference(resolution,[],[f8338,f2923]) ).
fof(f8574,plain,
( ~ spl0_137
| spl0_607 ),
inference(avatar_contradiction_clause,[],[f8569]) ).
fof(f8569,plain,
( $false
| ~ spl0_137
| spl0_607 ),
inference(resolution,[],[f8342,f2364]) ).
fof(f2364,plain,
( ! [X2] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f2363]) ).
fof(f2363,plain,
( spl0_137
<=> ! [X2] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f8342,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),v_i____,tc_nat)
| spl0_607 ),
inference(avatar_component_clause,[],[f8340]) ).
fof(f8340,plain,
( spl0_607
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),v_i____,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f8343,plain,
( spl0_606
| ~ spl0_607
| ~ spl0_539
| ~ spl0_587 ),
inference(avatar_split_clause,[],[f8263,f8209,f7458,f8340,f8336]) ).
fof(f7458,plain,
( spl0_539
<=> ! [X2,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f8209,plain,
( spl0_587
<=> ! [X0] :
( ~ c_lessequals(X0,v_i____,tc_nat)
| c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f8263,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),v_i____,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)
| ~ spl0_539
| ~ spl0_587 ),
inference(resolution,[],[f8210,f7459]) ).
fof(f7459,plain,
( ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) )
| ~ spl0_539 ),
inference(avatar_component_clause,[],[f7458]) ).
fof(f8210,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat)
| ~ c_lessequals(X0,v_i____,tc_nat) )
| ~ spl0_587 ),
inference(avatar_component_clause,[],[f8209]) ).
fof(f8316,plain,
spl0_605,
inference(avatar_split_clause,[],[f1628,f8314]) ).
fof(f8314,plain,
( spl0_605
<=> ! [X2] :
( hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X2,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)) = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f1628,plain,
! [X2] :
( hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X2,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)) = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(forward_demodulation,[],[f1100,f421]) ).
fof(f1100,axiom,
! [X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X2,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_0) ).
fof(f8312,plain,
spl0_604,
inference(avatar_split_clause,[],[f1612,f8310]) ).
fof(f1612,plain,
! [X9] :
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(X9,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ),
inference(forward_demodulation,[],[f1611,f1583]) ).
fof(f1611,plain,
! [X9] :
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(X9,hAPP(c_Suc,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ),
inference(forward_demodulation,[],[f59,f421]) ).
fof(f59,axiom,
! [X9] :
( c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Divides_Odiv__class_Omod(X9,hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__nat__equiv__def_0) ).
fof(f8308,plain,
spl0_603,
inference(avatar_split_clause,[],[f1604,f8306]) ).
fof(f1604,plain,
! [X9] :
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_Divides_Odiv__class_Omod(X9,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ),
inference(forward_demodulation,[],[f1603,f1583]) ).
fof(f1603,plain,
! [X9] :
( c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_Divides_Odiv__class_Omod(X9,hAPP(c_Suc,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ),
inference(forward_demodulation,[],[f58,f421]) ).
fof(f58,axiom,
! [X9] :
( ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != c_Divides_Odiv__class_Omod(X9,hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__nat__equiv__def_1) ).
fof(f8304,plain,
spl0_602,
inference(avatar_split_clause,[],[f1395,f8302]) ).
fof(f8302,plain,
( spl0_602
<=> ! [X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_HOL_Oone__class_Oone(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Oone__class_Oone(X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f1395,axiom,
! [X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_HOL_Oone__class_Oone(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Oone__class_Oone(X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__power2_0) ).
fof(f8300,plain,
spl0_601,
inference(avatar_split_clause,[],[f1282,f8298]) ).
fof(f8298,plain,
( spl0_601
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f1282,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power2__less__0_0) ).
fof(f8296,plain,
spl0_600,
inference(avatar_split_clause,[],[f1270,f8294]) ).
fof(f8294,plain,
( spl0_600
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f1270,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__eq__power2_1) ).
fof(f8292,plain,
spl0_599,
inference(avatar_split_clause,[],[f1269,f8290]) ).
fof(f8290,plain,
( spl0_599
<=> ! [X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f1269,axiom,
! [X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__power2_0) ).
fof(f8288,plain,
spl0_598,
inference(avatar_split_clause,[],[f1262,f8286]) ).
fof(f8286,plain,
( spl0_598
<=> ! [X2] : hAPP(c_Suc,hAPP(c_Suc,X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f1262,axiom,
! [X2] : hAPP(c_Suc,hAPP(c_Suc,X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__2__eq__Suc_0) ).
fof(f8251,plain,
spl0_597,
inference(avatar_split_clause,[],[f1261,f8249]) ).
fof(f1261,axiom,
! [X2] : hAPP(c_Suc,hAPP(c_Suc,X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__2__eq__Suc_H_0) ).
fof(f8247,plain,
spl0_596,
inference(avatar_split_clause,[],[f1258,f8245]) ).
fof(f8245,plain,
( spl0_596
<=> ! [X3] :
( ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_HOL_Oone__class_Oone(X3)) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f1258,axiom,
! [X3] :
( ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_HOL_Oone__class_Oone(X3)) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__add__one__is__two_0) ).
fof(f8243,plain,
spl0_595,
inference(avatar_split_clause,[],[f1255,f8241]) ).
fof(f8241,plain,
( spl0_595
<=> ! [X9,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ c_HOL_Oord__class_Oless(X9,c_Int_OBit1(c_Int_OPls),tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X3),c_HOL_Oone__class_Oone(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f1255,axiom,
! [X3,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ c_HOL_Oord__class_Oless(X9,c_Int_OBit1(c_Int_OPls),tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X3),c_HOL_Oone__class_Oone(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__special_I4_J_1) ).
fof(f8239,plain,
spl0_594,
inference(avatar_split_clause,[],[f1254,f8237]) ).
fof(f8237,plain,
( spl0_594
<=> ! [X9,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oord__class_Oless(X9,c_Int_OBit1(c_Int_OPls),tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X3),c_HOL_Oone__class_Oone(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f1254,axiom,
! [X3,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oord__class_Oless(X9,c_Int_OBit1(c_Int_OPls),tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X3),c_HOL_Oone__class_Oone(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__special_I4_J_0) ).
fof(f8235,plain,
spl0_593,
inference(avatar_split_clause,[],[f1253,f8233]) ).
fof(f8233,plain,
( spl0_593
<=> ! [X17,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ c_HOL_Oord__class_Oless(c_Int_OBit1(c_Int_OPls),X17,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_Int_Onumber__class_Onumber__of(X17,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f1253,axiom,
! [X3,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ c_HOL_Oord__class_Oless(c_Int_OBit1(c_Int_OPls),X17,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_Int_Onumber__class_Onumber__of(X17,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__special_I2_J_1) ).
fof(f8231,plain,
spl0_592,
inference(avatar_split_clause,[],[f1252,f8229]) ).
fof(f8229,plain,
( spl0_592
<=> ! [X17,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oord__class_Oless(c_Int_OBit1(c_Int_OPls),X17,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_Int_Onumber__class_Onumber__of(X17,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f1252,axiom,
! [X3,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oord__class_Oless(c_Int_OBit1(c_Int_OPls),X17,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_Int_Onumber__class_Onumber__of(X17,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__special_I2_J_0) ).
fof(f8227,plain,
spl0_591,
inference(avatar_split_clause,[],[f1201,f8225]) ).
fof(f8225,plain,
( spl0_591
<=> ! [X9,X17] :
( ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X9),X17),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f1201,axiom,
! [X9,X17] :
( ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X9),X17),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__power__nat_2) ).
fof(f8223,plain,
spl0_590,
inference(avatar_split_clause,[],[f1102,f8221]) ).
fof(f8221,plain,
( spl0_590
<=> ! [X34,X35] :
( ~ c_HOL_Oord__class_Oless(X35,c_Int_OPls,tc_Int_Oint)
| c_Int_Onumber__class_Onumber__of(X34,tc_nat) = c_HOL_Ominus__class_Ominus(c_Int_Onumber__class_Onumber__of(X34,tc_nat),c_Int_Onumber__class_Onumber__of(X35,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f1102,axiom,
! [X34,X35] :
( ~ c_HOL_Oord__class_Oless(X35,c_Int_OPls,tc_Int_Oint)
| c_Int_Onumber__class_Onumber__of(X34,tc_nat) = c_HOL_Ominus__class_Ominus(c_Int_Onumber__class_Onumber__of(X34,tc_nat),c_Int_Onumber__class_Onumber__of(X35,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__nat__number__of_0) ).
fof(f8219,plain,
spl0_589,
inference(avatar_split_clause,[],[f1093,f8217]) ).
fof(f8217,plain,
( spl0_589
<=> ! [X34,X35] :
( ~ c_HOL_Oord__class_Oless(X34,X35,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_OPls,X35,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X34,tc_nat),c_Int_Onumber__class_Onumber__of(X35,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f1093,axiom,
! [X34,X35] :
( ~ c_HOL_Oord__class_Oless(X34,X35,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_OPls,X35,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X34,tc_nat),c_Int_Onumber__class_Onumber__of(X35,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__nat__number__of_2) ).
fof(f8215,plain,
spl0_588,
inference(avatar_split_clause,[],[f1092,f8213]) ).
fof(f8213,plain,
( spl0_588
<=> ! [X34,X35] :
( ~ c_HOL_Oord__class_Oless(X34,X35,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_OPls,X35,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X34,tc_nat),c_Int_Onumber__class_Onumber__of(X35,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f1092,axiom,
! [X34,X35] :
( ~ c_HOL_Oord__class_Oless(X34,X35,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_OPls,X35,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X34,tc_nat),c_Int_Onumber__class_Onumber__of(X35,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__nat__number__of_0) ).
fof(f8211,plain,
( ~ spl0_32
| spl0_587
| ~ spl0_141
| ~ spl0_483 ),
inference(avatar_split_clause,[],[f6710,f5962,f2380,f8209,f1842]) ).
fof(f2380,plain,
( spl0_141
<=> c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f6710,plain,
( ! [X0] :
( ~ c_lessequals(X0,v_i____,tc_nat)
| ~ class_Orderings_Oorder(tc_nat)
| c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat) )
| ~ spl0_141
| ~ spl0_483 ),
inference(resolution,[],[f5963,f2382]) ).
fof(f2382,plain,
( c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat)
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f2380]) ).
fof(f8207,plain,
spl0_586,
inference(avatar_split_clause,[],[f1026,f8205]) ).
fof(f8205,plain,
( spl0_586
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),X2,tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f1026,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),X2,tc_nat) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self__is__m_0) ).
fof(f8203,plain,
spl0_585,
inference(avatar_split_clause,[],[f1025,f8201]) ).
fof(f8201,plain,
( spl0_585
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X1),X2,tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f1025,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X1),X2,tc_nat) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1__is__m_0) ).
fof(f8199,plain,
spl0_584,
inference(avatar_split_clause,[],[f925,f8197]) ).
fof(f8197,plain,
( spl0_584
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f925,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power2_0) ).
fof(f8195,plain,
spl0_583,
inference(avatar_split_clause,[],[f912,f8193]) ).
fof(f8193,plain,
( spl0_583
<=> ! [X9,X17] :
( ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
| c_HOL_Oord__class_Oless(X9,X17,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X9,X17,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f912,axiom,
! [X9,X17] :
( ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
| c_HOL_Oord__class_Oless(X9,X17,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X9,X17,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__difference__nat_1) ).
fof(f8191,plain,
spl0_582,
inference(avatar_split_clause,[],[f911,f8189]) ).
fof(f8189,plain,
( spl0_582
<=> ! [X9,X17] :
( ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Oord__class_Oless(X9,X17,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X9,X17,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f911,axiom,
! [X9,X17] :
( ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Oord__class_Oless(X9,X17,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X9,X17,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__difference__nat_0) ).
fof(f8187,plain,
spl0_581,
inference(avatar_split_clause,[],[f910,f8185]) ).
fof(f8185,plain,
( spl0_581
<=> ! [X6,X4,X15] :
( ~ c_HOL_Oord__class_Oless(X4,X6,tc_nat)
| hBOOL(hAPP(X15,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X15,c_HOL_Ominus__class_Ominus(X4,X6,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f910,axiom,
! [X6,X4,X15] :
( ~ c_HOL_Oord__class_Oless(X4,X6,tc_nat)
| hBOOL(hAPP(X15,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X15,c_HOL_Ominus__class_Ominus(X4,X6,tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split_0) ).
fof(f8183,plain,
spl0_580,
inference(avatar_split_clause,[],[f909,f8181]) ).
fof(f8181,plain,
( spl0_580
<=> ! [X0,X16,X14] :
( ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ominus__class_Ominus(X14,X0,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X0),X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f909,axiom,
! [X0,X16,X14] :
( ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ominus__class_Ominus(X14,X0,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X0),X14,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).
fof(f8179,plain,
spl0_579,
inference(avatar_split_clause,[],[f908,f8177]) ).
fof(f8177,plain,
( spl0_579
<=> ! [X0,X16,X14] :
( c_HOL_Oord__class_Oless(X16,c_HOL_Ominus__class_Ominus(X14,X0,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X0),X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f908,axiom,
! [X0,X16,X14] :
( c_HOL_Oord__class_Oless(X16,c_HOL_Ominus__class_Ominus(X14,X0,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X0),X14,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).
fof(f8175,plain,
spl0_578,
inference(avatar_split_clause,[],[f903,f8173]) ).
fof(f8173,plain,
( spl0_578
<=> ! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f903,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_1) ).
fof(f8171,plain,
spl0_577,
inference(avatar_split_clause,[],[f886,f8169]) ).
fof(f8169,plain,
( spl0_577
<=> ! [X9] : c_Fact_Ofact__class_Ofact(hAPP(c_Suc,X9),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X9)),c_Fact_Ofact__class_Ofact(X9,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f886,axiom,
! [X9] : c_Fact_Ofact__class_Ofact(hAPP(c_Suc,X9),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X9)),c_Fact_Ofact__class_Ofact(X9,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Fact_Ofact__Suc_0) ).
fof(f8167,plain,
( spl0_576
| ~ spl0_158
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f3772,f3507,f2452,f8164]) ).
fof(f8164,plain,
( spl0_576
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f3507,plain,
( spl0_294
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f3772,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)
| ~ spl0_158
| ~ spl0_294 ),
inference(resolution,[],[f3508,f2454]) ).
fof(f3508,plain,
( ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) )
| ~ spl0_294 ),
inference(avatar_component_clause,[],[f3507]) ).
fof(f8162,plain,
spl0_575,
inference(avatar_split_clause,[],[f839,f8160]) ).
fof(f8160,plain,
( spl0_575
<=> ! [X2,X1] : c_Divides_Odiv__class_Omod(hAPP(c_Suc,X1),X2,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f839,axiom,
! [X2,X1] : c_Divides_Odiv__class_Omod(hAPP(c_Suc,X1),X2,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).
fof(f8158,plain,
spl0_574,
inference(avatar_split_clause,[],[f824,f8156]) ).
fof(f8156,plain,
( spl0_574
<=> ! [X9,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ouminus__class_Ouminus(X9,X3) = c_HOL_Oinverse__class_Odivide(X9,c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f824,axiom,
! [X3,X9] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ouminus__class_Ouminus(X9,X3) = c_HOL_Oinverse__class_Odivide(X9,c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__minus1_0) ).
fof(f8154,plain,
spl0_573,
inference(avatar_split_clause,[],[f740,f8152]) ).
fof(f8152,plain,
( spl0_573
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Osemiring__0(X3)
| ~ class_Power_Opower(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(c_Suc,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f740,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Osemiring__0(X3)
| ~ class_Power_Opower(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(c_Suc,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
fof(f8150,plain,
spl0_572,
inference(avatar_split_clause,[],[f737,f8148]) ).
fof(f8148,plain,
( spl0_572
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| X4 = X6
| c_HOL_Ozero__class_Ozero(X3) = X6
| c_HOL_Oone__class_Oone(X3) != c_HOL_Oinverse__class_Odivide(X4,X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f737,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Ofield(X3)
| X4 = X6
| c_HOL_Ozero__class_Ozero(X3) = X6
| c_HOL_Oone__class_Oone(X3) != c_HOL_Oinverse__class_Odivide(X4,X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).
fof(f8146,plain,
spl0_571,
inference(avatar_split_clause,[],[f535,f8144]) ).
fof(f8144,plain,
( spl0_571
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oord__class_Oless(X9,X17,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X3),c_Int_Onumber__class_Onumber__of(X17,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f535,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oord__class_Oless(X9,X17,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X3),c_Int_Onumber__class_Onumber__of(X17,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__number__of_0) ).
fof(f8142,plain,
spl0_570,
inference(avatar_split_clause,[],[f534,f8140]) ).
fof(f8140,plain,
( spl0_570
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ c_HOL_Oord__class_Oless(X9,X17,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X3),c_Int_Onumber__class_Onumber__of(X17,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f534,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ c_HOL_Oord__class_Oless(X9,X17,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X3),c_Int_Onumber__class_Onumber__of(X17,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__number__of_1) ).
fof(f8138,plain,
spl0_569,
inference(avatar_split_clause,[],[f479,f8136]) ).
fof(f479,axiom,
! [X3,X9] :
( ~ class_Int_Onumber__ring(X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Oone__class_Oone(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3)),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__one__even__power_0) ).
fof(f8134,plain,
spl0_568,
inference(avatar_split_clause,[],[f410,f8132]) ).
fof(f8132,plain,
( spl0_568
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X2,tc_nat)
| c_lessequals(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f410,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X2,tc_nat)
| c_lessequals(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff_0) ).
fof(f8130,plain,
spl0_567,
inference(avatar_split_clause,[],[f295,f8128]) ).
fof(f8128,plain,
( spl0_567
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X6,X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f295,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X6,X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
fof(f8126,plain,
spl0_566,
inference(avatar_split_clause,[],[f294,f8124]) ).
fof(f8124,plain,
( spl0_566
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X4,X3) = X6
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f294,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X4,X3) = X6
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__unique_0) ).
fof(f8092,plain,
spl0_565,
inference(avatar_split_clause,[],[f291,f8090]) ).
fof(f8090,plain,
( spl0_565
<=> ! [X16,X0,X14] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X14,X0,tc_nat),X16,tc_nat)
| c_lessequals(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f291,axiom,
! [X0,X16,X14] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X14,X0,tc_nat),X16,tc_nat)
| c_lessequals(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv_0) ).
fof(f8088,plain,
spl0_564,
inference(avatar_split_clause,[],[f290,f8086]) ).
fof(f8086,plain,
( spl0_564
<=> ! [X16,X0,X14] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X14,X0,tc_nat),X16,tc_nat)
| ~ c_lessequals(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f290,axiom,
! [X0,X16,X14] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X14,X0,tc_nat),X16,tc_nat)
| ~ c_lessequals(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv_1) ).
fof(f8084,plain,
spl0_563,
inference(avatar_split_clause,[],[f226,f8082]) ).
fof(f8082,plain,
( spl0_563
<=> ! [X4,X9,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X4) != X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f226,axiom,
! [X3,X9,X4] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X4) != X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
fof(f8080,plain,
spl0_562,
inference(avatar_split_clause,[],[f224,f8078]) ).
fof(f8078,plain,
( spl0_562
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
| ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ouminus__class_Ouminus(X4,X3) = c_HOL_Oabs__class_Oabs(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f224,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
| ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ouminus__class_Ouminus(X4,X3) = c_HOL_Oabs__class_Oabs(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if__lattice_0) ).
fof(f8076,plain,
spl0_561,
inference(avatar_split_clause,[],[f213,f8074]) ).
fof(f8074,plain,
( spl0_561
<=> ! [X2,X1] :
( ~ c_lessequals(X2,X1,tc_nat)
| c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f213,axiom,
! [X2,X1] :
( ~ c_lessequals(X2,X1,tc_nat)
| c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__mod__geq_0) ).
fof(f8072,plain,
spl0_560,
inference(avatar_split_clause,[],[f161,f8070]) ).
fof(f8070,plain,
( spl0_560
<=> ! [X6,X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,X6,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X4),X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f161,axiom,
! [X3,X6,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,X6,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X4),X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).
fof(f8068,plain,
spl0_559,
inference(avatar_split_clause,[],[f160,f8066]) ).
fof(f8066,plain,
( spl0_559
<=> ! [X6,X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,X6,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f160,axiom,
! [X3,X6,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,X6,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).
fof(f8064,plain,
spl0_558,
inference(avatar_split_clause,[],[f106,f8062]) ).
fof(f8062,plain,
( spl0_558
<=> ! [X2,X0,X1] :
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f106,axiom,
! [X2,X0,X1] :
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
fof(f8060,plain,
spl0_557,
inference(avatar_split_clause,[],[f105,f8058]) ).
fof(f8058,plain,
( spl0_557
<=> ! [X2,X0,X1] :
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f105,axiom,
! [X2,X0,X1] :
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
fof(f8019,plain,
( spl0_556
| ~ spl0_291
| ~ spl0_440 ),
inference(avatar_split_clause,[],[f5303,f5180,f3495,f8016]) ).
fof(f8016,plain,
( spl0_556
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(v_i____,hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f5180,plain,
( spl0_440
<=> c_lessequals(v_i____,hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f5303,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(v_i____,hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_nat)
| ~ spl0_291
| ~ spl0_440 ),
inference(resolution,[],[f5182,f3496]) ).
fof(f5182,plain,
( c_lessequals(v_i____,hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_nat)
| ~ spl0_440 ),
inference(avatar_component_clause,[],[f5180]) ).
fof(f7525,plain,
spl0_555,
inference(avatar_split_clause,[],[f1435,f7523]) ).
fof(f7523,plain,
( spl0_555
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(c_Suc,X1) = X2
| c_HOL_Oord__class_Oless(hAPP(c_Suc,X1),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f1435,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(c_Suc,X1) = X2
| c_HOL_Oord__class_Oless(hAPP(c_Suc,X1),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
fof(f7521,plain,
spl0_554,
inference(avatar_split_clause,[],[f1431,f7519]) ).
fof(f7519,plain,
( spl0_554
<=> ! [X0,X16,X14] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X16,X14,tc_nat),X0,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X16,X0,tc_nat),X14,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f1431,axiom,
! [X0,X16,X14] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X16,X14,tc_nat),X0,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X16,X0,tc_nat),X14,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).
fof(f7517,plain,
spl0_553,
inference(avatar_split_clause,[],[f1417,f7515]) ).
fof(f1417,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(f7513,plain,
spl0_552,
inference(avatar_split_clause,[],[f1353,f7510]) ).
fof(f7510,plain,
( spl0_552
<=> c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f1353,axiom,
c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,v_ka____)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_i_0) ).
fof(f7508,plain,
spl0_551,
inference(avatar_split_clause,[],[f1227,f7506]) ).
fof(f7506,plain,
( spl0_551
<=> ! [X17,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oord__class_Oless(c_Int_OPls,X17,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X17,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f1227,axiom,
! [X3,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oord__class_Oless(c_Int_OPls,X17,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X17,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__special_I1_J_0) ).
fof(f7504,plain,
spl0_550,
inference(avatar_split_clause,[],[f1226,f7502]) ).
fof(f7502,plain,
( spl0_550
<=> ! [X17,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ c_HOL_Oord__class_Oless(c_Int_OPls,X17,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X17,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f1226,axiom,
! [X3,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ c_HOL_Oord__class_Oless(c_Int_OPls,X17,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X17,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__special_I1_J_1) ).
fof(f7500,plain,
spl0_549,
inference(avatar_split_clause,[],[f1225,f7498]) ).
fof(f7498,plain,
( spl0_549
<=> ! [X9,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oord__class_Oless(X9,c_Int_OPls,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f1225,axiom,
! [X3,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oord__class_Oless(X9,c_Int_OPls,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__special_I3_J_0) ).
fof(f7496,plain,
spl0_548,
inference(avatar_split_clause,[],[f1224,f7494]) ).
fof(f7494,plain,
( spl0_548
<=> ! [X9,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ c_HOL_Oord__class_Oless(X9,c_Int_OPls,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f1224,axiom,
! [X3,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ c_HOL_Oord__class_Oless(X9,c_Int_OPls,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__special_I3_J_1) ).
fof(f7492,plain,
spl0_547,
inference(avatar_split_clause,[],[f1091,f7490]) ).
fof(f7490,plain,
( spl0_547
<=> ! [X9,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(X9,c_Int_Onumber__class_Onumber__of(c_Int_OPls,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f1091,axiom,
! [X3,X9] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(X9,c_Int_Onumber__class_Onumber__of(c_Int_OPls,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__Numeral0_0) ).
fof(f7488,plain,
spl0_546,
inference(avatar_split_clause,[],[f1010,f7486]) ).
fof(f7486,plain,
( spl0_546
<=> ! [X9,X17,X3] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X9,X3),X17,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X9,X17,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f1010,axiom,
! [X3,X9,X17] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X9,X3),X17,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X9,X17,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ominus_0) ).
fof(f7484,plain,
spl0_545,
inference(avatar_split_clause,[],[f1007,f7482]) ).
fof(f7482,plain,
( spl0_545
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X6,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X3),X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f1007,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X6,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X3),X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).
fof(f7480,plain,
spl0_544,
inference(avatar_split_clause,[],[f967,f7478]) ).
fof(f967,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
fof(f7476,plain,
spl0_543,
inference(avatar_split_clause,[],[f948,f7474]) ).
fof(f7474,plain,
( spl0_543
<=> ! [X2,X1] :
( c_lessequals(X1,X2,tc_nat)
| hAPP(c_Suc,X2) = X1
| ~ c_lessequals(X1,hAPP(c_Suc,X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f948,axiom,
! [X2,X1] :
( c_lessequals(X1,X2,tc_nat)
| hAPP(c_Suc,X2) = X1
| ~ c_lessequals(X1,hAPP(c_Suc,X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucE_0) ).
fof(f7472,plain,
spl0_542,
inference(avatar_split_clause,[],[f923,f7470]) ).
fof(f7470,plain,
( spl0_542
<=> ! [X9,X2] :
( ~ 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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X9),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f923,axiom,
! [X2,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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X9),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__nat__eq_2) ).
fof(f7468,plain,
spl0_541,
inference(avatar_split_clause,[],[f914,f7466]) ).
fof(f7466,plain,
( spl0_541
<=> ! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f914,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).
fof(f7464,plain,
spl0_540,
inference(avatar_split_clause,[],[f895,f7462]) ).
fof(f7462,plain,
( spl0_540
<=> ! [X2,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f895,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).
fof(f7460,plain,
spl0_539,
inference(avatar_split_clause,[],[f894,f7458]) ).
fof(f894,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).
fof(f7456,plain,
spl0_538,
inference(avatar_split_clause,[],[f873,f7454]) ).
fof(f7454,plain,
( spl0_538
<=> ! [X1] : c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f873,axiom,
! [X1] : c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__self__div__2_0) ).
fof(f7452,plain,
spl0_537,
inference(avatar_split_clause,[],[f788,f7450]) ).
fof(f788,axiom,
! [X2,X3,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__zero__eq_0) ).
fof(f7448,plain,
( ~ spl0_534
| spl0_535
| ~ spl0_536
| ~ spl0_421
| ~ spl0_496 ),
inference(avatar_split_clause,[],[f7030,f6015,f4813,f7445,f7441,f7437]) ).
fof(f7437,plain,
( spl0_534
<=> class_Ring__and__Field_Oidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f7441,plain,
( spl0_535
<=> v_i____ = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f7445,plain,
( spl0_536
<=> class_Int_Onumber__ring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f4813,plain,
( spl0_421
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f6015,plain,
( spl0_496
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X9 = X17
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Ominus__class_Ominus(X9,X17,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f7030,plain,
( ~ class_Int_Onumber__ring(tc_nat)
| v_i____ = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))
| ~ class_Ring__and__Field_Oidom(tc_nat)
| ~ spl0_421
| ~ spl0_496 ),
inference(trivial_inequality_removal,[],[f7029]) ).
fof(f7029,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Int_Onumber__ring(tc_nat)
| v_i____ = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))
| ~ class_Ring__and__Field_Oidom(tc_nat)
| ~ spl0_421
| ~ spl0_496 ),
inference(superposition,[],[f6016,f4815]) ).
fof(f4815,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat)
| ~ spl0_421 ),
inference(avatar_component_clause,[],[f4813]) ).
fof(f6016,plain,
( ! [X3,X9,X17] :
( c_HOL_Ozero__class_Ozero(X3) != c_HOL_Ominus__class_Ominus(X9,X17,X3)
| ~ class_Int_Onumber__ring(X3)
| X9 = X17
| ~ class_Ring__and__Field_Oidom(X3) )
| ~ spl0_496 ),
inference(avatar_component_clause,[],[f6015]) ).
fof(f7435,plain,
spl0_533,
inference(avatar_split_clause,[],[f768,f7433]) ).
fof(f7433,plain,
( spl0_533
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X6,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X6,X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f768,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X6,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X6,X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__commute_0) ).
fof(f7431,plain,
spl0_532,
inference(avatar_split_clause,[],[f651,f7429]) ).
fof(f7429,plain,
( spl0_532
<=> ! [X9,X3] :
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ouminus__class_Ouminus(X9,X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3)),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f651,axiom,
! [X3,X9] :
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ouminus__class_Ouminus(X9,X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3)),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
fof(f7427,plain,
spl0_531,
inference(avatar_split_clause,[],[f423,f7425]) ).
fof(f7425,plain,
( spl0_531
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Ouminus__class_Ouminus(X6,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f423,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Ouminus__class_Ouminus(X6,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
fof(f7423,plain,
spl0_530,
inference(avatar_split_clause,[],[f394,f7421]) ).
fof(f394,axiom,
! [X2,X3,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power__eq_1) ).
fof(f7419,plain,
spl0_529,
inference(avatar_split_clause,[],[f321,f7417]) ).
fof(f7417,plain,
( spl0_529
<=> ! [X2,X1] :
( ~ c_lessequals(X2,X1,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f321,axiom,
! [X2,X1] :
( ~ c_lessequals(X2,X1,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).
fof(f7415,plain,
spl0_528,
inference(avatar_split_clause,[],[f274,f7413]) ).
fof(f7413,plain,
( spl0_528
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f274,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X6),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f7411,plain,
spl0_527,
inference(avatar_split_clause,[],[f271,f7409]) ).
fof(f7409,plain,
( spl0_527
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f271,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X5),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(f7407,plain,
spl0_526,
inference(avatar_split_clause,[],[f221,f7405]) ).
fof(f7405,plain,
( spl0_526
<=> ! [X9] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),X9)) = c_HOL_Ouminus__class_Ouminus(X9,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f221,axiom,
! [X9] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),X9)) = c_HOL_Ouminus__class_Ouminus(X9,tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__i__mult__minus_0) ).
fof(f7403,plain,
spl0_525,
inference(avatar_split_clause,[],[f220,f7401]) ).
fof(f7401,plain,
( spl0_525
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f220,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
fof(f7399,plain,
spl0_524,
inference(avatar_split_clause,[],[f64,f7397]) ).
fof(f7397,plain,
( spl0_524
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X4,X6,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),c_HOL_Ouminus__class_Ouminus(X6,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f64,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X4,X6,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),c_HOL_Ouminus__class_Ouminus(X6,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus_0) ).
fof(f7395,plain,
spl0_523,
inference(avatar_split_clause,[],[f63,f7393]) ).
fof(f7393,plain,
( spl0_523
<=> ! [X9,X17,X3] :
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X9,X17,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),c_HOL_Ouminus__class_Ouminus(X17,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f63,axiom,
! [X3,X9,X17] :
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X9,X17,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),c_HOL_Ouminus__class_Ouminus(X17,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
fof(f7391,plain,
spl0_522,
inference(avatar_split_clause,[],[f62,f7389]) ).
fof(f7389,plain,
( spl0_522
<=> ! [X9,X17,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X9,X17,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),c_HOL_Ouminus__class_Ouminus(X17,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f62,axiom,
! [X3,X9,X17] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X9,X17,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),c_HOL_Ouminus__class_Ouminus(X17,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__def_0) ).
fof(f7387,plain,
spl0_521,
inference(avatar_split_clause,[],[f10,f7385]) ).
fof(f7385,plain,
( spl0_521
<=> ! [X10,X11,X9,X13,X12,X3,X8] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X8,X9),c_HOL_Ozero__class_Ozero(tc_nat)) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f10,axiom,
! [X3,X10,X11,X8,X9,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X8,X9),c_HOL_Ozero__class_Ozero(tc_nat)) = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__0_0) ).
fof(f7287,plain,
( ~ spl0_520
| ~ spl0_200
| ~ spl0_270
| ~ spl0_505 ),
inference(avatar_split_clause,[],[f7175,f6055,f3022,f2654,f7284]) ).
fof(f7284,plain,
( spl0_520
<=> c_Parity_Oeven__odd__class_Oeven(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f3022,plain,
( spl0_270
<=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f6055,plain,
( spl0_505
<=> ! [X9] : ~ c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X9)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f7175,plain,
( ~ c_Parity_Oeven__odd__class_Oeven(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)
| ~ spl0_200
| ~ spl0_270
| ~ spl0_505 ),
inference(forward_demodulation,[],[f7174,f2656]) ).
fof(f7174,plain,
( ~ c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| ~ spl0_270
| ~ spl0_505 ),
inference(superposition,[],[f6056,f3023]) ).
fof(f3023,plain,
( ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))
| ~ spl0_270 ),
inference(avatar_component_clause,[],[f3022]) ).
fof(f6056,plain,
( ! [X9] : ~ c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X9)),tc_nat)
| ~ spl0_505 ),
inference(avatar_component_clause,[],[f6055]) ).
fof(f6874,plain,
( ~ spl0_518
| spl0_519
| ~ spl0_138
| ~ spl0_479 ),
inference(avatar_split_clause,[],[f6575,f5946,f2367,f6872,f6868]) ).
fof(f6868,plain,
( spl0_518
<=> class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f6872,plain,
( spl0_519
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f2367,plain,
( spl0_138
<=> ! [X1] : ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f5946,plain,
( spl0_479
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X6,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f6575,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) )
| ~ spl0_138
| ~ spl0_479 ),
inference(resolution,[],[f5947,f2368]) ).
fof(f2368,plain,
( ! [X1] : ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_138 ),
inference(avatar_component_clause,[],[f2367]) ).
fof(f5947,plain,
( ! [X3,X6,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X6,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) )
| ~ spl0_479 ),
inference(avatar_component_clause,[],[f5946]) ).
fof(f6311,plain,
( spl0_517
| ~ spl0_193
| ~ spl0_439 ),
inference(avatar_split_clause,[],[f5030,f4944,f2626,f6309]) ).
fof(f6309,plain,
( spl0_517
<=> ! [X0] : c_lessequals(v_i____,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f4944,plain,
( spl0_439
<=> ! [X0] :
( ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),X0,tc_nat)
| c_lessequals(v_i____,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f5030,plain,
( ! [X0] : c_lessequals(v_i____,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_nat)
| ~ spl0_193
| ~ spl0_439 ),
inference(resolution,[],[f4945,f2627]) ).
fof(f4945,plain,
( ! [X0] :
( ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),X0,tc_nat)
| c_lessequals(v_i____,X0,tc_nat) )
| ~ spl0_439 ),
inference(avatar_component_clause,[],[f4944]) ).
fof(f6172,plain,
( spl0_516
| ~ spl0_192
| ~ spl0_439 ),
inference(avatar_split_clause,[],[f5029,f4944,f2622,f6170]) ).
fof(f6170,plain,
( spl0_516
<=> ! [X0] : c_lessequals(v_i____,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f5029,plain,
( ! [X0] : c_lessequals(v_i____,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),X0),tc_nat)
| ~ spl0_192
| ~ spl0_439 ),
inference(resolution,[],[f4945,f2623]) ).
fof(f6098,plain,
spl0_515,
inference(avatar_split_clause,[],[f1610,f6096]) ).
fof(f6096,plain,
( spl0_515
<=> ! [X9] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_Divides_Odiv__class_Omod(X9,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f1610,plain,
! [X9] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_Divides_Odiv__class_Omod(X9,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ),
inference(forward_demodulation,[],[f1609,f1583]) ).
fof(f1609,plain,
! [X9] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_Divides_Odiv__class_Omod(X9,hAPP(c_Suc,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ),
inference(forward_demodulation,[],[f166,f421]) ).
fof(f166,axiom,
! [X9] :
( c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Divides_Odiv__class_Omod(X9,hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__nat__equiv__def_1) ).
fof(f6094,plain,
spl0_514,
inference(avatar_split_clause,[],[f1602,f6092]) ).
fof(f1602,plain,
! [X9] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X9,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ),
inference(forward_demodulation,[],[f1601,f1583]) ).
fof(f1601,plain,
! [X9] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X9,hAPP(c_Suc,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ),
inference(forward_demodulation,[],[f165,f421]) ).
fof(f165,axiom,
! [X9] :
( ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X9,hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__nat__equiv__def_0) ).
fof(f6090,plain,
spl0_513,
inference(avatar_split_clause,[],[f1587,f6088]) ).
fof(f6088,plain,
( spl0_513
<=> ! [X1] : c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f1587,plain,
! [X1] : c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),X1),
inference(forward_demodulation,[],[f917,f421]) ).
fof(f917,axiom,
! [X1] : hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__power__eq__Suc__0__iff_2) ).
fof(f6086,plain,
spl0_512,
inference(avatar_split_clause,[],[f1573,f6084]) ).
fof(f6084,plain,
( spl0_512
<=> ! [X48,X3,X46,X49,X15,X47] : hAPP(c_COMBB(X15,X46,X47,X3,X48),X49) = hAPP(X15,hAPP(X46,X49)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f1573,axiom,
! [X3,X48,X46,X49,X47,X15] : hAPP(c_COMBB(X15,X46,X47,X3,X48),X49) = hAPP(X15,hAPP(X46,X49)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
fof(f6082,plain,
spl0_511,
inference(avatar_split_clause,[],[f1424,f6080]) ).
fof(f6080,plain,
( spl0_511
<=> ! [X9,X17,X3] :
( ~ class_Int_Oring__char__0(X3)
| ~ class_Int_Onumber__ring(X3)
| X9 = X17
| c_Int_Onumber__class_Onumber__of(X9,X3) != c_Int_Onumber__class_Onumber__of(X17,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f1424,axiom,
! [X3,X9,X17] :
( ~ class_Int_Oring__char__0(X3)
| ~ class_Int_Onumber__ring(X3)
| X9 = X17
| c_Int_Onumber__class_Onumber__of(X9,X3) != c_Int_Onumber__class_Onumber__of(X17,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__number__of_0) ).
fof(f6078,plain,
spl0_510,
inference(avatar_split_clause,[],[f1422,f6076]) ).
fof(f6076,plain,
( spl0_510
<=> ! [X17,X3,X9,X32] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| X17 = X32
| c_HOL_Ominus__class_Ominus(X9,X9,X3) != c_HOL_Ominus__class_Ominus(X32,X17,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f1422,axiom,
! [X3,X9,X17,X32] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| X17 = X32
| c_HOL_Ominus__class_Ominus(X9,X9,X3) != c_HOL_Ominus__class_Ominus(X32,X17,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
fof(f6074,plain,
spl0_509,
inference(avatar_split_clause,[],[f1419,f6072]) ).
fof(f6072,plain,
( spl0_509
<=> ! [X17,X3,X9,X22] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X9,X17,X3)
| ~ c_HOL_Oord__class_Oless(X17,X22,X3)
| c_HOL_Oord__class_Oless(X9,X22,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f1419,axiom,
! [X3,X9,X17,X22] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X9,X17,X3)
| ~ c_HOL_Oord__class_Oless(X17,X22,X3)
| c_HOL_Oord__class_Oless(X9,X22,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f6070,plain,
( ~ spl0_30
| ~ spl0_508
| ~ spl0_158
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f3354,f3030,f2452,f6067,f1832]) ).
fof(f6067,plain,
( spl0_508
<=> c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f3354,plain,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat),tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| ~ spl0_158
| ~ spl0_272 ),
inference(resolution,[],[f3031,f2454]) ).
fof(f6065,plain,
spl0_507,
inference(avatar_split_clause,[],[f1418,f6063]) ).
fof(f6063,plain,
( spl0_507
<=> ! [X17,X3,X9,X22] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X17,X9,X3)
| ~ c_HOL_Oord__class_Oless(X22,X17,X3)
| c_HOL_Oord__class_Oless(X22,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f1418,axiom,
! [X3,X9,X17,X22] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X17,X9,X3)
| ~ c_HOL_Oord__class_Oless(X22,X17,X3)
| c_HOL_Oord__class_Oless(X22,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f6061,plain,
spl0_506,
inference(avatar_split_clause,[],[f1380,f6059]) ).
fof(f1380,axiom,
! [X0,X16,X14] :
( ~ c_HOL_Oord__class_Oless(X16,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X0,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(c_Suc,X16),X0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
fof(f6057,plain,
spl0_505,
inference(avatar_split_clause,[],[f1285,f6055]) ).
fof(f1285,axiom,
! [X9] : ~ c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X9)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__Suc__mult__two__ex_1) ).
fof(f6053,plain,
spl0_504,
inference(avatar_split_clause,[],[f1190,f6051]) ).
fof(f6051,plain,
( spl0_504
<=> ! [X2,X1,X26] :
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X26,X2,tc_nat),c_HOL_Ominus__class_Ominus(X26,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f1190,axiom,
! [X2,X1,X26] :
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X26,X2,tc_nat),c_HOL_Ominus__class_Ominus(X26,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
fof(f6049,plain,
spl0_503,
inference(avatar_split_clause,[],[f1189,f6047]) ).
fof(f6047,plain,
( spl0_503
<=> ! [X2,X1,X26] :
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X26,tc_nat),c_HOL_Ominus__class_Ominus(X2,X26,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f1189,axiom,
! [X2,X1,X26] :
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X26,tc_nat),c_HOL_Ominus__class_Ominus(X2,X26,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
fof(f6045,plain,
spl0_502,
inference(avatar_split_clause,[],[f1149,f6043]) ).
fof(f6043,plain,
( spl0_502
<=> ! [X1] : c_lessequals(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X1)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f1149,axiom,
! [X1] : c_lessequals(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X1)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__cube_0) ).
fof(f6041,plain,
spl0_501,
inference(avatar_split_clause,[],[f1101,f6039]) ).
fof(f6039,plain,
( spl0_501
<=> ! [X2,X16] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,hAPP(c_Suc,X16),tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f1101,axiom,
! [X2,X16] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,hAPP(c_Suc,X16),tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
fof(f6037,plain,
spl0_500,
inference(avatar_split_clause,[],[f1037,f6035]) ).
fof(f6035,plain,
( spl0_500
<=> ! [X9,X17] :
( c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X9),X17),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f1037,axiom,
! [X9,X17] :
( c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X9),X17),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__product__nat_0) ).
fof(f6033,plain,
spl0_499,
inference(avatar_split_clause,[],[f872,f6031]) ).
fof(f6031,plain,
( spl0_499
<=> ! [X2] :
( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Omod(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f872,axiom,
! [X2] :
( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Omod(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__even__mod__4__iff_1) ).
fof(f6029,plain,
spl0_498,
inference(avatar_split_clause,[],[f871,f6027]) ).
fof(f6027,plain,
( spl0_498
<=> ! [X2] :
( ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Omod(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f871,axiom,
! [X2] :
( ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Omod(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__even__mod__4__iff_0) ).
fof(f6021,plain,
spl0_497,
inference(avatar_split_clause,[],[f809,f6019]) ).
fof(f6019,plain,
( spl0_497
<=> ! [X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X3),c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f809,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X3),c_Power_Opower__class_Opower(X3),c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Ogb__semiring__axioms_H_0) ).
fof(f6017,plain,
spl0_496,
inference(avatar_split_clause,[],[f779,f6015]) ).
fof(f779,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X9 = X17
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Ominus__class_Ominus(X9,X17,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
fof(f6013,plain,
spl0_495,
inference(avatar_split_clause,[],[f756,f6011]) ).
fof(f6011,plain,
( spl0_495
<=> ! [X22,X3] :
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ouminus__class_Ouminus(X22,X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X22),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f756,axiom,
! [X3,X22] :
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ouminus__class_Ouminus(X22,X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X22),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__minus1__right_0) ).
fof(f6009,plain,
spl0_494,
inference(avatar_split_clause,[],[f755,f6007]) ).
fof(f6007,plain,
( spl0_494
<=> ! [X22,X3] :
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ouminus__class_Ouminus(X22,X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3)),X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f755,axiom,
! [X3,X22] :
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ouminus__class_Ouminus(X22,X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3)),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__minus1_0) ).
fof(f6005,plain,
spl0_493,
inference(avatar_split_clause,[],[f754,f6003]) ).
fof(f6003,plain,
( spl0_493
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_HOL_Oone__class_Oone(X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f754,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_HOL_Oone__class_Oone(X3)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
fof(f6001,plain,
spl0_492,
inference(avatar_split_clause,[],[f586,f5999]) ).
fof(f5999,plain,
( spl0_492
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X6,X3),X3)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f586,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X6,X3),X3)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
fof(f5997,plain,
spl0_491,
inference(avatar_split_clause,[],[f583,f5995]) ).
fof(f5995,plain,
( spl0_491
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X6,X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X3),X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f583,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X6,X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X3),X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
fof(f5993,plain,
spl0_490,
inference(avatar_split_clause,[],[f574,f5991]) ).
fof(f5991,plain,
( spl0_490
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X6,X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f574,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X6,X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
fof(f5989,plain,
spl0_489,
inference(avatar_split_clause,[],[f573,f5987]) ).
fof(f5987,plain,
( spl0_489
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X6,X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f573,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X6,X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
fof(f5985,plain,
spl0_488,
inference(avatar_split_clause,[],[f563,f5983]) ).
fof(f5983,plain,
( spl0_488
<=> ! [X9,X17,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X9,X17,X3)
| c_lessequals(X17,X9,X3)
| c_HOL_Oord__class_Oless(X9,X17,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f563,axiom,
! [X3,X9,X17] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X9,X17,X3)
| c_lessequals(X17,X9,X3)
| c_HOL_Oord__class_Oless(X9,X17,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
fof(f5981,plain,
( ~ spl0_30
| ~ spl0_487
| ~ spl0_158
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f3133,f2922,f2452,f5978,f1832]) ).
fof(f5978,plain,
( spl0_487
<=> c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f3133,plain,
( ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat),tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| ~ spl0_158
| ~ spl0_245 ),
inference(resolution,[],[f2923,f2454]) ).
fof(f5976,plain,
spl0_486,
inference(avatar_split_clause,[],[f553,f5974]) ).
fof(f5974,plain,
( spl0_486
<=> ! [X17,X3,X9,X22] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X9,X17,X3)
| ~ c_HOL_Oord__class_Oless(X17,X22,X3)
| c_HOL_Oord__class_Oless(X9,X22,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f553,axiom,
! [X3,X9,X17,X22] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X9,X17,X3)
| ~ c_HOL_Oord__class_Oless(X17,X22,X3)
| c_HOL_Oord__class_Oless(X9,X22,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f5972,plain,
spl0_485,
inference(avatar_split_clause,[],[f552,f5970]) ).
fof(f5970,plain,
( spl0_485
<=> ! [X17,X3,X9,X22] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X17,X22,X3)
| ~ c_HOL_Oord__class_Oless(X9,X17,X3)
| c_HOL_Oord__class_Oless(X9,X22,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f552,axiom,
! [X3,X9,X17,X22] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X17,X22,X3)
| ~ c_HOL_Oord__class_Oless(X9,X17,X3)
| c_HOL_Oord__class_Oless(X9,X22,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f5968,plain,
spl0_484,
inference(avatar_split_clause,[],[f551,f5966]) ).
fof(f551,axiom,
! [X3,X9,X17,X22] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X17,X9,X3)
| ~ c_HOL_Oord__class_Oless(X22,X17,X3)
| c_HOL_Oord__class_Oless(X22,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
fof(f5964,plain,
spl0_483,
inference(avatar_split_clause,[],[f550,f5962]) ).
fof(f550,axiom,
! [X3,X9,X17,X22] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X22,X17,X3)
| ~ c_HOL_Oord__class_Oless(X17,X9,X3)
| c_HOL_Oord__class_Oless(X22,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
fof(f5960,plain,
spl0_482,
inference(avatar_split_clause,[],[f548,f5958]) ).
fof(f5958,plain,
( spl0_482
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X6,c_HOL_Ouminus__class_Ouminus(X4,X3),X3)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X6,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f548,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X6,c_HOL_Ouminus__class_Ouminus(X4,X3),X3)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X6,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
fof(f5956,plain,
spl0_481,
inference(avatar_split_clause,[],[f546,f5954]) ).
fof(f546,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X6,X3),X4,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
fof(f5952,plain,
spl0_480,
inference(avatar_split_clause,[],[f540,f5950]) ).
fof(f5950,plain,
( spl0_480
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X6,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f540,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X6,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
fof(f5948,plain,
spl0_479,
inference(avatar_split_clause,[],[f539,f5946]) ).
fof(f539,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X6,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
fof(f5944,plain,
spl0_478,
inference(avatar_split_clause,[],[f469,f5942]) ).
fof(f5942,plain,
( spl0_478
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f469,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
fof(f5940,plain,
spl0_477,
inference(avatar_split_clause,[],[f468,f5938]) ).
fof(f5938,plain,
( spl0_477
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f468,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
fof(f5916,plain,
spl0_476,
inference(avatar_split_clause,[],[f460,f5914]) ).
fof(f5914,plain,
( spl0_476
<=> ! [X6,X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f460,axiom,
! [X3,X6,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X6),X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
fof(f5912,plain,
spl0_475,
inference(avatar_split_clause,[],[f459,f5910]) ).
fof(f5910,plain,
( spl0_475
<=> ! [X6,X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X4),X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f459,axiom,
! [X3,X6,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X6),X4),X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
fof(f5908,plain,
spl0_474,
inference(avatar_split_clause,[],[f456,f5906]) ).
fof(f456,axiom,
! [X3,X9,X17,X22] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X17,X9,X3)
| ~ c_lessequals(X22,X17,X3)
| c_lessequals(X22,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f5904,plain,
spl0_473,
inference(avatar_split_clause,[],[f454,f5902]) ).
fof(f454,axiom,
! [X3,X9,X17,X22] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X9,X17,X3)
| ~ c_lessequals(X17,X22,X3)
| c_lessequals(X9,X22,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f5900,plain,
spl0_472,
inference(avatar_split_clause,[],[f422,f5898]) ).
fof(f5898,plain,
( spl0_472
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ouminus__class_Ouminus(X4,X3) = c_HOL_Oabs__class_Oabs(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f422,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ouminus__class_Ouminus(X4,X3) = c_HOL_Oabs__class_Oabs(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__nonpos_0) ).
fof(f5896,plain,
spl0_471,
inference(avatar_split_clause,[],[f352,f5894]) ).
fof(f5894,plain,
( spl0_471
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f352,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
fof(f5892,plain,
spl0_470,
inference(avatar_split_clause,[],[f351,f5890]) ).
fof(f5890,plain,
( spl0_470
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f351,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
fof(f5888,plain,
spl0_469,
inference(avatar_split_clause,[],[f339,f5886]) ).
fof(f5886,plain,
( spl0_469
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
| ~ class_Orderings_Olinorder(X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = X4
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f339,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
| ~ class_Orderings_Olinorder(X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = X4
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if__lattice_1) ).
fof(f5884,plain,
spl0_468,
inference(avatar_split_clause,[],[f312,f5882]) ).
fof(f5882,plain,
( spl0_468
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X4,X6,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f312,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X4,X6,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
fof(f5880,plain,
spl0_467,
inference(avatar_split_clause,[],[f311,f5878]) ).
fof(f5878,plain,
( spl0_467
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X4,X6,X3)
| c_lessequals(c_HOL_Ominus__class_Ominus(X4,X6,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f311,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X4,X6,X3)
| c_lessequals(c_HOL_Ominus__class_Ominus(X4,X6,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
fof(f5872,plain,
spl0_466,
inference(avatar_split_clause,[],[f242,f5870]) ).
fof(f5870,plain,
( spl0_466
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X4,X6,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X6,X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f242,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X4,X6,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X6,X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
fof(f5868,plain,
spl0_465,
inference(avatar_split_clause,[],[f241,f5866]) ).
fof(f5866,plain,
( spl0_465
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X6,X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f241,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X4,X6,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X6,X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
fof(f5864,plain,
spl0_464,
inference(avatar_split_clause,[],[f223,f5862]) ).
fof(f5862,plain,
( spl0_464
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oabs__if(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ouminus__class_Ouminus(X4,X3) = c_HOL_Oabs__class_Oabs(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f223,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oabs__if(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ouminus__class_Ouminus(X4,X3) = c_HOL_Oabs__class_Oabs(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if_0) ).
fof(f5860,plain,
spl0_463,
inference(avatar_split_clause,[],[f222,f5858]) ).
fof(f5858,plain,
( spl0_463
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ouminus__class_Ouminus(X4,X3) = c_HOL_Oabs__class_Oabs(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f222,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ouminus__class_Ouminus(X4,X3) = c_HOL_Oabs__class_Oabs(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__neg_0) ).
fof(f5856,plain,
spl0_462,
inference(avatar_split_clause,[],[f208,f5854]) ).
fof(f5854,plain,
( spl0_462
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X3),X6,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X3),X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f208,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X3),X6,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X3),X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_1) ).
fof(f5852,plain,
spl0_461,
inference(avatar_split_clause,[],[f170,f5850]) ).
fof(f5850,plain,
( spl0_461
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f170,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).
fof(f5848,plain,
spl0_460,
inference(avatar_split_clause,[],[f169,f5846]) ).
fof(f5846,plain,
( spl0_460
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f169,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
fof(f5844,plain,
spl0_459,
inference(avatar_split_clause,[],[f155,f5842]) ).
fof(f5842,plain,
( spl0_459
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),X6,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f155,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),X6,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__D2_0) ).
fof(f5840,plain,
spl0_458,
inference(avatar_split_clause,[],[f142,f5838]) ).
fof(f5838,plain,
( spl0_458
<=> ! [X6,X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,X6,X3) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X6,X3),X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f142,axiom,
! [X3,X6,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,X6,X3) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X6,X3),X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
fof(f5836,plain,
spl0_457,
inference(avatar_split_clause,[],[f134,f5834]) ).
fof(f5834,plain,
( spl0_457
<=> ! [X2,X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Oabs__class_Oabs(X4,X3)),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f134,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Oabs__class_Oabs(X4,X3)),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power__abs_0) ).
fof(f5832,plain,
spl0_456,
inference(avatar_split_clause,[],[f127,f5830]) ).
fof(f5830,plain,
( spl0_456
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f127,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
fof(f5828,plain,
spl0_455,
inference(avatar_split_clause,[],[f126,f5826]) ).
fof(f5826,plain,
( spl0_455
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f126,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).
fof(f5824,plain,
spl0_454,
inference(avatar_split_clause,[],[f97,f5822]) ).
fof(f5822,plain,
( spl0_454
<=> ! [X10,X11,X9,X13,X12,X3,X8] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,X10),X9) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f97,axiom,
! [X3,X10,X11,X8,X9,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,X10),X9) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Omul__1_0) ).
fof(f5820,plain,
spl0_453,
inference(avatar_split_clause,[],[f96,f5818]) ).
fof(f5818,plain,
( spl0_453
<=> ! [X10,X11,X9,X13,X12,X3,X8] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,X13),X9) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f96,axiom,
! [X3,X10,X11,X8,X9,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,X13),X9) = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Omul__0_0) ).
fof(f5816,plain,
spl0_452,
inference(avatar_split_clause,[],[f79,f5814]) ).
fof(f5814,plain,
( spl0_452
<=> ! [X10,X11,X13,X4,X12,X3,X8] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,X4),X10) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f79,axiom,
! [X3,X10,X11,X8,X4,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,X4),X10) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I12_J_0) ).
fof(f5812,plain,
spl0_451,
inference(avatar_split_clause,[],[f77,f5810]) ).
fof(f5810,plain,
( spl0_451
<=> ! [X10,X11,X13,X4,X12,X3,X8] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,X4),X13) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f77,axiom,
! [X3,X10,X11,X8,X4,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X12,X4),X13) = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I10_J_0) ).
fof(f5808,plain,
spl0_450,
inference(avatar_split_clause,[],[f73,f5806]) ).
fof(f5806,plain,
( spl0_450
<=> ! [X10,X11,X13,X4,X12,X3,X8] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X11,X4),X13) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f73,axiom,
! [X3,X10,X11,X8,X4,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X11,X4),X13) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I6_J_0) ).
fof(f5804,plain,
spl0_449,
inference(avatar_split_clause,[],[f72,f5802]) ).
fof(f5802,plain,
( spl0_449
<=> ! [X10,X11,X13,X4,X12,X3,X8] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X11,X13),X4) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f72,axiom,
! [X3,X10,X11,X8,X4,X12,X13] :
( ~ c_Groebner__Basis_Ogb__semiring(X11,X12,X8,X13,X10,X3)
| hAPP(hAPP(X11,X13),X4) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I5_J_0) ).
fof(f5800,plain,
spl0_448,
inference(avatar_split_clause,[],[f67,f5798]) ).
fof(f5798,plain,
( spl0_448
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Odiv(X1,X0,tc_nat),c_Divides_Odiv__class_Odiv(X2,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f67,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Odiv(X1,X0,tc_nat),c_Divides_Odiv__class_Odiv(X2,X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__le__mono_0) ).
fof(f5796,plain,
spl0_447,
inference(avatar_split_clause,[],[f51,f5794]) ).
fof(f5794,plain,
( spl0_447
<=> ! [X2,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f51,axiom,
! [X2,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__add_0) ).
fof(f5792,plain,
( ~ spl0_445
| spl0_446
| ~ spl0_170
| ~ spl0_439 ),
inference(avatar_split_clause,[],[f5034,f4944,f2506,f5789,f5785]) ).
fof(f5785,plain,
( spl0_445
<=> class_OrderedGroup_Opordered__ab__group__add__abs(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f5789,plain,
( spl0_446
<=> c_lessequals(v_i____,c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f2506,plain,
( spl0_170
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(X4,c_HOL_Oabs__class_Oabs(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f5034,plain,
( c_lessequals(v_i____,c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat),tc_nat)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_nat)
| ~ spl0_170
| ~ spl0_439 ),
inference(resolution,[],[f4945,f2507]) ).
fof(f2507,plain,
( ! [X3,X4] :
( c_lessequals(X4,c_HOL_Oabs__class_Oabs(X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) )
| ~ spl0_170 ),
inference(avatar_component_clause,[],[f2506]) ).
fof(f5783,plain,
spl0_444,
inference(avatar_split_clause,[],[f50,f5781]) ).
fof(f5781,plain,
( spl0_444
<=> ! [X2,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f50,axiom,
! [X2,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__add_1) ).
fof(f5779,plain,
spl0_443,
inference(avatar_split_clause,[],[f48,f5777]) ).
fof(f5777,plain,
( spl0_443
<=> ! [X2,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f48,axiom,
! [X2,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__add_3) ).
fof(f5775,plain,
spl0_442,
inference(avatar_split_clause,[],[f44,f5773]) ).
fof(f5773,plain,
( spl0_442
<=> ! [X9,X17] :
( c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X17),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f44,axiom,
! [X9,X17] :
( c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X17),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__sum__nat_3) ).
fof(f5504,plain,
( spl0_441
| ~ spl0_174
| ~ spl0_439 ),
inference(avatar_split_clause,[],[f5023,f4944,f2522,f5502]) ).
fof(f5502,plain,
( spl0_441
<=> ! [X0] :
( c_lessequals(v_i____,X0,tc_nat)
| c_lessequals(X0,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f5023,plain,
( ! [X0] :
( c_lessequals(v_i____,X0,tc_nat)
| c_lessequals(X0,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat) )
| ~ spl0_174
| ~ spl0_439 ),
inference(resolution,[],[f4945,f2523]) ).
fof(f5183,plain,
( spl0_440
| ~ spl0_203
| ~ spl0_439 ),
inference(avatar_split_clause,[],[f5027,f4944,f2667,f5180]) ).
fof(f2667,plain,
( spl0_203
<=> ! [X0] : c_lessequals(X0,hAPP(c_Suc,X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f5027,plain,
( c_lessequals(v_i____,hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____))),tc_nat)
| ~ spl0_203
| ~ spl0_439 ),
inference(resolution,[],[f4945,f2668]) ).
fof(f2668,plain,
( ! [X0] : c_lessequals(X0,hAPP(c_Suc,X0),tc_nat)
| ~ spl0_203 ),
inference(avatar_component_clause,[],[f2667]) ).
fof(f4946,plain,
( spl0_439
| ~ spl0_184
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f4391,f4082,f2583,f4944]) ).
fof(f2583,plain,
( spl0_184
<=> c_lessequals(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f4391,plain,
( ! [X0] :
( ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),X0,tc_nat)
| c_lessequals(v_i____,X0,tc_nat) )
| ~ spl0_184
| ~ spl0_346 ),
inference(resolution,[],[f4083,f2585]) ).
fof(f2585,plain,
( c_lessequals(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat)
| ~ spl0_184 ),
inference(avatar_component_clause,[],[f2583]) ).
fof(f4900,plain,
spl0_438,
inference(avatar_split_clause,[],[f1590,f4897]) ).
fof(f4897,plain,
( spl0_438
<=> c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) = hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f1590,plain,
c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) = hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),
inference(forward_demodulation,[],[f1589,f1583]) ).
fof(f1589,plain,
c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) = hAPP(c_Suc,hAPP(c_Suc,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))),
inference(forward_demodulation,[],[f1246,f421]) ).
fof(f1246,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) = hAPP(c_Suc,hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_numeral__3__eq__3_0) ).
fof(f4895,plain,
~ spl0_437,
inference(avatar_split_clause,[],[f1438,f4892]) ).
fof(f1438,axiom,
~ c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_False_0) ).
fof(f4890,plain,
spl0_436,
inference(avatar_split_clause,[],[f1416,f4888]) ).
fof(f4886,plain,
spl0_435,
inference(avatar_split_clause,[],[f1399,f4884]) ).
fof(f4884,plain,
( spl0_435
<=> ! [X4,X3] :
( ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X3)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f1399,axiom,
! [X3,X4] :
( ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X3)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__numeral__1__right_0) ).
fof(f4882,plain,
spl0_434,
inference(avatar_split_clause,[],[f1398,f4880]) ).
fof(f4880,plain,
( spl0_434
<=> ! [X4,X3] :
( ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X3)),X4) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f1398,axiom,
! [X3,X4] :
( ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X3)),X4) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__numeral__1_0) ).
fof(f4878,plain,
spl0_433,
inference(avatar_split_clause,[],[f1388,f4876]) ).
fof(f4876,plain,
( spl0_433
<=> ! [X9,X17,X3] :
( ~ class_Orderings_Olinorder(X3)
| X9 = X17
| c_HOL_Oord__class_Oless(X9,X17,X3)
| c_HOL_Oord__class_Oless(X17,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f1388,axiom,
! [X3,X9,X17] :
( ~ class_Orderings_Olinorder(X3)
| X9 = X17
| c_HOL_Oord__class_Oless(X9,X17,X3)
| c_HOL_Oord__class_Oless(X17,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
fof(f4874,plain,
spl0_432,
inference(avatar_split_clause,[],[f1381,f4872]) ).
fof(f4872,plain,
( spl0_432
<=> ! [X9,X17,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| X9 = X17
| c_HOL_Oord__class_Oless(X9,X17,X3)
| c_HOL_Oord__class_Oless(X17,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f1381,axiom,
! [X3,X9,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| X9 = X17
| c_HOL_Oord__class_Oless(X9,X17,X3)
| c_HOL_Oord__class_Oless(X17,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
fof(f4856,plain,
spl0_431,
inference(avatar_split_clause,[],[f1321,f4854]) ).
fof(f4854,plain,
( spl0_431
<=> ! [X2,X1] :
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(c_Suc,X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f1321,axiom,
! [X2,X1] :
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(c_Suc,X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucE_0) ).
fof(f4852,plain,
spl0_430,
inference(avatar_split_clause,[],[f1318,f4850]) ).
fof(f4850,plain,
( spl0_430
<=> ! [X2,X1] : c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X1),hAPP(c_Suc,X2),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f1318,axiom,
! [X2,X1] : c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X1),hAPP(c_Suc,X2),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
fof(f4848,plain,
spl0_429,
inference(avatar_split_clause,[],[f1303,f4846]) ).
fof(f4846,plain,
( spl0_429
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X3),X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f1303,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X3),X3) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__numeral__1_0) ).
fof(f4844,plain,
spl0_428,
inference(avatar_split_clause,[],[f1202,f4842]) ).
fof(f4842,plain,
( spl0_428
<=> ! [X9,X17] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X9),X17),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f1202,axiom,
! [X9,X17] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X9),X17),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__power__nat_1) ).
fof(f4840,plain,
spl0_427,
inference(avatar_split_clause,[],[f1183,f4838]) ).
fof(f4838,plain,
( spl0_427
<=> ! [X2,X16] :
( ~ c_lessequals(X16,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X2,X16,tc_nat),tc_nat) = X16 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f1183,axiom,
! [X2,X16] :
( ~ c_lessequals(X16,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X2,X16,tc_nat),tc_nat) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
fof(f4836,plain,
spl0_426,
inference(avatar_split_clause,[],[f989,f4834]) ).
fof(f4834,plain,
( spl0_426
<=> ! [X0,X16,X14] :
( c_HOL_Oord__class_Oless(X16,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f989,axiom,
! [X0,X16,X14] :
( c_HOL_Oord__class_Oless(X16,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14),X0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
fof(f4832,plain,
spl0_425,
inference(avatar_split_clause,[],[f988,f4830]) ).
fof(f4830,plain,
( spl0_425
<=> ! [X22,X9,X17] :
( ~ c_HOL_Oord__class_Oless(X9,X22,tc_nat)
| c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X22),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f988,axiom,
! [X9,X17,X22] :
( ~ c_HOL_Oord__class_Oless(X9,X22,tc_nat)
| c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X22),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
fof(f4828,plain,
spl0_424,
inference(avatar_split_clause,[],[f987,f4826]) ).
fof(f4826,plain,
( spl0_424
<=> ! [X22,X9,X17] :
( ~ c_HOL_Oord__class_Oless(X9,X17,tc_nat)
| c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X22),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f987,axiom,
! [X9,X17,X22] :
( ~ c_HOL_Oord__class_Oless(X9,X17,tc_nat)
| c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X22),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
fof(f4824,plain,
spl0_423,
inference(avatar_split_clause,[],[f860,f4822]) ).
fof(f4822,plain,
( spl0_423
<=> ! [X2,X1] :
( X1 = X2
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,hAPP(c_Suc,X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f860,axiom,
! [X2,X1] :
( X1 = X2
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,hAPP(c_Suc,X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
fof(f4820,plain,
spl0_422,
inference(avatar_split_clause,[],[f785,f4818]) ).
fof(f4818,plain,
( spl0_422
<=> ! [X9,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_HOL_Ozero__class_Ozero(tc_nat)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f785,axiom,
! [X3,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_HOL_Ozero__class_Ozero(tc_nat)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_3) ).
fof(f4816,plain,
( spl0_421
| ~ spl0_184
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f3739,f3495,f2583,f4813]) ).
fof(f3739,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat)
| ~ spl0_184
| ~ spl0_291 ),
inference(resolution,[],[f3496,f2585]) ).
fof(f4811,plain,
spl0_420,
inference(avatar_split_clause,[],[f782,f4809]) ).
fof(f4809,plain,
( spl0_420
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X6,X4,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X4,X6,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f782,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X6,X4,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X4,X6,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
fof(f4807,plain,
spl0_419,
inference(avatar_split_clause,[],[f781,f4805]) ).
fof(f4805,plain,
( spl0_419
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X6,X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f781,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X6),X6,X3) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
fof(f4803,plain,
spl0_418,
inference(avatar_split_clause,[],[f776,f4801]) ).
fof(f4801,plain,
( spl0_418
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ominus__class_Ominus(X4,X6,X3)),X6) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f776,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ominus__class_Ominus(X4,X6,X3)),X6) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
fof(f4799,plain,
spl0_417,
inference(avatar_split_clause,[],[f735,f4797]) ).
fof(f4797,plain,
( spl0_417
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oone__class_Oone(X3) = c_HOL_Oinverse__class_Odivide(X4,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f735,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oone__class_Oone(X3) = c_HOL_Oinverse__class_Odivide(X4,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__self_0) ).
fof(f4795,plain,
spl0_416,
inference(avatar_split_clause,[],[f568,f4793]) ).
fof(f568,axiom,
! [X3,X9,X17] :
( ~ class_Orderings_Olinorder(X3)
| X9 = X17
| ~ c_lessequals(X9,X17,X3)
| c_HOL_Oord__class_Oless(X9,X17,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
fof(f4791,plain,
spl0_415,
inference(avatar_split_clause,[],[f566,f4789]) ).
fof(f4789,plain,
( spl0_415
<=> ! [X6,X4,X3] :
( ~ class_Orderings_Oorder(X3)
| X4 = X6
| ~ c_lessequals(X6,X4,X3)
| c_HOL_Oord__class_Oless(X6,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f566,axiom,
! [X3,X6,X4] :
( ~ class_Orderings_Oorder(X3)
| X4 = X6
| ~ c_lessequals(X6,X4,X3)
| c_HOL_Oord__class_Oless(X6,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
fof(f4787,plain,
spl0_414,
inference(avatar_split_clause,[],[f472,f4785]) ).
fof(f4785,plain,
( spl0_414
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f472,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
fof(f4783,plain,
spl0_413,
inference(avatar_split_clause,[],[f471,f4781]) ).
fof(f4781,plain,
( spl0_413
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f471,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
fof(f4779,plain,
spl0_412,
inference(avatar_split_clause,[],[f431,f4777]) ).
fof(f4777,plain,
( spl0_412
<=> ! [X9,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),c_HOL_Ozero__class_Ozero(X3)) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f431,axiom,
! [X3,X9] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),c_HOL_Ozero__class_Ozero(X3)) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
fof(f4775,plain,
spl0_411,
inference(avatar_split_clause,[],[f399,f4773]) ).
fof(f4773,plain,
( spl0_411
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),c_HOL_Ouminus__class_Ouminus(X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f399,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),c_HOL_Ouminus__class_Ouminus(X4,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus_0) ).
fof(f4770,plain,
spl0_410,
inference(avatar_split_clause,[],[f398,f4768]) ).
fof(f4768,plain,
( spl0_410
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X4,X3)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f398,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X4,X3)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
fof(f4766,plain,
spl0_409,
inference(avatar_split_clause,[],[f397,f4764]) ).
fof(f4764,plain,
( spl0_409
<=> ! [X6,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X6,X3)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f397,axiom,
! [X3,X6] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ouminus__class_Ouminus(X6,X3)),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).
fof(f4762,plain,
spl0_408,
inference(avatar_split_clause,[],[f382,f4760]) ).
fof(f4760,plain,
( spl0_408
<=> ! [X16,X1,X14] :
( ~ c_lessequals(X16,X14,tc_nat)
| c_lessequals(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X14),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f382,axiom,
! [X1,X16,X14] :
( ~ c_lessequals(X16,X14,tc_nat)
| c_lessequals(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X14),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).
fof(f4758,plain,
spl0_407,
inference(avatar_split_clause,[],[f381,f4756]) ).
fof(f4756,plain,
( spl0_407
<=> ! [X16,X1,X14] :
( ~ c_lessequals(X16,X14,tc_nat)
| c_lessequals(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f381,axiom,
! [X1,X16,X14] :
( ~ c_lessequals(X16,X14,tc_nat)
| c_lessequals(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).
fof(f4754,plain,
spl0_406,
inference(avatar_split_clause,[],[f380,f4752]) ).
fof(f4752,plain,
( spl0_406
<=> ! [X2,X0,X1] :
( c_lessequals(X0,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f380,axiom,
! [X2,X0,X1] :
( c_lessequals(X0,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_1) ).
fof(f4750,plain,
spl0_405,
inference(avatar_split_clause,[],[f379,f4748]) ).
fof(f4748,plain,
( spl0_405
<=> ! [X2,X0,X1] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f379,axiom,
! [X2,X0,X1] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_0) ).
fof(f4746,plain,
spl0_404,
inference(avatar_split_clause,[],[f359,f4744]) ).
fof(f4744,plain,
( spl0_404
<=> ! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f359,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
fof(f4741,plain,
spl0_403,
inference(avatar_split_clause,[],[f330,f4739]) ).
fof(f4739,plain,
( spl0_403
<=> ! [X2,X15] :
( hBOOL(hAPP(X15,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X15,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f330,axiom,
! [X2,X15] :
( hBOOL(hAPP(X15,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X15,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div_0) ).
fof(f4736,plain,
spl0_402,
inference(avatar_split_clause,[],[f328,f4734]) ).
fof(f4734,plain,
( spl0_402
<=> ! [X1,X15] :
( ~ hBOOL(hAPP(X15,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X15,c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f328,axiom,
! [X1,X15] :
( ~ hBOOL(hAPP(X15,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X15,c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div_H_6) ).
fof(f4732,plain,
spl0_401,
inference(avatar_split_clause,[],[f318,f4730]) ).
fof(f4730,plain,
( spl0_401
<=> ! [X9,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f318,axiom,
! [X3,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_0) ).
fof(f4728,plain,
spl0_400,
inference(avatar_split_clause,[],[f272,f4726]) ).
fof(f4726,plain,
( spl0_400
<=> ! [X2,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f272,axiom,
! [X2,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
fof(f4724,plain,
spl0_399,
inference(avatar_split_clause,[],[f263,f4722]) ).
fof(f4722,plain,
( spl0_399
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f263,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__abs__iff_1) ).
fof(f4720,plain,
spl0_398,
inference(avatar_split_clause,[],[f258,f4718]) ).
fof(f4718,plain,
( spl0_398
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f258,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).
fof(f4716,plain,
spl0_397,
inference(avatar_split_clause,[],[f257,f4714]) ).
fof(f4714,plain,
( spl0_397
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f257,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).
fof(f4712,plain,
spl0_396,
inference(avatar_split_clause,[],[f256,f4710]) ).
fof(f4710,plain,
( spl0_396
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f256,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).
fof(f4708,plain,
spl0_395,
inference(avatar_split_clause,[],[f255,f4706]) ).
fof(f4706,plain,
( spl0_395
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f255,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).
fof(f4704,plain,
spl0_394,
inference(avatar_split_clause,[],[f254,f4702]) ).
fof(f4702,plain,
( spl0_394
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f254,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).
fof(f4700,plain,
spl0_393,
inference(avatar_split_clause,[],[f253,f4698]) ).
fof(f4698,plain,
( spl0_393
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f253,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).
fof(f4696,plain,
spl0_392,
inference(avatar_split_clause,[],[f252,f4694]) ).
fof(f4694,plain,
( spl0_392
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f252,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).
fof(f4692,plain,
spl0_391,
inference(avatar_split_clause,[],[f251,f4690]) ).
fof(f4690,plain,
( spl0_391
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f251,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).
fof(f4688,plain,
( ~ spl0_390
| spl0_384
| ~ spl0_181
| ~ spl0_365 ),
inference(avatar_split_clause,[],[f4500,f4166,f2550,f4507,f4685]) ).
fof(f4685,plain,
( spl0_390
<=> class_OrderedGroup_Ogroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f4507,plain,
( spl0_384
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f2550,plain,
( spl0_181
<=> ! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f4166,plain,
( spl0_365
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X4 = X6
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Ominus__class_Ominus(X4,X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f4500,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_OrderedGroup_Ogroup__add(tc_nat) )
| ~ spl0_181
| ~ spl0_365 ),
inference(trivial_inequality_removal,[],[f4497]) ).
fof(f4497,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_181
| ~ spl0_365 ),
inference(superposition,[],[f4167,f2551]) ).
fof(f2551,plain,
( ! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ spl0_181 ),
inference(avatar_component_clause,[],[f2550]) ).
fof(f4167,plain,
( ! [X3,X6,X4] :
( c_HOL_Ozero__class_Ozero(X3) != c_HOL_Ominus__class_Ominus(X4,X6,X3)
| X4 = X6
| ~ class_OrderedGroup_Ogroup__add(X3) )
| ~ spl0_365 ),
inference(avatar_component_clause,[],[f4166]) ).
fof(f4683,plain,
spl0_389,
inference(avatar_split_clause,[],[f243,f4681]) ).
fof(f4681,plain,
( spl0_389
<=> ! [X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oone__class_Oone(X3) = c_Divides_Odiv__class_Odiv(X4,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f243,axiom,
! [X3,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oone__class_Oone(X3) = c_Divides_Odiv__class_Odiv(X4,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__self_0) ).
fof(f4679,plain,
spl0_388,
inference(avatar_split_clause,[],[f219,f4677]) ).
fof(f4677,plain,
( spl0_388
<=> ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f219,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).
fof(f4675,plain,
spl0_387,
inference(avatar_split_clause,[],[f218,f4673]) ).
fof(f4673,plain,
( spl0_387
<=> ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f218,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).
fof(f4671,plain,
spl0_386,
inference(avatar_split_clause,[],[f198,f4669]) ).
fof(f4669,plain,
( spl0_386
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f198,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__zero__iff_0) ).
fof(f4667,plain,
spl0_385,
inference(avatar_split_clause,[],[f189,f4665]) ).
fof(f4665,plain,
( spl0_385
<=> ! [X9,X17,X3] :
( ~ class_Orderings_Oorder(X3)
| X9 = X17
| ~ c_lessequals(X17,X9,X3)
| ~ c_lessequals(X9,X17,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f189,axiom,
! [X3,X9,X17] :
( ~ class_Orderings_Oorder(X3)
| X9 = X17
| ~ c_lessequals(X17,X9,X3)
| ~ c_lessequals(X9,X17,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
fof(f4509,plain,
( ~ spl0_383
| spl0_384
| ~ spl0_181
| ~ spl0_364 ),
inference(avatar_split_clause,[],[f4492,f4155,f2550,f4507,f4503]) ).
fof(f4503,plain,
( spl0_383
<=> class_OrderedGroup_Oab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f4155,plain,
( spl0_364
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| X4 = X6
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Ominus__class_Ominus(X4,X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f4492,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_181
| ~ spl0_364 ),
inference(trivial_inequality_removal,[],[f4489]) ).
fof(f4489,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_181
| ~ spl0_364 ),
inference(superposition,[],[f4156,f2551]) ).
fof(f4156,plain,
( ! [X3,X6,X4] :
( c_HOL_Ozero__class_Ozero(X3) != c_HOL_Ominus__class_Ominus(X4,X6,X3)
| X4 = X6
| ~ class_OrderedGroup_Oab__group__add(X3) )
| ~ spl0_364 ),
inference(avatar_component_clause,[],[f4155]) ).
fof(f4463,plain,
( spl0_382
| ~ spl0_141
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f3774,f3507,f2380,f4460]) ).
fof(f4460,plain,
( spl0_382
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f3774,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat)
| ~ spl0_141
| ~ spl0_294 ),
inference(resolution,[],[f3508,f2382]) ).
fof(f4285,plain,
( spl0_381
| ~ spl0_217
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4205,f4114,f2724,f4282]) ).
fof(f4282,plain,
( spl0_381
<=> c_HOL_Oord__class_Oless(c_Int_OPls,c_Int_OBit1(c_Int_OPls),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f2724,plain,
( spl0_217
<=> ! [X0] :
( c_HOL_Oord__class_Oless(c_Int_OPls,X0,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_OPls,c_Int_OBit0(X0),tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f4114,plain,
( spl0_354
<=> c_HOL_Oord__class_Oless(c_Int_OPls,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f4205,plain,
( c_HOL_Oord__class_Oless(c_Int_OPls,c_Int_OBit1(c_Int_OPls),tc_Int_Oint)
| ~ spl0_217
| ~ spl0_354 ),
inference(resolution,[],[f4116,f2725]) ).
fof(f2725,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Int_OPls,c_Int_OBit0(X0),tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_OPls,X0,tc_Int_Oint) )
| ~ spl0_217 ),
inference(avatar_component_clause,[],[f2724]) ).
fof(f4116,plain,
( c_HOL_Oord__class_Oless(c_Int_OPls,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_Int_Oint)
| ~ spl0_354 ),
inference(avatar_component_clause,[],[f4114]) ).
fof(f4237,plain,
spl0_380,
inference(avatar_split_clause,[],[f1583,f4234]) ).
fof(f4234,plain,
( spl0_380
<=> c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) = hAPP(c_Suc,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f4232,plain,
spl0_379,
inference(avatar_split_clause,[],[f1582,f4230]) ).
fof(f4230,plain,
( spl0_379
<=> ! [X9] : c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X9),c_HOL_Ozero__class_Ozero(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f1582,plain,
! [X9] : c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X9),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(forward_demodulation,[],[f915,f421]) ).
fof(f915,axiom,
! [X9] : hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X9),c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__power__eq__Suc__0__iff_1) ).
fof(f4228,plain,
spl0_378,
inference(avatar_split_clause,[],[f1441,f4226]) ).
fof(f4226,plain,
( spl0_378
<=> ! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X1),hAPP(c_Suc,X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f1441,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X1),hAPP(c_Suc,X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
fof(f4224,plain,
spl0_377,
inference(avatar_split_clause,[],[f1440,f4222]) ).
fof(f4222,plain,
( spl0_377
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(c_Suc,X1),hAPP(c_Suc,X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f1440,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(c_Suc,X1),hAPP(c_Suc,X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
fof(f4220,plain,
spl0_376,
inference(avatar_split_clause,[],[f1302,f4218]) ).
fof(f4218,plain,
( spl0_376
<=> ! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_HOL_Oone__class_Oone(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Oone__class_Oone(X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f1302,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_HOL_Oone__class_Oone(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_HOL_Oone__class_Oone(X3)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).
fof(f4216,plain,
spl0_375,
inference(avatar_split_clause,[],[f1274,f4214]) ).
fof(f4214,plain,
( spl0_375
<=> ! [X9] : c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X9),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f1274,axiom,
! [X9] : c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),X9),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__mult__two__ex_1) ).
fof(f4204,plain,
spl0_374,
inference(avatar_split_clause,[],[f1195,f4202]) ).
fof(f4202,plain,
( spl0_374
<=> ! [X9,X17] :
( ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X9,X17,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f1195,axiom,
! [X9,X17] :
( ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X9,X17,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__difference__nat_3) ).
fof(f4200,plain,
spl0_373,
inference(avatar_split_clause,[],[f1194,f4198]) ).
fof(f4198,plain,
( spl0_373
<=> ! [X9,X17] :
( c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X9,X17,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f1194,axiom,
! [X9,X17] :
( c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X9,X17,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__difference__nat_4) ).
fof(f4196,plain,
spl0_372,
inference(avatar_split_clause,[],[f1013,f4194]) ).
fof(f4194,plain,
( spl0_372
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(X4,c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f1013,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero_0) ).
fof(f4192,plain,
spl0_371,
inference(avatar_split_clause,[],[f905,f4190]) ).
fof(f4190,plain,
( spl0_371
<=> ! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f905,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
fof(f4188,plain,
spl0_370,
inference(avatar_split_clause,[],[f904,f4186]) ).
fof(f4186,plain,
( spl0_370
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f904,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
fof(f4184,plain,
spl0_369,
inference(avatar_split_clause,[],[f878,f4182]) ).
fof(f4182,plain,
( spl0_369
<=> ! [X34,X35] :
( c_HOL_Oord__class_Oless(X34,X35,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X34,tc_nat),c_Int_Onumber__class_Onumber__of(X35,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f878,axiom,
! [X34,X35] :
( c_HOL_Oord__class_Oless(X34,X35,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X34,tc_nat),c_Int_Onumber__class_Onumber__of(X35,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__nat__number__of_1) ).
fof(f4180,plain,
spl0_368,
inference(avatar_split_clause,[],[f838,f4178]) ).
fof(f4178,plain,
( spl0_368
<=> ! [X2,X1] :
( ~ c_lessequals(X2,X1,tc_nat)
| c_lessequals(hAPP(c_Suc,X2),hAPP(c_Suc,X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f838,axiom,
! [X2,X1] :
( ~ c_lessequals(X2,X1,tc_nat)
| c_lessequals(hAPP(c_Suc,X2),hAPP(c_Suc,X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
fof(f4176,plain,
spl0_367,
inference(avatar_split_clause,[],[f837,f4174]) ).
fof(f4174,plain,
( spl0_367
<=> ! [X2,X1] :
( c_lessequals(X2,X1,tc_nat)
| ~ c_lessequals(hAPP(c_Suc,X2),hAPP(c_Suc,X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f837,axiom,
! [X2,X1] :
( c_lessequals(X2,X1,tc_nat)
| ~ c_lessequals(hAPP(c_Suc,X2),hAPP(c_Suc,X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
fof(f4172,plain,
spl0_366,
inference(avatar_split_clause,[],[f791,f4170]) ).
fof(f4170,plain,
( spl0_366
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oone__class_Oone(X3) = c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f791,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oone__class_Oone(X3) = c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__one_0) ).
fof(f4168,plain,
spl0_365,
inference(avatar_split_clause,[],[f778,f4166]) ).
fof(f778,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X4 = X6
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Ominus__class_Ominus(X4,X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
fof(f4157,plain,
spl0_364,
inference(avatar_split_clause,[],[f777,f4155]) ).
fof(f777,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| X4 = X6
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Ominus__class_Ominus(X4,X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
fof(f4153,plain,
spl0_363,
inference(avatar_split_clause,[],[f726,f4151]) ).
fof(f4151,plain,
( spl0_363
<=> ! [X9,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oone__class_Oone(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f726,axiom,
! [X3,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oone__class_Oone(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X9),c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
fof(f4149,plain,
spl0_362,
inference(avatar_split_clause,[],[f725,f4147]) ).
fof(f4147,plain,
( spl0_362
<=> ! [X4,X3] :
( ~ class_Power_Opower(X3)
| c_HOL_Oone__class_Oone(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f725,axiom,
! [X3,X4] :
( ~ class_Power_Opower(X3)
| c_HOL_Oone__class_Oone(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).
fof(f4145,plain,
spl0_361,
inference(avatar_split_clause,[],[f722,f4143]) ).
fof(f4143,plain,
( spl0_361
<=> ! [X4,X3] :
( ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Int_Onumber__class_Onumber__of(c_Int_OPls,X3)),X4) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f722,axiom,
! [X3,X4] :
( ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Int_Onumber__class_Onumber__of(c_Int_OPls,X3)),X4) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__numeral__0_0) ).
fof(f4141,plain,
spl0_360,
inference(avatar_split_clause,[],[f721,f4139]) ).
fof(f4139,plain,
( spl0_360
<=> ! [X4,X3] :
( ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),c_Int_Onumber__class_Onumber__of(c_Int_OPls,X3)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f721,axiom,
! [X3,X4] :
( ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),c_Int_Onumber__class_Onumber__of(c_Int_OPls,X3)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__numeral__0__right_0) ).
fof(f4137,plain,
spl0_359,
inference(avatar_split_clause,[],[f620,f4135]) ).
fof(f4135,plain,
( spl0_359
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_HOL_Ozero__class_Ozero(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f620,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_HOL_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f4133,plain,
spl0_358,
inference(avatar_split_clause,[],[f618,f4131]) ).
fof(f4131,plain,
( spl0_358
<=> ! [X6,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f618,axiom,
! [X3,X6] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
fof(f4129,plain,
spl0_357,
inference(avatar_split_clause,[],[f617,f4127]) ).
fof(f4127,plain,
( spl0_357
<=> ! [X4,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_HOL_Ozero__class_Ozero(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f617,axiom,
! [X3,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_HOL_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).
fof(f4125,plain,
spl0_356,
inference(avatar_split_clause,[],[f615,f4123]) ).
fof(f4123,plain,
( spl0_356
<=> ! [X9,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f615,axiom,
! [X3,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
fof(f4121,plain,
spl0_355,
inference(avatar_split_clause,[],[f614,f4119]) ).
fof(f4119,plain,
( spl0_355
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f614,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
fof(f4117,plain,
( spl0_354
| ~ spl0_223
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3793,f3540,f2748,f4114]) ).
fof(f2748,plain,
( spl0_223
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f3540,plain,
( spl0_302
<=> ! [X34] :
( c_HOL_Oord__class_Oless(c_Int_OPls,X34,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f3793,plain,
( c_HOL_Oord__class_Oless(c_Int_OPls,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_Int_Oint)
| ~ spl0_223
| ~ spl0_302 ),
inference(resolution,[],[f3541,f2750]) ).
fof(f2750,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
| ~ spl0_223 ),
inference(avatar_component_clause,[],[f2748]) ).
fof(f3541,plain,
( ! [X34] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_Int_OPls,X34,tc_Int_Oint) )
| ~ spl0_302 ),
inference(avatar_component_clause,[],[f3540]) ).
fof(f4112,plain,
spl0_353,
inference(avatar_split_clause,[],[f613,f4110]) ).
fof(f4110,plain,
( spl0_353
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_HOL_Ozero__class_Ozero(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f613,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_HOL_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
fof(f4108,plain,
spl0_352,
inference(avatar_split_clause,[],[f612,f4106]) ).
fof(f4106,plain,
( spl0_352
<=> ! [X6,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f612,axiom,
! [X3,X6] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
fof(f4104,plain,
spl0_351,
inference(avatar_split_clause,[],[f611,f4102]) ).
fof(f4102,plain,
( spl0_351
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_HOL_Ozero__class_Ozero(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f611,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Ozero__class_Ozero(X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_HOL_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
fof(f4100,plain,
spl0_350,
inference(avatar_split_clause,[],[f564,f4098]) ).
fof(f4098,plain,
( spl0_350
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X3),X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f564,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X4,X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X3),X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_0) ).
fof(f4096,plain,
spl0_349,
inference(avatar_split_clause,[],[f541,f4094]) ).
fof(f4094,plain,
( spl0_349
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),c_HOL_Oone__class_Oone(X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f541,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),c_HOL_Oone__class_Oone(X3)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).
fof(f4092,plain,
spl0_348,
inference(avatar_split_clause,[],[f529,f4090]) ).
fof(f4090,plain,
( spl0_348
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X4),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f529,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X4),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
fof(f4088,plain,
spl0_347,
inference(avatar_split_clause,[],[f458,f4086]) ).
fof(f4086,plain,
( spl0_347
<=> ! [X9,X7] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X7),X9),X7,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f458,axiom,
! [X9,X7] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X7),X9),X7,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__eq__0__iff_1) ).
fof(f4084,plain,
spl0_346,
inference(avatar_split_clause,[],[f451,f4082]) ).
fof(f451,axiom,
! [X0,X16,X14] :
( ~ c_lessequals(X16,X14,tc_nat)
| ~ c_lessequals(X14,X0,tc_nat)
| c_lessequals(X16,X0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).
fof(f4079,plain,
spl0_345,
inference(avatar_split_clause,[],[f447,f4077]) ).
fof(f4077,plain,
( spl0_345
<=> ! [X2,X15] :
( hBOOL(hAPP(X15,X2))
| ~ hBOOL(hAPP(X15,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f447,axiom,
! [X2,X15] :
( hBOOL(hAPP(X15,X2))
| ~ hBOOL(hAPP(X15,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mod_0) ).
fof(f4074,plain,
spl0_344,
inference(avatar_split_clause,[],[f446,f4072]) ).
fof(f4072,plain,
( spl0_344
<=> ! [X2,X15] :
( ~ hBOOL(hAPP(X15,X2))
| hBOOL(hAPP(X15,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f446,axiom,
! [X2,X15] :
( ~ hBOOL(hAPP(X15,X2))
| hBOOL(hAPP(X15,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mod_5) ).
fof(f4063,plain,
spl0_343,
inference(avatar_split_clause,[],[f444,f4061]) ).
fof(f4061,plain,
( spl0_343
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oabs__class_Oabs(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f444,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oabs__class_Oabs(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
fof(f4059,plain,
spl0_342,
inference(avatar_split_clause,[],[f412,f4057]) ).
fof(f4057,plain,
( spl0_342
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f412,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__pos_0) ).
fof(f4055,plain,
spl0_341,
inference(avatar_split_clause,[],[f390,f4053]) ).
fof(f4053,plain,
( spl0_341
<=> ! [X2,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f390,axiom,
! [X2,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
fof(f4051,plain,
spl0_340,
inference(avatar_split_clause,[],[f346,f4049]) ).
fof(f4049,plain,
( spl0_340
<=> ! [X2,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_Fact_Ofact__class_Ofact(X1,tc_nat),c_Fact_Ofact__class_Ofact(X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f346,axiom,
! [X2,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_Fact_Ofact__class_Ofact(X1,tc_nat),c_Fact_Ofact__class_Ofact(X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fact__mono__nat_0) ).
fof(f4047,plain,
spl0_339,
inference(avatar_split_clause,[],[f345,f4045]) ).
fof(f4045,plain,
( spl0_339
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(X4,X6,X3)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f345,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(X4,X6,X3)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__D1_0) ).
fof(f4043,plain,
spl0_338,
inference(avatar_split_clause,[],[f340,f4041]) ).
fof(f4041,plain,
( spl0_338
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oabs__if(X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = X4
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f340,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oabs__if(X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = X4
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if_1) ).
fof(f4039,plain,
spl0_337,
inference(avatar_split_clause,[],[f280,f4037]) ).
fof(f4037,plain,
( spl0_337
<=> ! [X6,X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X4,X6,X3),X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f280,axiom,
! [X3,X6,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X4,X6,X3),X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__trivial_0) ).
fof(f4035,plain,
spl0_336,
inference(avatar_split_clause,[],[f231,f4033]) ).
fof(f4033,plain,
( spl0_336
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f231,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__le__divisor_0) ).
fof(f4031,plain,
spl0_335,
inference(avatar_split_clause,[],[f228,f4029]) ).
fof(f4029,plain,
( spl0_335
<=> ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f228,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
fof(f4027,plain,
spl0_334,
inference(avatar_split_clause,[],[f199,f4025]) ).
fof(f4025,plain,
( spl0_334
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Ouminus__class_Ouminus(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f199,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Ouminus__class_Ouminus(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
fof(f4023,plain,
( spl0_333
| ~ spl0_134
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3447,f3058,f2348,f4021]) ).
fof(f2348,plain,
( spl0_134
<=> ! [X9] : ~ c_HOL_Oord__class_Oless(X9,X9,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f3447,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X0),X0,tc_nat)
| ~ spl0_134
| ~ spl0_279 ),
inference(resolution,[],[f3059,f2349]) ).
fof(f2349,plain,
( ! [X9] : ~ c_HOL_Oord__class_Oless(X9,X9,tc_nat)
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f2348]) ).
fof(f4019,plain,
spl0_332,
inference(avatar_split_clause,[],[f195,f4017]) ).
fof(f4017,plain,
( spl0_332
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X4 = X6
| c_HOL_Ouminus__class_Ouminus(X4,X3) != c_HOL_Ouminus__class_Ouminus(X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f195,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X4 = X6
| c_HOL_Ouminus__class_Ouminus(X4,X3) != c_HOL_Ouminus__class_Ouminus(X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
fof(f4015,plain,
spl0_331,
inference(avatar_split_clause,[],[f194,f4013]) ).
fof(f4013,plain,
( spl0_331
<=> ! [X9,X17,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| X9 = X17
| c_HOL_Ouminus__class_Ouminus(X17,X3) != c_HOL_Ouminus__class_Ouminus(X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f194,axiom,
! [X3,X9,X17] :
( ~ class_Lattices_Oboolean__algebra(X3)
| X9 = X17
| c_HOL_Ouminus__class_Ouminus(X17,X3) != c_HOL_Ouminus__class_Ouminus(X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
fof(f4011,plain,
spl0_330,
inference(avatar_split_clause,[],[f188,f4009]) ).
fof(f188,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__nonneg_0) ).
fof(f4007,plain,
spl0_329,
inference(avatar_split_clause,[],[f128,f4005]) ).
fof(f4005,plain,
( spl0_329
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f128,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).
fof(f4003,plain,
spl0_328,
inference(avatar_split_clause,[],[f25,f4001]) ).
fof(f4001,plain,
( spl0_328
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f25,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),X4),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
fof(f3852,plain,
( ~ spl0_83
| ~ spl0_327
| ~ spl0_125
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f3135,f2922,f2307,f3849,f2097]) ).
fof(f3849,plain,
( spl0_327
<=> c_lessequals(c_Int_OPls,c_Int_OMin,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f2307,plain,
( spl0_125
<=> c_HOL_Oord__class_Oless(c_Int_OMin,c_Int_OPls,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f3135,plain,
( ~ c_lessequals(c_Int_OPls,c_Int_OMin,tc_Int_Oint)
| ~ class_Orderings_Opreorder(tc_Int_Oint)
| ~ spl0_125
| ~ spl0_245 ),
inference(resolution,[],[f2923,f2309]) ).
fof(f2309,plain,
( c_HOL_Oord__class_Oless(c_Int_OMin,c_Int_OPls,tc_Int_Oint)
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f2307]) ).
fof(f3645,plain,
( spl0_326
| ~ spl0_83
| ~ spl0_125
| ~ spl0_242 ),
inference(avatar_split_clause,[],[f3101,f2910,f2307,f2097,f3642]) ).
fof(f3642,plain,
( spl0_326
<=> c_lessequals(c_Int_OMin,c_Int_OPls,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f2910,plain,
( spl0_242
<=> ! [X9,X17,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X9,X17,X3)
| c_lessequals(X9,X17,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f3101,plain,
( ~ class_Orderings_Opreorder(tc_Int_Oint)
| c_lessequals(c_Int_OMin,c_Int_OPls,tc_Int_Oint)
| ~ spl0_125
| ~ spl0_242 ),
inference(resolution,[],[f2911,f2309]) ).
fof(f2911,plain,
( ! [X3,X9,X17] :
( ~ c_HOL_Oord__class_Oless(X9,X17,X3)
| ~ class_Orderings_Opreorder(X3)
| c_lessequals(X9,X17,X3) )
| ~ spl0_242 ),
inference(avatar_component_clause,[],[f2910]) ).
fof(f3640,plain,
spl0_325,
inference(avatar_split_clause,[],[f1625,f3638]) ).
fof(f3638,plain,
( spl0_325
<=> ! [X2] :
( ~ c_HOL_Oord__class_Oless(X2,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f1625,plain,
! [X2] :
( ~ c_HOL_Oord__class_Oless(X2,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2 ),
inference(forward_demodulation,[],[f848,f421]) ).
fof(f848,axiom,
! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| ~ c_HOL_Oord__class_Oless(X2,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
fof(f3636,plain,
spl0_324,
inference(avatar_split_clause,[],[f1581,f3633]) ).
fof(f3633,plain,
( spl0_324
<=> c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Fact_Ofact__class_Ofact(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f1581,plain,
c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Fact_Ofact__class_Ofact(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f202,f421]) ).
fof(f202,axiom,
hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Fact_Ofact__class_Ofact(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fact__Suc__0__nat_0) ).
fof(f3631,plain,
spl0_323,
inference(avatar_split_clause,[],[f1406,f3629]) ).
fof(f3629,plain,
( spl0_323
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_HOL_Oone__class_Oone(X3)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f1406,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_HOL_Oone__class_Oone(X3)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
fof(f3627,plain,
spl0_322,
inference(avatar_split_clause,[],[f1405,f3625]) ).
fof(f3625,plain,
( spl0_322
<=> ! [X9,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oone__class_Oone(X3)),X9) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f1405,axiom,
! [X3,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oone__class_Oone(X3)),X9) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
fof(f3623,plain,
spl0_321,
inference(avatar_split_clause,[],[f1404,f3621]) ).
fof(f3621,plain,
( spl0_321
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oone__class_Oone(X3)),X4) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f1404,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oone__class_Oone(X3)),X4) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).
fof(f3619,plain,
spl0_320,
inference(avatar_split_clause,[],[f1403,f3617]) ).
fof(f3617,plain,
( spl0_320
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oone__class_Oone(X3)),X4) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f1403,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Oone__class_Oone(X3)),X4) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
fof(f3615,plain,
spl0_319,
inference(avatar_split_clause,[],[f1402,f3613]) ).
fof(f3613,plain,
( spl0_319
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_HOL_Oone__class_Oone(X3)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f1402,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X4),c_HOL_Oone__class_Oone(X3)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
fof(f3611,plain,
spl0_318,
inference(avatar_split_clause,[],[f1387,f3609]) ).
fof(f3609,plain,
( spl0_318
<=> ! [X9,X17] :
( X9 = X17
| c_HOL_Oord__class_Oless(X9,X17,tc_nat)
| c_HOL_Oord__class_Oless(X17,X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f1387,axiom,
! [X9,X17] :
( X9 = X17
| c_HOL_Oord__class_Oless(X9,X17,tc_nat)
| c_HOL_Oord__class_Oless(X17,X9,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
fof(f3607,plain,
spl0_317,
inference(avatar_split_clause,[],[f1322,f3605]) ).
fof(f3605,plain,
( spl0_317
<=> ! [X2,X0,X14] :
( ~ c_HOL_Oord__class_Oless(X14,X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X14,X2,tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f1322,axiom,
! [X2,X0,X14] :
( ~ c_HOL_Oord__class_Oless(X14,X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X14,X2,tc_nat),X0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
fof(f3603,plain,
( spl0_316
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f3091,f2906,f3601]) ).
fof(f3601,plain,
( spl0_316
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f3091,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_241 ),
inference(factoring,[],[f2907]) ).
fof(f3599,plain,
( spl0_315
| ~ spl0_121
| ~ spl0_249
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f3594,f3590,f2938,f2287,f3596]) ).
fof(f3596,plain,
( spl0_315
<=> hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f3590,plain,
( spl0_314
<=> hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f3594,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Complex_Ocomplex)
| ~ spl0_121
| ~ spl0_249
| ~ spl0_314 ),
inference(forward_demodulation,[],[f3592,f3192]) ).
fof(f3592,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_314 ),
inference(avatar_component_clause,[],[f3590]) ).
fof(f3593,plain,
spl0_314,
inference(avatar_split_clause,[],[f1204,f3590]) ).
fof(f1204,axiom,
hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_i__mult__eq2_0) ).
fof(f3588,plain,
spl0_313,
inference(avatar_split_clause,[],[f1203,f3586]) ).
fof(f3586,plain,
( spl0_313
<=> ! [X9,X17] :
( c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X9),X17),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f1203,axiom,
! [X9,X17] :
( c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X9),X17),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__power__nat_0) ).
fof(f3584,plain,
spl0_312,
inference(avatar_split_clause,[],[f1199,f3582]) ).
fof(f3582,plain,
( spl0_312
<=> ! [X2,X1] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f1199,axiom,
! [X2,X1] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
fof(f3580,plain,
spl0_311,
inference(avatar_split_clause,[],[f1198,f3578]) ).
fof(f3578,plain,
( spl0_311
<=> ! [X2,X1] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),X2,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f1198,axiom,
! [X2,X1] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),X2,tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
fof(f3576,plain,
spl0_310,
inference(avatar_split_clause,[],[f1147,f3574]) ).
fof(f3574,plain,
( spl0_310
<=> ! [X9,X17] :
( ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X9),X17),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f1147,axiom,
! [X9,X17] :
( ~ c_Parity_Oeven__odd__class_Oeven(X17,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X9),X17),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__product__nat_2) ).
fof(f3572,plain,
spl0_309,
inference(avatar_split_clause,[],[f1146,f3570]) ).
fof(f3570,plain,
( spl0_309
<=> ! [X9,X17] :
( ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X9),X17),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f1146,axiom,
! [X9,X17] :
( ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X9),X17),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__product__nat_1) ).
fof(f3568,plain,
spl0_308,
inference(avatar_split_clause,[],[f985,f3566]) ).
fof(f3566,plain,
( spl0_308
<=> ! [X2,X1] :
( X1 = X2
| ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f985,axiom,
! [X2,X1] :
( X1 = X2
| ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).
fof(f3563,plain,
spl0_307,
inference(avatar_split_clause,[],[f922,f3561]) ).
fof(f3561,plain,
( spl0_307
<=> ! [X9] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X9),c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f922,axiom,
! [X9] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X9),c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__nat__eq_1) ).
fof(f3558,plain,
spl0_306,
inference(avatar_split_clause,[],[f850,f3556]) ).
fof(f3556,plain,
( spl0_306
<=> ! [X16,X1] : c_HOL_Oord__class_Oless(X16,hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X16)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f850,axiom,
! [X1,X16] : c_HOL_Oord__class_Oless(X16,hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X16)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
fof(f3554,plain,
spl0_305,
inference(avatar_split_clause,[],[f849,f3552]) ).
fof(f3552,plain,
( spl0_305
<=> ! [X9,X1] : c_HOL_Oord__class_Oless(X1,hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X9)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f849,axiom,
! [X1,X9] : c_HOL_Oord__class_Oless(X1,hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X9)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
fof(f3550,plain,
spl0_304,
inference(avatar_split_clause,[],[f775,f3548]) ).
fof(f3548,plain,
( spl0_304
<=> ! [X9,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ominus__class_Ominus(X9,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f775,axiom,
! [X3,X9] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ominus__class_Ominus(X9,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
fof(f3546,plain,
spl0_303,
inference(avatar_split_clause,[],[f489,f3544]) ).
fof(f3544,plain,
( spl0_303
<=> ! [X34] :
( ~ c_HOL_Oord__class_Oless(c_Int_OPls,X34,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f489,axiom,
! [X34] :
( ~ c_HOL_Oord__class_Oless(c_Int_OPls,X34,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__0__number__of_1) ).
fof(f3542,plain,
spl0_302,
inference(avatar_split_clause,[],[f488,f3540]) ).
fof(f488,axiom,
! [X34] :
( c_HOL_Oord__class_Oless(c_Int_OPls,X34,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(X34,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__0__number__of_0) ).
fof(f3538,plain,
spl0_301,
inference(avatar_split_clause,[],[f437,f3536]) ).
fof(f3536,plain,
( spl0_301
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),c_HOL_Ozero__class_Ozero(X3)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f437,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),c_HOL_Ozero__class_Ozero(X3)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f3534,plain,
spl0_300,
inference(avatar_split_clause,[],[f433,f3532]) ).
fof(f3532,plain,
( spl0_300
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X4) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f433,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X4) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f3530,plain,
spl0_299,
inference(avatar_split_clause,[],[f432,f3528]) ).
fof(f3528,plain,
( spl0_299
<=> ! [X9,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X9) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f432,axiom,
! [X3,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X9) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
fof(f3526,plain,
spl0_298,
inference(avatar_split_clause,[],[f430,f3524]) ).
fof(f3524,plain,
( spl0_298
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),c_HOL_Ozero__class_Ozero(X3)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f430,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),c_HOL_Ozero__class_Ozero(X3)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f3522,plain,
spl0_297,
inference(avatar_split_clause,[],[f429,f3520]) ).
fof(f3520,plain,
( spl0_297
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X4) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f429,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X4) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f3518,plain,
( ~ spl0_30
| ~ spl0_296
| ~ spl0_141
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f3366,f3030,f2380,f3515,f1832]) ).
fof(f3515,plain,
( spl0_296
<=> c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),v_i____,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f3366,plain,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),v_i____,tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| ~ spl0_141
| ~ spl0_272 ),
inference(resolution,[],[f3031,f2382]) ).
fof(f3513,plain,
spl0_295,
inference(avatar_split_clause,[],[f428,f3511]) ).
fof(f3511,plain,
( spl0_295
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),c_HOL_Ozero__class_Ozero(X3)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f428,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),c_HOL_Ozero__class_Ozero(X3)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f3509,plain,
spl0_294,
inference(avatar_split_clause,[],[f418,f3507]) ).
fof(f418,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__less_0) ).
fof(f3505,plain,
spl0_293,
inference(avatar_split_clause,[],[f260,f3503]) ).
fof(f3503,plain,
( spl0_293
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f260,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
fof(f3501,plain,
spl0_292,
inference(avatar_split_clause,[],[f248,f3499]) ).
fof(f3499,plain,
( spl0_292
<=> ! [X2,X1] :
( c_lessequals(X1,X2,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f248,axiom,
! [X2,X1] :
( c_lessequals(X1,X2,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).
fof(f3497,plain,
spl0_291,
inference(avatar_split_clause,[],[f247,f3495]) ).
fof(f247,axiom,
! [X2,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).
fof(f3493,plain,
spl0_290,
inference(avatar_split_clause,[],[f237,f3491]) ).
fof(f237,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X4,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__le__zero_0) ).
fof(f3489,plain,
spl0_289,
inference(avatar_split_clause,[],[f191,f3487]) ).
fof(f3487,plain,
( spl0_289
<=> ! [X9,X17] :
( X9 = X17
| c_HOL_Oord__class_Oless(X17,X9,tc_Int_Oint)
| c_HOL_Oord__class_Oless(X9,X17,tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f191,axiom,
! [X9,X17] :
( X9 = X17
| c_HOL_Oord__class_Oless(X17,X9,tc_Int_Oint)
| c_HOL_Oord__class_Oless(X9,X17,tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zless__linear_0) ).
fof(f3485,plain,
spl0_288,
inference(avatar_split_clause,[],[f190,f3483]) ).
fof(f3483,plain,
( spl0_288
<=> ! [X2,X1] :
( X1 = X2
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f190,axiom,
! [X2,X1] :
( X1 = X2
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).
fof(f3481,plain,
spl0_287,
inference(avatar_split_clause,[],[f104,f3479]) ).
fof(f3479,plain,
( spl0_287
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f104,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).
fof(f3477,plain,
spl0_286,
inference(avatar_split_clause,[],[f60,f3475]) ).
fof(f3475,plain,
( spl0_286
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X4,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f60,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X4,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
fof(f3472,plain,
spl0_285,
inference(avatar_split_clause,[],[f8,f3470]) ).
fof(f3470,plain,
( spl0_285
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ouminus__class_Ouminus(X4,X3) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f8,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ouminus__class_Ouminus(X4,X3) != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
fof(f3344,plain,
( spl0_284
| ~ spl0_141
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f3318,f2994,f2380,f3341]) ).
fof(f3341,plain,
( spl0_284
<=> v_i____ = c_Divides_Odiv__class_Omod(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f3318,plain,
( v_i____ = c_Divides_Odiv__class_Omod(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat)
| ~ spl0_141
| ~ spl0_263 ),
inference(resolution,[],[f2995,f2382]) ).
fof(f3197,plain,
( ~ spl0_30
| ~ spl0_283
| ~ spl0_141
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f3142,f2922,f2380,f3194,f1832]) ).
fof(f3194,plain,
( spl0_283
<=> c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),v_i____,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f3142,plain,
( ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),v_i____,tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| ~ spl0_141
| ~ spl0_245 ),
inference(resolution,[],[f2923,f2382]) ).
fof(f3080,plain,
( spl0_282
| ~ spl0_77
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2811,f2634,f2067,f3077]) ).
fof(f3077,plain,
( spl0_282
<=> c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f2067,plain,
( spl0_77
<=> class_OrderedGroup_Ogroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f2634,plain,
( spl0_195
<=> ! [X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f2811,plain,
( c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| ~ spl0_77
| ~ spl0_195 ),
inference(resolution,[],[f2635,f2069]) ).
fof(f2069,plain,
( class_OrderedGroup_Ogroup__add(tc_Int_Oint)
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f2067]) ).
fof(f2635,plain,
( ! [X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) )
| ~ spl0_195 ),
inference(avatar_component_clause,[],[f2634]) ).
fof(f3068,plain,
spl0_281,
inference(avatar_split_clause,[],[f1580,f3066]) ).
fof(f3066,plain,
( spl0_281
<=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X1,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f1580,plain,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X1,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f299,f421]) ).
fof(f299,axiom,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X1,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__1_0) ).
fof(f3064,plain,
spl0_280,
inference(avatar_split_clause,[],[f1391,f3062]) ).
fof(f3062,plain,
( spl0_280
<=> ! [X2] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f1391,axiom,
! [X2] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__unity_0) ).
fof(f3060,plain,
spl0_279,
inference(avatar_split_clause,[],[f1369,f3058]) ).
fof(f1369,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,hAPP(c_Suc,X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).
fof(f3056,plain,
spl0_278,
inference(avatar_split_clause,[],[f1368,f3054]) ).
fof(f1368,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X1),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
fof(f3052,plain,
spl0_277,
inference(avatar_split_clause,[],[f1349,f3050]) ).
fof(f1349,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,hAPP(c_Suc,X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
fof(f3048,plain,
( spl0_276
| ~ spl0_80
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f2810,f2618,f2082,f3046]) ).
fof(f3046,plain,
( spl0_276
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(X0,X0,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f2082,plain,
( spl0_80
<=> class_Divides_Osemiring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f2618,plain,
( spl0_191
<=> ! [X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(X4,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f2810,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(X0,X0,tc_Int_Oint)
| ~ spl0_80
| ~ spl0_191 ),
inference(resolution,[],[f2619,f2084]) ).
fof(f2084,plain,
( class_Divides_Osemiring__div(tc_Int_Oint)
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f2082]) ).
fof(f2619,plain,
( ! [X3,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(X4,X4,X3) )
| ~ spl0_191 ),
inference(avatar_component_clause,[],[f2618]) ).
fof(f3044,plain,
spl0_275,
inference(avatar_split_clause,[],[f1348,f3042]) ).
fof(f3042,plain,
( spl0_275
<=> ! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,hAPP(c_Suc,X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f1348,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,hAPP(c_Suc,X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
fof(f3040,plain,
spl0_274,
inference(avatar_split_clause,[],[f1342,f3038]) ).
fof(f3038,plain,
( spl0_274
<=> ! [X6,X4,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X6,X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f1342,axiom,
! [X3,X6,X4] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X6,X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f3036,plain,
spl0_273,
inference(avatar_split_clause,[],[f1341,f3034]) ).
fof(f3034,plain,
( spl0_273
<=> ! [X9,X17,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X17,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X17,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f1341,axiom,
! [X3,X9,X17] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X17,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X17,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f3032,plain,
spl0_272,
inference(avatar_split_clause,[],[f1339,f3030]) ).
fof(f1339,axiom,
! [X3,X9,X17] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X9,X17,X3)
| ~ c_HOL_Oord__class_Oless(X17,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
fof(f3028,plain,
spl0_271,
inference(avatar_split_clause,[],[f1315,f3026]) ).
fof(f3026,plain,
( spl0_271
<=> ! [X45,X42] :
( X42 = X45
| hAPP(c_Suc,X42) != hAPP(c_Suc,X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f1315,axiom,
! [X45,X42] :
( X42 = X45
| hAPP(c_Suc,X42) != hAPP(c_Suc,X45) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
fof(f3024,plain,
spl0_270,
inference(avatar_split_clause,[],[f1040,f3022]) ).
fof(f1040,axiom,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_2) ).
fof(f3020,plain,
spl0_269,
inference(avatar_split_clause,[],[f1039,f3018]) ).
fof(f3018,plain,
( spl0_269
<=> ! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f1039,axiom,
! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_1) ).
fof(f3016,plain,
spl0_268,
inference(avatar_split_clause,[],[f1014,f3014]) ).
fof(f3014,plain,
( spl0_268
<=> ! [X17,X3] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X3),X17,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f1014,axiom,
! [X3,X17] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X3),X17,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
fof(f3012,plain,
spl0_267,
inference(avatar_split_clause,[],[f1011,f3010]) ).
fof(f3010,plain,
( spl0_267
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f1011,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
fof(f3008,plain,
spl0_266,
inference(avatar_split_clause,[],[f997,f3006]) ).
fof(f3006,plain,
( spl0_266
<=> ! [X0,X26] :
( c_HOL_Oord__class_Oless(X0,X26,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_OBit0(X0),c_Int_OBit0(X26),tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f997,axiom,
! [X0,X26] :
( c_HOL_Oord__class_Oless(X0,X26,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_OBit0(X0),c_Int_OBit0(X26),tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I14_J_0) ).
fof(f3004,plain,
( spl0_265
| ~ spl0_29
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f2809,f2618,f1827,f3002]) ).
fof(f3002,plain,
( spl0_265
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f1827,plain,
( spl0_29
<=> class_Divides_Osemiring__div(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f2809,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat)
| ~ spl0_29
| ~ spl0_191 ),
inference(resolution,[],[f2619,f1829]) ).
fof(f1829,plain,
( class_Divides_Osemiring__div(tc_nat)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f1827]) ).
fof(f3000,plain,
spl0_264,
inference(avatar_split_clause,[],[f994,f2998]) ).
fof(f2998,plain,
( spl0_264
<=> ! [X41,X40] :
( ~ c_HOL_Oord__class_Oless(X40,X41,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_OBit0(X40),c_Int_OBit0(X41),tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f994,axiom,
! [X40,X41] :
( ~ c_HOL_Oord__class_Oless(X40,X41,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_OBit0(X40),c_Int_OBit0(X41),tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__int__code_I13_J_1) ).
fof(f2996,plain,
spl0_263,
inference(avatar_split_clause,[],[f986,f2994]) ).
fof(f986,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_0) ).
fof(f2992,plain,
spl0_262,
inference(avatar_split_clause,[],[f958,f2990]) ).
fof(f2990,plain,
( spl0_262
<=> ! [X2,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(hAPP(c_Suc,X2),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f958,axiom,
! [X2,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(hAPP(c_Suc,X2),X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
fof(f2988,plain,
spl0_261,
inference(avatar_split_clause,[],[f957,f2986]) ).
fof(f2986,plain,
( spl0_261
<=> ! [X2,X1] :
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(hAPP(c_Suc,X2),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f957,axiom,
! [X2,X1] :
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(hAPP(c_Suc,X2),X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
fof(f2984,plain,
spl0_260,
inference(avatar_split_clause,[],[f901,f2982]) ).
fof(f2982,plain,
( spl0_260
<=> ! [X9,X17] :
( ~ c_HOL_Oord__class_Oless(X9,X17,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X9,X17,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f901,axiom,
! [X9,X17] :
( ~ c_HOL_Oord__class_Oless(X9,X17,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X9,X17,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__difference__nat_2) ).
fof(f2980,plain,
spl0_259,
inference(avatar_split_clause,[],[f857,f2978]) ).
fof(f857,axiom,
! [X2,X1] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(c_Suc,X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
fof(f2976,plain,
spl0_258,
inference(avatar_split_clause,[],[f856,f2974]) ).
fof(f2974,plain,
( spl0_258
<=> ! [X2,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,hAPP(c_Suc,X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f856,axiom,
! [X2,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,hAPP(c_Suc,X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
fof(f2972,plain,
spl0_257,
inference(avatar_split_clause,[],[f853,f2970]) ).
fof(f2970,plain,
( spl0_257
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_lessequals(hAPP(c_Suc,X2),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f853,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_lessequals(hAPP(c_Suc,X2),X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).
fof(f2968,plain,
spl0_256,
inference(avatar_split_clause,[],[f852,f2966]) ).
fof(f2966,plain,
( spl0_256
<=> ! [X2,X1] :
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_lessequals(hAPP(c_Suc,X2),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f852,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_lessequals(hAPP(c_Suc,X2),X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
fof(f2964,plain,
spl0_255,
inference(avatar_split_clause,[],[f843,f2962]) ).
fof(f2962,plain,
( spl0_255
<=> ! [X41,X40] :
( c_HOL_Oord__class_Oless(X40,X41,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_OBit1(X40),c_Int_OBit0(X41),tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f843,axiom,
! [X40,X41] :
( c_HOL_Oord__class_Oless(X40,X41,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_OBit1(X40),c_Int_OBit0(X41),tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__int__code_I15_J_0) ).
fof(f2960,plain,
( spl0_254
| ~ spl0_80
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f2808,f2614,f2082,f2958]) ).
fof(f2958,plain,
( spl0_254
<=> ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f2614,plain,
( spl0_190
<=> ! [X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,c_HOL_Ozero__class_Ozero(X3),X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f2808,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X0
| ~ spl0_80
| ~ spl0_190 ),
inference(resolution,[],[f2615,f2084]) ).
fof(f2615,plain,
( ! [X3,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,c_HOL_Ozero__class_Ozero(X3),X3) = X4 )
| ~ spl0_190 ),
inference(avatar_component_clause,[],[f2614]) ).
fof(f2956,plain,
spl0_253,
inference(avatar_split_clause,[],[f842,f2954]) ).
fof(f842,axiom,
! [X2,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,hAPP(c_Suc,X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucI_0) ).
fof(f2952,plain,
spl0_252,
inference(avatar_split_clause,[],[f841,f2950]) ).
fof(f2950,plain,
( spl0_252
<=> ! [X2,X1] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(hAPP(c_Suc,X1),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f841,axiom,
! [X2,X1] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(hAPP(c_Suc,X1),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
fof(f2948,plain,
spl0_251,
inference(avatar_split_clause,[],[f835,f2946]) ).
fof(f2946,plain,
( spl0_251
<=> ! [X0,X26] :
( c_HOL_Oord__class_Oless(X0,X26,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_OBit1(X0),c_Int_OBit1(X26),tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f835,axiom,
! [X0,X26] :
( c_HOL_Oord__class_Oless(X0,X26,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_OBit1(X0),c_Int_OBit1(X26),tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I17_J_0) ).
fof(f2944,plain,
spl0_250,
inference(avatar_split_clause,[],[f834,f2942]) ).
fof(f2942,plain,
( spl0_250
<=> ! [X0,X26] :
( ~ c_HOL_Oord__class_Oless(X0,X26,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_OBit1(X0),c_Int_OBit1(X26),tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f834,axiom,
! [X0,X26] :
( ~ c_HOL_Oord__class_Oless(X0,X26,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_OBit1(X0),c_Int_OBit1(X26),tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I17_J_1) ).
fof(f2940,plain,
spl0_249,
inference(avatar_split_clause,[],[f790,f2938]) ).
fof(f790,axiom,
! [X3] :
( ~ class_Int_Onumber__ring(X3)
| c_Int_Onumber__class_Onumber__of(c_Int_OMin,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_number__of__Min_0) ).
fof(f2936,plain,
spl0_248,
inference(avatar_split_clause,[],[f742,f2934]) ).
fof(f2934,plain,
( spl0_248
<=> ! [X0,X26] :
( ~ c_HOL_Oord__class_Oless(X0,X26,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_OBit1(X0),c_Int_OBit0(X26),tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f742,axiom,
! [X0,X26] :
( ~ c_HOL_Oord__class_Oless(X0,X26,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_OBit1(X0),c_Int_OBit0(X26),tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I16_J_1) ).
fof(f2932,plain,
spl0_247,
inference(avatar_split_clause,[],[f582,f2930]) ).
fof(f2930,plain,
( spl0_247
<=> ! [X9,X17,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X9,X17,X3)
| ~ c_HOL_Oord__class_Oless(X17,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f582,axiom,
! [X3,X9,X17] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X9,X17,X3)
| ~ c_HOL_Oord__class_Oless(X17,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
fof(f2928,plain,
spl0_246,
inference(avatar_split_clause,[],[f580,f2926]) ).
fof(f2926,plain,
( spl0_246
<=> ! [X9,X17,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X17,X9,X3)
| c_HOL_Oord__class_Oless(X9,X17,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f580,axiom,
! [X3,X9,X17] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X17,X9,X3)
| c_HOL_Oord__class_Oless(X9,X17,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
fof(f2924,plain,
spl0_245,
inference(avatar_split_clause,[],[f575,f2922]) ).
fof(f575,axiom,
! [X3,X9,X17] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X17,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X17,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f2920,plain,
spl0_244,
inference(avatar_split_clause,[],[f561,f2918]) ).
fof(f2918,plain,
( spl0_244
<=> ! [X9,X17,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X9,X17,X3)
| c_lessequals(X9,X17,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f561,axiom,
! [X3,X9,X17] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X9,X17,X3)
| c_lessequals(X9,X17,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f2916,plain,
( spl0_243
| ~ spl0_29
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f2807,f2614,f1827,f2914]) ).
fof(f2914,plain,
( spl0_243
<=> ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f2807,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0
| ~ spl0_29
| ~ spl0_190 ),
inference(resolution,[],[f2615,f1829]) ).
fof(f2912,plain,
spl0_242,
inference(avatar_split_clause,[],[f560,f2910]) ).
fof(f560,axiom,
! [X3,X9,X17] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X9,X17,X3)
| c_lessequals(X9,X17,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f2908,plain,
spl0_241,
inference(avatar_split_clause,[],[f476,f2906]) ).
fof(f476,axiom,
! [X3,X9,X17] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X9,X17,X3)
| c_lessequals(X17,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f2904,plain,
spl0_240,
inference(avatar_split_clause,[],[f445,f2902]) ).
fof(f2902,plain,
( spl0_240
<=> ! [X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f445,axiom,
! [X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).
fof(f2900,plain,
spl0_239,
inference(avatar_split_clause,[],[f353,f2898]) ).
fof(f2898,plain,
( spl0_239
<=> ! [X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f353,axiom,
! [X3,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__0_0) ).
fof(f2896,plain,
spl0_238,
inference(avatar_split_clause,[],[f300,f2894]) ).
fof(f2894,plain,
( spl0_238
<=> ! [X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(X4,c_HOL_Oone__class_Oone(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f300,axiom,
! [X3,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(X4,c_HOL_Oone__class_Oone(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__1_0) ).
fof(f2892,plain,
spl0_237,
inference(avatar_split_clause,[],[f285,f2890]) ).
fof(f2890,plain,
( spl0_237
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Oabs__class_Oabs(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f285,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Oabs__class_Oabs(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__minus__self_0) ).
fof(f2888,plain,
spl0_236,
inference(avatar_split_clause,[],[f215,f2886]) ).
fof(f2886,plain,
( spl0_236
<=> ! [X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f215,axiom,
! [X3,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__0_0) ).
fof(f2884,plain,
spl0_235,
inference(avatar_split_clause,[],[f214,f2882]) ).
fof(f2882,plain,
( spl0_235
<=> ! [X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Odiv(X4,c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f214,axiom,
! [X3,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Odiv(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__0_0) ).
fof(f2880,plain,
spl0_234,
inference(avatar_split_clause,[],[f119,f2878]) ).
fof(f2878,plain,
( spl0_234
<=> ! [X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f119,axiom,
! [X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__zero__iff_1) ).
fof(f2857,plain,
( spl0_233
| ~ spl0_158
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f2579,f2546,f2452,f2854]) ).
fof(f2854,plain,
( spl0_233
<=> c_lessequals(c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f2579,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)
| ~ spl0_158
| ~ spl0_180 ),
inference(resolution,[],[f2547,f2454]) ).
fof(f2791,plain,
spl0_232,
inference(avatar_split_clause,[],[f1599,f2788]) ).
fof(f2788,plain,
( spl0_232
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f1599,plain,
c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(forward_demodulation,[],[f1598,f1039]) ).
fof(f1598,plain,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(forward_demodulation,[],[f164,f1039]) ).
fof(f164,axiom,
! [X2,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__div__cancel__disj_0) ).
fof(f2786,plain,
spl0_231,
inference(avatar_split_clause,[],[f1579,f2784]) ).
fof(f2784,plain,
( spl0_231
<=> ! [X2] : c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Fact_Ofact__class_Ofact(X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f1579,plain,
! [X2] : c_lessequals(c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Fact_Ofact__class_Ofact(X2,tc_nat),tc_nat),
inference(forward_demodulation,[],[f417,f421]) ).
fof(f417,axiom,
! [X2] : c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),c_Fact_Ofact__class_Ofact(X2,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fact__ge__Suc__0__nat_0) ).
fof(f2782,plain,
spl0_230,
inference(avatar_split_clause,[],[f1578,f2780]) ).
fof(f2780,plain,
( spl0_230
<=> ! [X1] : c_Divides_Odiv__class_Odiv(X1,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f1578,plain,
! [X1] : c_Divides_Odiv__class_Odiv(X1,c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat) = X1,
inference(forward_demodulation,[],[f9,f421]) ).
fof(f9,axiom,
! [X1] : c_Divides_Odiv__class_Odiv(X1,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__1_0) ).
fof(f2778,plain,
spl0_229,
inference(avatar_split_clause,[],[f1577,f2775]) ).
fof(f2775,plain,
( spl0_229
<=> c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f2773,plain,
spl0_228,
inference(avatar_split_clause,[],[f1345,f2771]) ).
fof(f2771,plain,
( spl0_228
<=> ! [X3] :
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Oone__class_Oone(X3) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f1345,axiom,
! [X3] :
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Oone__class_Oone(X3) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_numeral__1__eq__1_0) ).
fof(f2769,plain,
spl0_227,
inference(avatar_split_clause,[],[f1306,f2767]) ).
fof(f2767,plain,
( spl0_227
<=> ! [X2,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),hAPP(c_Suc,X1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f1306,axiom,
! [X2,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),hAPP(c_Suc,X1),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
fof(f2765,plain,
spl0_226,
inference(avatar_split_clause,[],[f1298,f2763]) ).
fof(f2763,plain,
( spl0_226
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(X4,c_HOL_Oone__class_Oone(X3),X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f1298,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(X4,c_HOL_Oone__class_Oone(X3),X3) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__1_0) ).
fof(f2761,plain,
( spl0_225
| ~ spl0_121
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f2572,f2534,f2287,f2758]) ).
fof(f2758,plain,
( spl0_225
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f2534,plain,
( spl0_177
<=> ! [X3] :
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f2572,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Complex_Ocomplex)
| ~ spl0_121
| ~ spl0_177 ),
inference(resolution,[],[f2535,f2289]) ).
fof(f2535,plain,
( ! [X3] :
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,X3) )
| ~ spl0_177 ),
inference(avatar_component_clause,[],[f2534]) ).
fof(f2756,plain,
spl0_224,
inference(avatar_split_clause,[],[f1277,f2753]) ).
fof(f2753,plain,
( spl0_224
<=> c_Complex_Oii = c_FFT__Mirabelle_Oroot(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f1277,axiom,
c_Complex_Oii = c_FFT__Mirabelle_Oroot(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root4_0) ).
fof(f2751,plain,
spl0_223,
inference(avatar_split_clause,[],[f1271,f2748]) ).
fof(f1271,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos2_0) ).
fof(f2746,plain,
spl0_222,
inference(avatar_split_clause,[],[f1163,f2744]) ).
fof(f2744,plain,
( spl0_222
<=> ! [X1] : c_lessequals(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f1163,axiom,
! [X1] : c_lessequals(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X1),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__square_0) ).
fof(f2742,plain,
spl0_221,
inference(avatar_split_clause,[],[f976,f2740]) ).
fof(f2740,plain,
( spl0_221
<=> ! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f976,axiom,
! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
fof(f2738,plain,
spl0_220,
inference(avatar_split_clause,[],[f974,f2736]) ).
fof(f974,axiom,
! [X16,X14] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X16),X16,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
fof(f2734,plain,
spl0_219,
inference(avatar_split_clause,[],[f973,f2732]) ).
fof(f973,axiom,
! [X16,X14] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X14),X16,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
fof(f2730,plain,
spl0_218,
inference(avatar_split_clause,[],[f864,f2728]) ).
fof(f2728,plain,
( spl0_218
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Int_OPls,X0,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_OPls,c_Int_OBit0(X0),tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f864,axiom,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Int_OPls,X0,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_OPls,c_Int_OBit0(X0),tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I4_J_1) ).
fof(f2726,plain,
spl0_217,
inference(avatar_split_clause,[],[f863,f2724]) ).
fof(f863,axiom,
! [X0] :
( c_HOL_Oord__class_Oless(c_Int_OPls,X0,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_OPls,c_Int_OBit0(X0),tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I4_J_0) ).
fof(f2722,plain,
spl0_216,
inference(avatar_split_clause,[],[f862,f2720]) ).
fof(f2720,plain,
( spl0_216
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_Int_OPls,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_OBit0(X0),c_Int_OPls,tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f862,axiom,
! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_Int_OPls,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_OBit0(X0),c_Int_OPls,tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I10_J_1) ).
fof(f2718,plain,
spl0_215,
inference(avatar_split_clause,[],[f861,f2716]) ).
fof(f2716,plain,
( spl0_215
<=> ! [X0] :
( c_HOL_Oord__class_Oless(X0,c_Int_OPls,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_OBit0(X0),c_Int_OPls,tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f861,axiom,
! [X0] :
( c_HOL_Oord__class_Oless(X0,c_Int_OPls,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_OBit0(X0),c_Int_OPls,tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I10_J_0) ).
fof(f2714,plain,
( spl0_214
| ~ spl0_88
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f2571,f2534,f2122,f2711]) ).
fof(f2711,plain,
( spl0_214
<=> c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f2571,plain,
( c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Int_Oint)
| ~ spl0_88
| ~ spl0_177 ),
inference(resolution,[],[f2535,f2124]) ).
fof(f2709,plain,
spl0_213,
inference(avatar_split_clause,[],[f808,f2707]) ).
fof(f2707,plain,
( spl0_213
<=> ! [X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(X4,c_HOL_Oone__class_Oone(X3),X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f808,axiom,
! [X3,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(X4,c_HOL_Oone__class_Oone(X3),X3) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__1_0) ).
fof(f2705,plain,
spl0_212,
inference(avatar_split_clause,[],[f806,f2703]) ).
fof(f2703,plain,
( spl0_212
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oone__class_Oone(X3) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f806,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oone__class_Oone(X3) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__one_0) ).
fof(f2701,plain,
spl0_211,
inference(avatar_split_clause,[],[f773,f2699]) ).
fof(f2699,plain,
( spl0_211
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X4,c_HOL_Ozero__class_Ozero(X3),X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f773,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X4,c_HOL_Ozero__class_Ozero(X3),X3) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
fof(f2697,plain,
spl0_210,
inference(avatar_split_clause,[],[f772,f2695]) ).
fof(f2695,plain,
( spl0_210
<=> ! [X9,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ominus__class_Ominus(X9,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f772,axiom,
! [X3,X9] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ominus__class_Ominus(X9,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
fof(f2693,plain,
spl0_209,
inference(avatar_split_clause,[],[f771,f2691]) ).
fof(f2691,plain,
( spl0_209
<=> ! [X9,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ominus__class_Ominus(X9,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f771,axiom,
! [X3,X9] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ominus__class_Ominus(X9,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
fof(f2689,plain,
spl0_208,
inference(avatar_split_clause,[],[f739,f2687]) ).
fof(f2687,plain,
( spl0_208
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_Int_OPls,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_OBit1(X0),c_Int_OPls,tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f739,axiom,
! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_Int_OPls,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_OBit1(X0),c_Int_OPls,tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I12_J_1) ).
fof(f2685,plain,
spl0_207,
inference(avatar_split_clause,[],[f738,f2683]) ).
fof(f2683,plain,
( spl0_207
<=> ! [X0] :
( c_HOL_Oord__class_Oless(X0,c_Int_OPls,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_OBit1(X0),c_Int_OPls,tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f738,axiom,
! [X0] :
( c_HOL_Oord__class_Oless(X0,c_Int_OPls,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_OBit1(X0),c_Int_OPls,tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I12_J_0) ).
fof(f2681,plain,
spl0_206,
inference(avatar_split_clause,[],[f543,f2679]) ).
fof(f2679,plain,
( spl0_206
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X4,X3),X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f543,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X4,X3),X3) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__minus_0) ).
fof(f2677,plain,
spl0_205,
inference(avatar_split_clause,[],[f473,f2675]) ).
fof(f2675,plain,
( spl0_205
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f473,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).
fof(f2673,plain,
spl0_204,
inference(avatar_split_clause,[],[f442,f2671]) ).
fof(f2671,plain,
( spl0_204
<=> ! [X9,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X9,X3),X3) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f442,axiom,
! [X3,X9] :
( ~ class_Lattices_Oboolean__algebra(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X9,X3),X3) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).
fof(f2669,plain,
( spl0_203
| ~ spl0_147
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f2566,f2522,f2406,f2667]) ).
fof(f2406,plain,
( spl0_147
<=> ! [X2] : ~ c_lessequals(hAPP(c_Suc,X2),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f2566,plain,
( ! [X0] : c_lessequals(X0,hAPP(c_Suc,X0),tc_nat)
| ~ spl0_147
| ~ spl0_174 ),
inference(resolution,[],[f2523,f2407]) ).
fof(f2407,plain,
( ! [X2] : ~ c_lessequals(hAPP(c_Suc,X2),X2,tc_nat)
| ~ spl0_147 ),
inference(avatar_component_clause,[],[f2406]) ).
fof(f2665,plain,
spl0_202,
inference(avatar_split_clause,[],[f436,f2663]) ).
fof(f2663,plain,
( spl0_202
<=> ! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f436,axiom,
! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
fof(f2661,plain,
spl0_201,
inference(avatar_split_clause,[],[f434,f2659]) ).
fof(f2659,plain,
( spl0_201
<=> ! [X9] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Ozero__class_Ozero(tc_nat)) = X9 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f434,axiom,
! [X9] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Ozero__class_Ozero(tc_nat)) = X9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
fof(f2657,plain,
spl0_200,
inference(avatar_split_clause,[],[f421,f2654]) ).
fof(f2652,plain,
spl0_199,
inference(avatar_split_clause,[],[f416,f2650]) ).
fof(f2650,plain,
( spl0_199
<=> ! [X0] :
( c_HOL_Oord__class_Oless(X0,c_Int_OMin,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_OBit1(X0),c_Int_OMin,tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f416,axiom,
! [X0] :
( c_HOL_Oord__class_Oless(X0,c_Int_OMin,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_OBit1(X0),c_Int_OMin,tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I13_J_0) ).
fof(f2648,plain,
spl0_198,
inference(avatar_split_clause,[],[f415,f2646]) ).
fof(f2646,plain,
( spl0_198
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_Int_OMin,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_OBit1(X0),c_Int_OMin,tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f415,axiom,
! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_Int_OMin,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_OBit1(X0),c_Int_OMin,tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I13_J_1) ).
fof(f2644,plain,
spl0_197,
inference(avatar_split_clause,[],[f361,f2642]) ).
fof(f2642,plain,
( spl0_197
<=> ! [X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f361,axiom,
! [X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
fof(f2640,plain,
spl0_196,
inference(avatar_split_clause,[],[f334,f2638]) ).
fof(f2638,plain,
( spl0_196
<=> ! [X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f334,axiom,
! [X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
fof(f2636,plain,
spl0_195,
inference(avatar_split_clause,[],[f333,f2634]) ).
fof(f333,axiom,
! [X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__zero_0) ).
fof(f2632,plain,
spl0_194,
inference(avatar_split_clause,[],[f317,f2630]) ).
fof(f2630,plain,
( spl0_194
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f317,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).
fof(f2628,plain,
spl0_193,
inference(avatar_split_clause,[],[f308,f2626]) ).
fof(f308,axiom,
! [X2,X1] : c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add2_0) ).
fof(f2624,plain,
spl0_192,
inference(avatar_split_clause,[],[f307,f2622]) ).
fof(f307,axiom,
! [X1,X9] : c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X9),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__add_1) ).
fof(f2620,plain,
spl0_191,
inference(avatar_split_clause,[],[f270,f2618]) ).
fof(f270,axiom,
! [X3,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(X4,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__self_0) ).
fof(f2616,plain,
spl0_190,
inference(avatar_split_clause,[],[f269,f2614]) ).
fof(f269,axiom,
! [X3,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,c_HOL_Ozero__class_Ozero(X3),X3) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
fof(f2612,plain,
spl0_189,
inference(avatar_split_clause,[],[f267,f2610]) ).
fof(f2610,plain,
( spl0_189
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Int_OMin,X0,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_OMin,c_Int_OBit1(X0),tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f267,axiom,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Int_OMin,X0,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_OMin,c_Int_OBit1(X0),tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I9_J_1) ).
fof(f2608,plain,
spl0_188,
inference(avatar_split_clause,[],[f266,f2606]) ).
fof(f2606,plain,
( spl0_188
<=> ! [X0] :
( c_HOL_Oord__class_Oless(c_Int_OMin,X0,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_OMin,c_Int_OBit1(X0),tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f266,axiom,
! [X0] :
( c_HOL_Oord__class_Oless(c_Int_OMin,X0,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_OMin,c_Int_OBit1(X0),tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I9_J_0) ).
fof(f2604,plain,
spl0_187,
inference(avatar_split_clause,[],[f265,f2602]) ).
fof(f2602,plain,
( spl0_187
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Int_OMin,X0,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_OMin,c_Int_OBit0(X0),tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f265,axiom,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Int_OMin,X0,tc_Int_Oint)
| c_HOL_Oord__class_Oless(c_Int_OMin,c_Int_OBit0(X0),tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I8_J_1) ).
fof(f2600,plain,
spl0_186,
inference(avatar_split_clause,[],[f264,f2598]) ).
fof(f2598,plain,
( spl0_186
<=> ! [X0] :
( c_HOL_Oord__class_Oless(c_Int_OMin,X0,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_OMin,c_Int_OBit0(X0),tc_Int_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f264,axiom,
! [X0] :
( c_HOL_Oord__class_Oless(c_Int_OMin,X0,tc_Int_Oint)
| ~ c_HOL_Oord__class_Oless(c_Int_OMin,c_Int_OBit0(X0),tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I8_J_0) ).
fof(f2596,plain,
spl0_185,
inference(avatar_split_clause,[],[f196,f2594]) ).
fof(f2594,plain,
( spl0_185
<=> ! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f196,axiom,
! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
fof(f2586,plain,
( spl0_184
| ~ spl0_141
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f2580,f2546,f2380,f2583]) ).
fof(f2580,plain,
( c_lessequals(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat)
| ~ spl0_141
| ~ spl0_180 ),
inference(resolution,[],[f2547,f2382]) ).
fof(f2560,plain,
spl0_183,
inference(avatar_split_clause,[],[f1409,f2558]) ).
fof(f2558,plain,
( spl0_183
<=> ! [X0,X26] :
( X0 = X26
| c_Int_OBit1(X0) != c_Int_OBit1(X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f1409,axiom,
! [X0,X26] :
( X0 = X26
| c_Int_OBit1(X0) != c_Int_OBit1(X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I51_J_0) ).
fof(f2556,plain,
spl0_182,
inference(avatar_split_clause,[],[f1305,f2554]) ).
fof(f2554,plain,
( spl0_182
<=> ! [X0,X26] :
( X0 = X26
| c_Int_OBit0(X0) != c_Int_OBit0(X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f1305,axiom,
! [X0,X26] :
( X0 = X26
| c_Int_OBit0(X0) != c_Int_OBit0(X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I48_J_0) ).
fof(f2552,plain,
spl0_181,
inference(avatar_split_clause,[],[f1193,f2550]) ).
fof(f1193,axiom,
! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
fof(f2548,plain,
spl0_180,
inference(avatar_split_clause,[],[f977,f2546]) ).
fof(f977,axiom,
! [X9,X17] :
( ~ c_HOL_Oord__class_Oless(X9,X17,tc_nat)
| c_lessequals(X9,X17,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
fof(f2544,plain,
spl0_179,
inference(avatar_split_clause,[],[f961,f2542]) ).
fof(f2542,plain,
( spl0_179
<=> ! [X9] :
( c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,X9),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f961,axiom,
! [X9] :
( c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,X9),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__Suc_1) ).
fof(f2540,plain,
spl0_178,
inference(avatar_split_clause,[],[f960,f2538]) ).
fof(f2538,plain,
( spl0_178
<=> ! [X9] :
( ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,X9),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f960,axiom,
! [X9] :
( ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(hAPP(c_Suc,X9),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__Suc_0) ).
fof(f2536,plain,
spl0_177,
inference(avatar_split_clause,[],[f723,f2534]) ).
fof(f723,axiom,
! [X3] :
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_number__of__Pls_0) ).
fof(f2532,plain,
spl0_176,
inference(avatar_split_clause,[],[f643,f2530]) ).
fof(f2530,plain,
( spl0_176
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f643,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
fof(f2528,plain,
spl0_175,
inference(avatar_split_clause,[],[f542,f2526]) ).
fof(f2526,plain,
( spl0_175
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f542,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
fof(f2524,plain,
spl0_174,
inference(avatar_split_clause,[],[f477,f2522]) ).
fof(f477,axiom,
! [X2,X1] :
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
fof(f2520,plain,
spl0_173,
inference(avatar_split_clause,[],[f407,f2518]) ).
fof(f2518,plain,
( spl0_173
<=> ! [X2] :
( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f407,axiom,
! [X2] :
( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__pos_0) ).
fof(f2516,plain,
spl0_172,
inference(avatar_split_clause,[],[f310,f2514]) ).
fof(f2514,plain,
( spl0_172
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f310,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
fof(f2512,plain,
spl0_171,
inference(avatar_split_clause,[],[f296,f2510]) ).
fof(f2510,plain,
( spl0_171
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f296,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
fof(f2508,plain,
spl0_170,
inference(avatar_split_clause,[],[f286,f2506]) ).
fof(f286,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(X4,c_HOL_Oabs__class_Oabs(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).
fof(f2499,plain,
spl0_169,
inference(avatar_split_clause,[],[f1575,f2497]) ).
fof(f2497,plain,
( spl0_169
<=> ! [X52,X53,X3] :
( X52 = X53
| ~ c_fequal(X52,X53,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f1575,axiom,
! [X3,X52,X53] :
( X52 = X53
| ~ c_fequal(X52,X53,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f2495,plain,
spl0_168,
inference(avatar_split_clause,[],[f1401,f2493]) ).
fof(f2493,plain,
( spl0_168
<=> ! [X26] :
( c_Int_OPls = X26
| c_Int_OPls != c_Int_OBit0(X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f1401,axiom,
! [X26] :
( c_Int_OPls = X26
| c_Int_OPls != c_Int_OBit0(X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I38_J_0) ).
fof(f2491,plain,
spl0_167,
inference(avatar_split_clause,[],[f1196,f2489]) ).
fof(f2489,plain,
( spl0_167
<=> ! [X2,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f1196,axiom,
! [X2,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
fof(f2487,plain,
spl0_166,
inference(avatar_split_clause,[],[f1186,f2485]) ).
fof(f2485,plain,
( spl0_166
<=> ! [X1] : c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f1186,axiom,
! [X1] : c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
fof(f2483,plain,
spl0_165,
inference(avatar_split_clause,[],[f1185,f2481]) ).
fof(f2481,plain,
( spl0_165
<=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f1185,axiom,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
fof(f2479,plain,
spl0_164,
inference(avatar_split_clause,[],[f846,f2477]) ).
fof(f2477,plain,
( spl0_164
<=> ! [X9] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X9),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f846,axiom,
! [X9] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X9),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
fof(f2475,plain,
spl0_163,
inference(avatar_split_clause,[],[f831,f2473]) ).
fof(f2473,plain,
( spl0_163
<=> ! [X26] :
( c_Int_OMin = X26
| c_Int_OMin != c_Int_OBit1(X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f831,axiom,
! [X26] :
( c_Int_OMin = X26
| c_Int_OMin != c_Int_OBit1(X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I43_J_0) ).
fof(f2471,plain,
spl0_162,
inference(avatar_split_clause,[],[f805,f2469]) ).
fof(f2469,plain,
( spl0_162
<=> ! [X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oone__class_Oone(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f805,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oone__class_Oone(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
fof(f2467,plain,
spl0_161,
inference(avatar_split_clause,[],[f409,f2465]) ).
fof(f2465,plain,
( spl0_161
<=> ! [X2,X1] : c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f409,axiom,
! [X2,X1] : c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__eq__dividend_0) ).
fof(f2463,plain,
spl0_160,
inference(avatar_split_clause,[],[f355,f2461]) ).
fof(f2461,plain,
( spl0_160
<=> ! [X2,X1] : c_lessequals(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f355,axiom,
! [X2,X1] : c_lessequals(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat),X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__le__dividend_0) ).
fof(f2459,plain,
spl0_159,
inference(avatar_split_clause,[],[f41,f2457]) ).
fof(f2457,plain,
( spl0_159
<=> ! [X2] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Fact_Ofact__class_Ofact(X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f41,axiom,
! [X2] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Fact_Ofact__class_Ofact(X2,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fact__gt__zero__nat_0) ).
fof(f2455,plain,
spl0_158,
inference(avatar_split_clause,[],[f1444,f2452]) ).
fof(f1444,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f2450,plain,
spl0_157,
inference(avatar_split_clause,[],[f1448,f2448]) ).
fof(f2448,plain,
( spl0_157
<=> ! [X50,X51] :
( ~ class_Orderings_Oorder(X51)
| class_Orderings_Oorder(tc_fun(X50,X51)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f1448,axiom,
! [X50,X51] :
( ~ class_Orderings_Oorder(X51)
| class_Orderings_Oorder(tc_fun(X50,X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f2446,plain,
spl0_156,
inference(avatar_split_clause,[],[f1447,f2444]) ).
fof(f2444,plain,
( spl0_156
<=> ! [X50,X51] :
( ~ class_Orderings_Opreorder(X51)
| class_Orderings_Opreorder(tc_fun(X50,X51)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f1447,axiom,
! [X50,X51] :
( ~ class_Orderings_Opreorder(X51)
| class_Orderings_Opreorder(tc_fun(X50,X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f2442,plain,
spl0_155,
inference(avatar_split_clause,[],[f1446,f2440]) ).
fof(f2440,plain,
( spl0_155
<=> ! [X50,X51] :
( ~ class_Lattices_Oboolean__algebra(X51)
| class_Lattices_Oboolean__algebra(tc_fun(X50,X51)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f1446,axiom,
! [X50,X51] :
( ~ class_Lattices_Oboolean__algebra(X51)
| class_Lattices_Oboolean__algebra(tc_fun(X50,X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
fof(f2438,plain,
spl0_154,
inference(avatar_split_clause,[],[f1378,f2436]) ).
fof(f1378,axiom,
! [X2] : c_HOL_Oord__class_Oless(X2,hAPP(c_Suc,X2),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).
fof(f2434,plain,
spl0_153,
inference(avatar_split_clause,[],[f1327,f2432]) ).
fof(f2432,plain,
( spl0_153
<=> ! [X9,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X9,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f1327,axiom,
! [X3,X9] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X9,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f2430,plain,
spl0_152,
inference(avatar_split_clause,[],[f1326,f2428]) ).
fof(f2428,plain,
( spl0_152
<=> ! [X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X9,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f1326,axiom,
! [X3,X9] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X9,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f2426,plain,
spl0_151,
inference(avatar_split_clause,[],[f1323,f2424]) ).
fof(f2424,plain,
( spl0_151
<=> ! [X9,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X9,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f1323,axiom,
! [X3,X9] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X9,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f2422,plain,
spl0_150,
inference(avatar_split_clause,[],[f955,f2420]) ).
fof(f2420,plain,
( spl0_150
<=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(c_Suc,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f955,axiom,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(c_Suc,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
fof(f2418,plain,
spl0_149,
inference(avatar_split_clause,[],[f930,f2415]) ).
fof(f2415,plain,
( spl0_149
<=> c_FFT__Mirabelle_Oroot(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f930,axiom,
c_FFT__Mirabelle_Oroot(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root0_0) ).
fof(f2413,plain,
spl0_148,
inference(avatar_split_clause,[],[f875,f2410]) ).
fof(f2410,plain,
( spl0_148
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f2408,plain,
spl0_147,
inference(avatar_split_clause,[],[f840,f2406]) ).
fof(f840,axiom,
! [X2] : ~ c_lessequals(hAPP(c_Suc,X2),X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
fof(f2404,plain,
spl0_146,
inference(avatar_split_clause,[],[f501,f2402]) ).
fof(f2402,plain,
( spl0_146
<=> ! [X4] : c_FFT__Mirabelle_OIFFT(c_HOL_Ozero__class_Ozero(tc_nat),X4) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f501,axiom,
! [X4] : c_FFT__Mirabelle_OIFFT(c_HOL_Ozero__class_Ozero(tc_nat),X4) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IFFT_Osimps_I1_J_0) ).
fof(f2400,plain,
spl0_145,
inference(avatar_split_clause,[],[f449,f2398]) ).
fof(f2398,plain,
( spl0_145
<=> ! [X9,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X9,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f449,axiom,
! [X3,X9] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X9,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f2396,plain,
spl0_144,
inference(avatar_split_clause,[],[f448,f2394]) ).
fof(f2394,plain,
( spl0_144
<=> ! [X9,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X9,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f448,axiom,
! [X3,X9] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X9,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f2392,plain,
spl0_143,
inference(avatar_split_clause,[],[f133,f2389]) ).
fof(f2389,plain,
( spl0_143
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f133,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__number__of__Min_0) ).
fof(f2387,plain,
spl0_142,
inference(avatar_split_clause,[],[f122,f2385]) ).
fof(f2385,plain,
( spl0_142
<=> ! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Fact_Ofact__class_Ofact(X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f122,axiom,
! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Fact_Ofact__class_Ofact(X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fact__nonzero__nat_0) ).
fof(f2383,plain,
spl0_141,
inference(avatar_split_clause,[],[f1443,f2380]) ).
fof(f1443,axiom,
c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2377,plain,
spl0_140,
inference(avatar_split_clause,[],[f1436,f2375]) ).
fof(f2375,plain,
( spl0_140
<=> ! [X0,X26] : c_Int_OBit0(X0) != c_Int_OBit1(X26) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1436,axiom,
! [X0,X26] : c_Int_OBit0(X0) != c_Int_OBit1(X26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I49_J_0) ).
fof(f2373,plain,
spl0_139,
inference(avatar_split_clause,[],[f1372,f2371]) ).
fof(f2371,plain,
( spl0_139
<=> ! [X2] : hAPP(c_Suc,X2) != X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f1372,axiom,
! [X2] : hAPP(c_Suc,X2) != X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
fof(f2369,plain,
spl0_138,
inference(avatar_split_clause,[],[f982,f2367]) ).
fof(f982,axiom,
! [X1] : ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
fof(f2365,plain,
spl0_137,
inference(avatar_split_clause,[],[f405,f2363]) ).
fof(f405,axiom,
! [X2] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le0_0) ).
fof(f2359,plain,
spl0_136,
inference(avatar_split_clause,[],[f1574,f2357]) ).
fof(f2357,plain,
( spl0_136
<=> ! [X9,X3] : c_fequal(X9,X9,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f1574,axiom,
! [X3,X9] : c_fequal(X9,X9,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f2355,plain,
spl0_135,
inference(avatar_split_clause,[],[f1352,f2352]) ).
fof(f2352,plain,
( spl0_135
<=> c_Int_OPls = c_Int_OBit0(c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f1352,axiom,
c_Int_OPls = c_Int_OBit0(c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I38_J_1) ).
fof(f2350,plain,
spl0_134,
inference(avatar_split_clause,[],[f1325,f2348]) ).
fof(f1325,axiom,
! [X9] : ~ c_HOL_Oord__class_Oless(X9,X9,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
fof(f2346,plain,
spl0_133,
inference(avatar_split_clause,[],[f1313,f2344]) ).
fof(f2344,plain,
( spl0_133
<=> ! [X26] : c_Int_OPls != c_Int_OBit1(X26) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f1313,axiom,
! [X26] : c_Int_OPls != c_Int_OBit1(X26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I39_J_0) ).
fof(f2342,plain,
~ spl0_132,
inference(avatar_split_clause,[],[f1205,f2339]) ).
fof(f2339,plain,
( spl0_132
<=> c_Complex_Oii = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1205,axiom,
c_Complex_Oii != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__i__not__one_0) ).
fof(f2337,plain,
spl0_131,
inference(avatar_split_clause,[],[f992,f2335]) ).
fof(f2335,plain,
( spl0_131
<=> ! [X26] : c_Int_OMin != c_Int_OBit0(X26) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f992,axiom,
! [X26] : c_Int_OMin != c_Int_OBit0(X26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I42_J_0) ).
fof(f2333,plain,
spl0_130,
inference(avatar_split_clause,[],[f829,f2330]) ).
fof(f2330,plain,
( spl0_130
<=> c_Int_OMin = c_Int_OBit1(c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f829,axiom,
c_Int_OMin = c_Int_OBit1(c_Int_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Bit1__Min_0) ).
fof(f2328,plain,
spl0_129,
inference(avatar_split_clause,[],[f452,f2326]) ).
fof(f2326,plain,
( spl0_129
<=> ! [X2] : c_lessequals(X2,X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f452,axiom,
! [X2] : c_lessequals(X2,X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).
fof(f2324,plain,
~ spl0_128,
inference(avatar_split_clause,[],[f326,f2321]) ).
fof(f2321,plain,
( spl0_128
<=> c_HOL_Oord__class_Oless(c_Int_OPls,c_Int_OMin,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f326,axiom,
~ c_HOL_Oord__class_Oless(c_Int_OPls,c_Int_OMin,tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I3_J_0) ).
fof(f2319,plain,
spl0_127,
inference(avatar_split_clause,[],[f303,f2317]) ).
fof(f2317,plain,
( spl0_127
<=> ! [X9] : ~ c_HOL_Oord__class_Oless(X9,X9,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f303,axiom,
! [X9] : ~ c_HOL_Oord__class_Oless(X9,X9,tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zless__le_1) ).
fof(f2315,plain,
spl0_126,
inference(avatar_split_clause,[],[f293,f2312]) ).
fof(f2312,plain,
( spl0_126
<=> c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f293,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(f2310,plain,
spl0_125,
inference(avatar_split_clause,[],[f244,f2307]) ).
fof(f244,axiom,
c_HOL_Oord__class_Oless(c_Int_OMin,c_Int_OPls,tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I6_J_0) ).
fof(f2305,plain,
~ spl0_124,
inference(avatar_split_clause,[],[f962,f2302]) ).
fof(f2302,plain,
( spl0_124
<=> c_Int_OMin = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f962,axiom,
c_Int_OMin != c_Int_OPls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I37_J_0) ).
fof(f2300,plain,
spl0_123,
inference(avatar_split_clause,[],[f1571,f2297]) ).
fof(f2297,plain,
( spl0_123
<=> class_Int_Onumber(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1571,axiom,
class_Int_Onumber(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber) ).
fof(f2295,plain,
spl0_122,
inference(avatar_split_clause,[],[f1570,f2292]) ).
fof(f2292,plain,
( spl0_122
<=> class_Power_Opower(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f1570,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).
fof(f2290,plain,
spl0_121,
inference(avatar_split_clause,[],[f1569,f2287]) ).
fof(f1569,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
fof(f2285,plain,
spl0_120,
inference(avatar_split_clause,[],[f1568,f2282]) ).
fof(f2282,plain,
( spl0_120
<=> class_Int_Oring__char__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1568,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(f2280,plain,
spl0_119,
inference(avatar_split_clause,[],[f1567,f2277]) ).
fof(f2277,plain,
( spl0_119
<=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f1567,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
fof(f2275,plain,
spl0_118,
inference(avatar_split_clause,[],[f1566,f2272]) ).
fof(f2272,plain,
( spl0_118
<=> class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f1566,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
fof(f2270,plain,
spl0_117,
inference(avatar_split_clause,[],[f1565,f2267]) ).
fof(f2267,plain,
( spl0_117
<=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f1565,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
fof(f2265,plain,
spl0_116,
inference(avatar_split_clause,[],[f1564,f2262]) ).
fof(f2262,plain,
( spl0_116
<=> class_RealVector_Oreal__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f1564,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).
fof(f2260,plain,
spl0_115,
inference(avatar_split_clause,[],[f1563,f2257]) ).
fof(f2257,plain,
( spl0_115
<=> class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f1563,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).
fof(f2255,plain,
spl0_114,
inference(avatar_split_clause,[],[f1562,f2252]) ).
fof(f2252,plain,
( spl0_114
<=> class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f1562,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
fof(f2250,plain,
spl0_113,
inference(avatar_split_clause,[],[f1561,f2247]) ).
fof(f2247,plain,
( spl0_113
<=> class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f1561,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
fof(f2245,plain,
spl0_112,
inference(avatar_split_clause,[],[f1560,f2242]) ).
fof(f2242,plain,
( spl0_112
<=> class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f1560,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
fof(f2240,plain,
spl0_111,
inference(avatar_split_clause,[],[f1559,f2237]) ).
fof(f2237,plain,
( spl0_111
<=> class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f1559,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
fof(f2235,plain,
spl0_110,
inference(avatar_split_clause,[],[f1558,f2232]) ).
fof(f2232,plain,
( spl0_110
<=> class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1558,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
fof(f2230,plain,
spl0_109,
inference(avatar_split_clause,[],[f1557,f2227]) ).
fof(f2227,plain,
( spl0_109
<=> class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1557,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
fof(f2225,plain,
spl0_108,
inference(avatar_split_clause,[],[f1556,f2222]) ).
fof(f2222,plain,
( spl0_108
<=> class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f1556,axiom,
class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) ).
fof(f2220,plain,
spl0_107,
inference(avatar_split_clause,[],[f1555,f2217]) ).
fof(f2217,plain,
( spl0_107
<=> class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1555,axiom,
class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) ).
fof(f2215,plain,
spl0_106,
inference(avatar_split_clause,[],[f1554,f2212]) ).
fof(f2212,plain,
( spl0_106
<=> class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1554,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).
fof(f2210,plain,
spl0_105,
inference(avatar_split_clause,[],[f1553,f2207]) ).
fof(f2207,plain,
( spl0_105
<=> class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1553,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
fof(f2205,plain,
spl0_104,
inference(avatar_split_clause,[],[f1552,f2202]) ).
fof(f2202,plain,
( spl0_104
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1552,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
fof(f2200,plain,
spl0_103,
inference(avatar_split_clause,[],[f1551,f2197]) ).
fof(f2197,plain,
( spl0_103
<=> class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1551,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
fof(f2195,plain,
spl0_102,
inference(avatar_split_clause,[],[f1550,f2192]) ).
fof(f2192,plain,
( spl0_102
<=> class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f1550,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
fof(f2190,plain,
spl0_101,
inference(avatar_split_clause,[],[f1549,f2187]) ).
fof(f2187,plain,
( spl0_101
<=> class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1549,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
fof(f2185,plain,
spl0_100,
inference(avatar_split_clause,[],[f1548,f2182]) ).
fof(f2182,plain,
( spl0_100
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1548,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
fof(f2180,plain,
spl0_99,
inference(avatar_split_clause,[],[f1547,f2177]) ).
fof(f2177,plain,
( spl0_99
<=> class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1547,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
fof(f2175,plain,
spl0_98,
inference(avatar_split_clause,[],[f1546,f2172]) ).
fof(f2172,plain,
( spl0_98
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f1546,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(f2170,plain,
spl0_97,
inference(avatar_split_clause,[],[f1545,f2167]) ).
fof(f1545,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
fof(f2165,plain,
spl0_96,
inference(avatar_split_clause,[],[f1544,f2162]) ).
fof(f2162,plain,
( spl0_96
<=> class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1544,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
fof(f2160,plain,
spl0_95,
inference(avatar_split_clause,[],[f1543,f2157]) ).
fof(f2157,plain,
( spl0_95
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1543,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
fof(f2155,plain,
spl0_94,
inference(avatar_split_clause,[],[f1542,f2152]) ).
fof(f2152,plain,
( spl0_94
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1542,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
fof(f2150,plain,
spl0_93,
inference(avatar_split_clause,[],[f1541,f2147]) ).
fof(f2147,plain,
( spl0_93
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f1541,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f2145,plain,
spl0_92,
inference(avatar_split_clause,[],[f1540,f2142]) ).
fof(f2142,plain,
( spl0_92
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f1540,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f2140,plain,
spl0_91,
inference(avatar_split_clause,[],[f1539,f2137]) ).
fof(f1539,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f2135,plain,
spl0_90,
inference(avatar_split_clause,[],[f1538,f2132]) ).
fof(f2132,plain,
( spl0_90
<=> class_Int_Onumber(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f1538,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).
fof(f2130,plain,
spl0_89,
inference(avatar_split_clause,[],[f1537,f2127]) ).
fof(f2127,plain,
( spl0_89
<=> class_Power_Opower(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f1537,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Power_Opower) ).
fof(f2125,plain,
spl0_88,
inference(avatar_split_clause,[],[f1536,f2122]) ).
fof(f1536,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).
fof(f2120,plain,
spl0_87,
inference(avatar_split_clause,[],[f1535,f2117]) ).
fof(f2117,plain,
( spl0_87
<=> class_Int_Oring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f1535,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).
fof(f2115,plain,
spl0_86,
inference(avatar_split_clause,[],[f1534,f2112]) ).
fof(f1534,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).
fof(f2110,plain,
spl0_85,
inference(avatar_split_clause,[],[f1533,f2107]) ).
fof(f2107,plain,
( spl0_85
<=> class_Divides_Oring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f1533,axiom,
class_Divides_Oring__div(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Divides_Oring__div) ).
fof(f2105,plain,
spl0_84,
inference(avatar_split_clause,[],[f1532,f2102]) ).
fof(f1532,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).
fof(f2100,plain,
spl0_83,
inference(avatar_split_clause,[],[f1531,f2097]) ).
fof(f1531,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).
fof(f2095,plain,
spl0_82,
inference(avatar_split_clause,[],[f1530,f2092]) ).
fof(f2092,plain,
( spl0_82
<=> class_Ring__and__Field_Oidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f1530,axiom,
class_Ring__and__Field_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).
fof(f2090,plain,
spl0_81,
inference(avatar_split_clause,[],[f1529,f2087]) ).
fof(f2087,plain,
( spl0_81
<=> class_Ring__and__Field_Oring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f1529,axiom,
class_Ring__and__Field_Oring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring) ).
fof(f2085,plain,
spl0_80,
inference(avatar_split_clause,[],[f1528,f2082]) ).
fof(f1528,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Divides_Osemiring__div) ).
fof(f2080,plain,
spl0_79,
inference(avatar_split_clause,[],[f1527,f2077]) ).
fof(f2077,plain,
( spl0_79
<=> class_Ring__and__Field_Oabs__if(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f1527,axiom,
class_Ring__and__Field_Oabs__if(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oabs__if) ).
fof(f2075,plain,
spl0_78,
inference(avatar_split_clause,[],[f1526,f2072]) ).
fof(f2072,plain,
( spl0_78
<=> class_Ring__and__Field_Oring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f1526,axiom,
class_Ring__and__Field_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1) ).
fof(f2070,plain,
spl0_77,
inference(avatar_split_clause,[],[f1525,f2067]) ).
fof(f1525,axiom,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).
fof(f2065,plain,
spl0_76,
inference(avatar_split_clause,[],[f1524,f2062]) ).
fof(f2062,plain,
( spl0_76
<=> class_OrderedGroup_Omonoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1524,axiom,
class_OrderedGroup_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__add) ).
fof(f2060,plain,
spl0_75,
inference(avatar_split_clause,[],[f1523,f2057]) ).
fof(f2057,plain,
( spl0_75
<=> class_Ring__and__Field_Osemiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1523,axiom,
class_Ring__and__Field_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring) ).
fof(f2055,plain,
spl0_74,
inference(avatar_split_clause,[],[f1522,f2052]) ).
fof(f2052,plain,
( spl0_74
<=> class_OrderedGroup_Omonoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f1522,axiom,
class_OrderedGroup_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).
fof(f2050,plain,
spl0_73,
inference(avatar_split_clause,[],[f1521,f2047]) ).
fof(f2047,plain,
( spl0_73
<=> class_Ring__and__Field_Omult__mono(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f1521,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(f2045,plain,
spl0_72,
inference(avatar_split_clause,[],[f1520,f2042]) ).
fof(f2042,plain,
( spl0_72
<=> class_Ring__and__Field_Omult__zero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f1520,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(f2040,plain,
spl0_71,
inference(avatar_split_clause,[],[f1519,f2037]) ).
fof(f2037,plain,
( spl0_71
<=> class_OrderedGroup_Oab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f1519,axiom,
class_OrderedGroup_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).
fof(f2035,plain,
spl0_70,
inference(avatar_split_clause,[],[f1518,f2032]) ).
fof(f2032,plain,
( spl0_70
<=> class_Ring__and__Field_Omult__mono1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f1518,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(f2030,plain,
spl0_69,
inference(avatar_split_clause,[],[f1517,f2027]) ).
fof(f2027,plain,
( spl0_69
<=> class_Ring__and__Field_Osemiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1517,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(f2025,plain,
spl0_68,
inference(avatar_split_clause,[],[f1516,f2022]) ).
fof(f2022,plain,
( spl0_68
<=> class_Ring__and__Field_Osemiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f1516,axiom,
class_Ring__and__Field_Osemiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__1) ).
fof(f2020,plain,
spl0_67,
inference(avatar_split_clause,[],[f1515,f2017]) ).
fof(f2017,plain,
( spl0_67
<=> class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f1515,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1) ).
fof(f2015,plain,
spl0_66,
inference(avatar_split_clause,[],[f1514,f2012]) ).
fof(f1514,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(f2010,plain,
spl0_65,
inference(avatar_split_clause,[],[f1513,f2007]) ).
fof(f2007,plain,
( spl0_65
<=> class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f1513,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(f2005,plain,
spl0_64,
inference(avatar_split_clause,[],[f1512,f2002]) ).
fof(f2002,plain,
( spl0_64
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f1512,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).
fof(f2000,plain,
spl0_63,
inference(avatar_split_clause,[],[f1511,f1997]) ).
fof(f1997,plain,
( spl0_63
<=> class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f1511,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) ).
fof(f1995,plain,
spl0_62,
inference(avatar_split_clause,[],[f1510,f1992]) ).
fof(f1992,plain,
( spl0_62
<=> class_Ring__and__Field_Olordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f1510,axiom,
class_Ring__and__Field_Olordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Olordered__ring) ).
fof(f1990,plain,
spl0_61,
inference(avatar_split_clause,[],[f1509,f1987]) ).
fof(f1987,plain,
( spl0_61
<=> class_Ring__and__Field_Opordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f1509,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(f1985,plain,
spl0_60,
inference(avatar_split_clause,[],[f1508,f1982]) ).
fof(f1982,plain,
( spl0_60
<=> class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f1508,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) ).
fof(f1980,plain,
spl0_59,
inference(avatar_split_clause,[],[f1507,f1977]) ).
fof(f1977,plain,
( spl0_59
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f1507,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1975,plain,
spl0_58,
inference(avatar_split_clause,[],[f1506,f1972]) ).
fof(f1972,plain,
( spl0_58
<=> class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f1506,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) ).
fof(f1970,plain,
spl0_57,
inference(avatar_split_clause,[],[f1505,f1967]) ).
fof(f1967,plain,
( spl0_57
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f1505,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(f1965,plain,
spl0_56,
inference(avatar_split_clause,[],[f1504,f1962]) ).
fof(f1962,plain,
( spl0_56
<=> class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f1504,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(f1960,plain,
spl0_55,
inference(avatar_split_clause,[],[f1503,f1957]) ).
fof(f1957,plain,
( spl0_55
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f1503,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(f1955,plain,
spl0_54,
inference(avatar_split_clause,[],[f1502,f1952]) ).
fof(f1952,plain,
( spl0_54
<=> class_Ring__and__Field_Oordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f1502,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(f1950,plain,
spl0_53,
inference(avatar_split_clause,[],[f1501,f1947]) ).
fof(f1947,plain,
( spl0_53
<=> class_Ring__and__Field_Opordered__ring__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f1501,axiom,
class_Ring__and__Field_Opordered__ring__abs(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs) ).
fof(f1945,plain,
spl0_52,
inference(avatar_split_clause,[],[f1500,f1942]) ).
fof(f1942,plain,
( spl0_52
<=> class_Ring__and__Field_Opordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f1500,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(f1940,plain,
spl0_51,
inference(avatar_split_clause,[],[f1499,f1937]) ).
fof(f1937,plain,
( spl0_51
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f1499,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1935,plain,
spl0_50,
inference(avatar_split_clause,[],[f1498,f1932]) ).
fof(f1932,plain,
( spl0_50
<=> class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f1498,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add) ).
fof(f1930,plain,
spl0_49,
inference(avatar_split_clause,[],[f1497,f1927]) ).
fof(f1927,plain,
( spl0_49
<=> class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f1497,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).
fof(f1925,plain,
spl0_48,
inference(avatar_split_clause,[],[f1496,f1922]) ).
fof(f1496,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(f1920,plain,
spl0_47,
inference(avatar_split_clause,[],[f1495,f1917]) ).
fof(f1917,plain,
( spl0_47
<=> class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f1495,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(f1915,plain,
spl0_46,
inference(avatar_split_clause,[],[f1494,f1912]) ).
fof(f1912,plain,
( spl0_46
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f1494,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1910,plain,
spl0_45,
inference(avatar_split_clause,[],[f1493,f1907]) ).
fof(f1907,plain,
( spl0_45
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f1493,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(f1905,plain,
spl0_44,
inference(avatar_split_clause,[],[f1492,f1902]) ).
fof(f1902,plain,
( spl0_44
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f1492,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1900,plain,
spl0_43,
inference(avatar_split_clause,[],[f1491,f1897]) ).
fof(f1897,plain,
( spl0_43
<=> class_OrderedGroup_Olordered__ab__group__add__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f1491,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__abs) ).
fof(f1895,plain,
spl0_42,
inference(avatar_split_clause,[],[f1490,f1892]) ).
fof(f1490,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs) ).
fof(f1890,plain,
spl0_41,
inference(avatar_split_clause,[],[f1489,f1887]) ).
fof(f1887,plain,
( spl0_41
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f1489,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1885,plain,
spl0_40,
inference(avatar_split_clause,[],[f1488,f1882]) ).
fof(f1882,plain,
( spl0_40
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f1488,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(f1880,plain,
spl0_39,
inference(avatar_split_clause,[],[f1487,f1877]) ).
fof(f1487,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(f1875,plain,
spl0_38,
inference(avatar_split_clause,[],[f1486,f1872]) ).
fof(f1872,plain,
( spl0_38
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1486,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(f1870,plain,
spl0_37,
inference(avatar_split_clause,[],[f1485,f1867]) ).
fof(f1867,plain,
( spl0_37
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f1485,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(f1865,plain,
spl0_36,
inference(avatar_split_clause,[],[f1484,f1862]) ).
fof(f1862,plain,
( spl0_36
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f1484,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1860,plain,
spl0_35,
inference(avatar_split_clause,[],[f1483,f1857]) ).
fof(f1857,plain,
( spl0_35
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f1483,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f1855,plain,
spl0_34,
inference(avatar_split_clause,[],[f1482,f1852]) ).
fof(f1852,plain,
( spl0_34
<=> class_Int_Onumber(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f1482,axiom,
class_Int_Onumber(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).
fof(f1850,plain,
spl0_33,
inference(avatar_split_clause,[],[f1481,f1847]) ).
fof(f1847,plain,
( spl0_33
<=> class_Power_Opower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f1481,axiom,
class_Power_Opower(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
fof(f1845,plain,
spl0_32,
inference(avatar_split_clause,[],[f1480,f1842]) ).
fof(f1480,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f1840,plain,
spl0_31,
inference(avatar_split_clause,[],[f1479,f1837]) ).
fof(f1837,plain,
( spl0_31
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f1479,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f1835,plain,
spl0_30,
inference(avatar_split_clause,[],[f1478,f1832]) ).
fof(f1478,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f1830,plain,
spl0_29,
inference(avatar_split_clause,[],[f1477,f1827]) ).
fof(f1477,axiom,
class_Divides_Osemiring__div(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
fof(f1825,plain,
spl0_28,
inference(avatar_split_clause,[],[f1476,f1822]) ).
fof(f1822,plain,
( spl0_28
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f1476,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f1820,plain,
spl0_27,
inference(avatar_split_clause,[],[f1475,f1817]) ).
fof(f1817,plain,
( spl0_27
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f1475,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(f1815,plain,
spl0_26,
inference(avatar_split_clause,[],[f1474,f1812]) ).
fof(f1812,plain,
( spl0_26
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f1474,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(f1810,plain,
spl0_25,
inference(avatar_split_clause,[],[f1473,f1807]) ).
fof(f1807,plain,
( spl0_25
<=> class_Ring__and__Field_Omult__mono(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f1473,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
fof(f1805,plain,
spl0_24,
inference(avatar_split_clause,[],[f1472,f1802]) ).
fof(f1802,plain,
( spl0_24
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f1472,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f1800,plain,
spl0_23,
inference(avatar_split_clause,[],[f1471,f1797]) ).
fof(f1797,plain,
( spl0_23
<=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f1471,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
fof(f1795,plain,
spl0_22,
inference(avatar_split_clause,[],[f1470,f1792]) ).
fof(f1792,plain,
( spl0_22
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f1470,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
fof(f1790,plain,
spl0_21,
inference(avatar_split_clause,[],[f1469,f1787]) ).
fof(f1787,plain,
( spl0_21
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f1469,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(f1785,plain,
spl0_20,
inference(avatar_split_clause,[],[f1468,f1782]) ).
fof(f1782,plain,
( spl0_20
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f1468,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(f1780,plain,
spl0_19,
inference(avatar_split_clause,[],[f1467,f1777]) ).
fof(f1777,plain,
( spl0_19
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f1467,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f1775,plain,
spl0_18,
inference(avatar_split_clause,[],[f1466,f1772]) ).
fof(f1772,plain,
( spl0_18
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1466,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(f1770,plain,
spl0_17,
inference(avatar_split_clause,[],[f1465,f1767]) ).
fof(f1767,plain,
( spl0_17
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f1465,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f1765,plain,
spl0_16,
inference(avatar_split_clause,[],[f1464,f1762]) ).
fof(f1762,plain,
( spl0_16
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f1464,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1760,plain,
spl0_15,
inference(avatar_split_clause,[],[f1463,f1757]) ).
fof(f1757,plain,
( spl0_15
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f1463,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f1755,plain,
spl0_14,
inference(avatar_split_clause,[],[f1462,f1752]) ).
fof(f1462,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(f1750,plain,
spl0_13,
inference(avatar_split_clause,[],[f1461,f1747]) ).
fof(f1747,plain,
( spl0_13
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f1461,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f1745,plain,
spl0_12,
inference(avatar_split_clause,[],[f1460,f1742]) ).
fof(f1742,plain,
( spl0_12
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f1460,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(f1740,plain,
spl0_11,
inference(avatar_split_clause,[],[f1459,f1737]) ).
fof(f1737,plain,
( spl0_11
<=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f1459,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
fof(f1735,plain,
spl0_10,
inference(avatar_split_clause,[],[f1458,f1732]) ).
fof(f1732,plain,
( spl0_10
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f1458,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
fof(f1730,plain,
spl0_9,
inference(avatar_split_clause,[],[f1457,f1727]) ).
fof(f1727,plain,
( spl0_9
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f1457,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1725,plain,
spl0_8,
inference(avatar_split_clause,[],[f1456,f1722]) ).
fof(f1722,plain,
( spl0_8
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f1456,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1720,plain,
spl0_7,
inference(avatar_split_clause,[],[f1455,f1717]) ).
fof(f1717,plain,
( spl0_7
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f1455,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1715,plain,
spl0_6,
inference(avatar_split_clause,[],[f1454,f1712]) ).
fof(f1712,plain,
( spl0_6
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f1454,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1710,plain,
spl0_5,
inference(avatar_split_clause,[],[f1453,f1707]) ).
fof(f1707,plain,
( spl0_5
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f1453,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(f1705,plain,
spl0_4,
inference(avatar_split_clause,[],[f1452,f1702]) ).
fof(f1702,plain,
( spl0_4
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f1452,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(f1700,plain,
spl0_3,
inference(avatar_split_clause,[],[f1451,f1697]) ).
fof(f1697,plain,
( spl0_3
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f1451,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(f1695,plain,
spl0_2,
inference(avatar_split_clause,[],[f1450,f1692]) ).
fof(f1692,plain,
( spl0_2
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f1450,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1690,plain,
spl0_1,
inference(avatar_split_clause,[],[f1449,f1687]) ).
fof(f1687,plain,
( spl0_1
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f1449,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV716-1 : TPTP v8.2.0. Released v4.1.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 06:56:38 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (1970)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.46 % (2005)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)
% 0.19/0.47 % (2002)WARNING: value z3 for option sas not known
% 0.19/0.47 % (2000)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.19/0.47 % (2001)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.19/0.47 % (2002)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)
% 0.19/0.47 % (2004)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)
% 0.19/0.47 % (2006)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)
% 0.19/0.47 % (2003)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 2.59/0.82 TRYING [1]
% 2.85/0.88 TRYING [2]
% 7.99/1.61 TRYING [1]
% 9.02/1.75 TRYING [3]
% 9.24/1.76 TRYING [1]
% 9.24/1.76 TRYING [2]
% 9.24/1.79 TRYING [2]
% 12.16/2.19 TRYING [3]
% 14.99/2.61 % (2004)First to succeed.
% 15.46/2.67 % (2004)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1970"
% 15.46/2.68 % (2004)Refutation found. Thanks to Tanya!
% 15.46/2.68 % SZS status Unsatisfiable for theBenchmark
% 15.46/2.68 % SZS output start Proof for theBenchmark
% See solution above
% 15.46/2.71 % (2004)------------------------------
% 15.46/2.71 % (2004)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 15.46/2.71 % (2004)Termination reason: Refutation
% 15.46/2.71
% 15.46/2.71 % (2004)Memory used [KB]: 19950
% 15.46/2.71 % (2004)Time elapsed: 2.223 s
% 15.46/2.71 % (2004)Instructions burned: 4475 (million)
% 15.46/2.71 % (1970)Success in time 2.358 s
%------------------------------------------------------------------------------