TSTP Solution File: SWW287+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW287+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 11:35:48 EDT 2024
% Result : Theorem 15.91s 2.66s
% Output : Refutation 15.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2375
% Syntax : Number of formulae : 7605 (1799 unt; 0 def)
% Number of atoms : 20361 (4741 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 20262 (7506 ~;7746 |; 806 &)
% (1884 <=>;2318 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 1438 (1436 usr;1344 prp; 0-5 aty)
% Number of functors : 56 ( 56 usr; 12 con; 0-5 aty)
% Number of variables : 16215 (16131 !; 84 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f38938,plain,
$false,
inference(avatar_sat_refutation,[],[f6039,f6044,f6049,f6054,f6059,f6064,f6069,f6074,f6079,f6084,f6089,f6094,f6099,f6104,f6109,f6114,f6119,f6124,f6129,f6134,f6139,f6144,f6149,f6154,f6159,f6164,f6169,f6174,f6179,f6184,f6189,f6194,f6199,f6204,f6209,f6214,f6219,f6224,f6229,f6234,f6239,f6244,f6249,f6254,f6259,f6264,f6269,f6274,f6279,f6284,f6289,f6294,f6299,f6304,f6309,f6314,f6319,f6324,f6329,f6334,f6339,f6344,f6349,f6354,f6359,f6364,f6369,f6374,f6379,f6384,f6389,f6394,f6399,f6404,f6409,f6414,f6419,f6424,f6429,f6434,f6439,f6444,f6449,f6454,f6459,f6464,f6469,f6474,f6479,f6484,f6489,f6494,f6499,f6504,f6509,f6514,f6519,f6524,f6529,f6534,f6539,f6544,f6549,f6554,f6559,f6564,f6569,f6574,f6579,f6584,f6589,f6594,f6599,f6604,f6609,f6614,f6619,f6624,f6629,f6634,f6639,f6644,f6649,f6654,f6659,f6664,f6669,f6674,f6679,f6684,f6689,f6694,f6699,f6704,f6709,f6714,f6719,f6724,f6729,f6734,f6739,f6744,f6749,f6754,f6767,f6771,f6775,f6779,f6783,f6787,f6792,f6797,f6801,f6805,f6809,f6813,f6817,f6821,f6825,f6829,f6833,f6837,f6841,f6845,f6849,f6853,f6857,f6861,f6865,f6869,f6873,f6877,f6881,f6885,f6889,f6893,f6897,f6901,f6905,f6909,f6913,f6917,f6921,f6925,f6929,f6933,f6937,f6941,f6945,f6949,f6953,f6957,f6961,f6965,f6969,f6973,f6977,f6981,f6985,f6989,f6993,f6997,f7001,f7005,f7009,f7013,f7017,f7021,f7025,f7029,f7033,f7037,f7042,f7047,f7052,f7057,f7062,f7067,f7072,f7077,f7081,f7085,f7089,f7093,f7097,f7101,f7105,f7109,f7113,f7117,f7121,f7125,f7129,f7133,f7137,f7142,f7147,f7151,f7155,f7159,f7163,f7167,f7171,f7175,f7179,f7183,f7187,f7191,f7195,f7199,f7203,f7207,f7211,f7215,f7219,f7223,f7227,f7231,f7235,f7239,f7243,f7247,f7264,f7268,f7273,f7277,f7281,f7285,f7289,f7293,f7297,f7301,f7305,f7309,f7313,f7317,f7321,f7325,f7329,f7333,f7337,f7357,f7370,f7375,f7384,f7391,f7395,f7399,f7403,f7407,f7411,f7415,f7419,f7423,f7427,f7431,f7435,f7439,f7443,f7447,f7451,f7455,f7459,f7463,f7468,f7472,f7476,f7480,f7484,f7488,f7492,f7496,f7500,f7504,f7508,f7513,f7518,f7522,f7526,f7530,f7534,f7538,f7549,f7626,f7660,f7712,f7723,f7727,f7731,f7735,f7739,f7743,f7747,f7751,f7756,f7760,f7764,f7768,f7772,f7776,f7780,f7784,f7788,f7792,f7796,f7800,f7804,f7808,f7812,f7816,f7820,f7824,f7828,f7832,f7836,f7840,f7844,f7848,f7852,f7856,f7860,f7864,f7875,f7922,f8014,f8065,f8077,f8081,f8085,f8089,f8093,f8097,f8101,f8105,f8109,f8113,f8117,f8121,f8125,f8129,f8133,f8137,f8141,f8145,f8150,f8154,f8158,f8162,f8166,f8170,f8174,f8178,f8182,f8186,f8190,f8195,f8199,f8203,f8207,f8211,f8215,f8219,f8223,f8227,f8231,f8235,f8240,f8244,f8248,f8252,f8256,f8260,f8264,f8268,f8272,f8276,f8280,f8285,f8289,f8293,f8297,f8301,f8305,f8309,f8313,f8317,f8321,f8325,f8330,f8334,f8338,f8342,f8346,f8350,f8354,f8358,f8532,f8721,f8858,f8924,f8928,f8932,f8936,f8940,f8944,f8948,f8952,f8964,f8968,f8972,f8976,f8980,f8984,f8988,f8992,f8996,f9000,f9008,f9012,f9016,f9020,f9024,f9028,f9032,f9036,f9040,f9044,f9051,f9055,f9059,f9063,f9067,f9071,f9075,f9079,f9083,f9087,f9094,f9098,f9102,f9106,f9110,f9114,f9118,f9122,f9126,f9130,f9143,f9147,f9151,f9155,f9159,f9163,f9167,f9171,f9175,f9179,f9183,f9187,f9191,f9195,f9199,f9203,f9207,f9311,f9416,f9528,f9778,f9791,f9795,f9799,f9803,f9807,f9811,f9815,f9819,f9823,f9827,f9831,f9835,f9839,f9843,f9847,f9851,f9855,f9859,f9863,f9867,f9871,f9875,f9879,f9883,f9887,f9891,f9895,f9899,f9903,f9907,f9911,f9915,f9919,f9923,f9927,f9931,f9935,f9939,f9943,f9947,f9951,f9955,f9959,f9963,f9967,f9971,f9975,f9979,f10019,f10160,f10383,f10517,f10632,f10640,f10644,f10648,f10652,f10656,f10660,f10664,f10668,f10672,f10676,f10680,f10684,f10688,f10692,f10696,f10700,f10704,f10708,f10712,f10716,f10720,f10724,f10728,f10732,f10736,f10740,f10744,f10748,f10752,f10756,f10760,f10764,f10768,f10772,f10776,f10780,f10784,f10788,f10792,f10796,f10800,f10807,f10811,f10815,f10819,f10823,f10827,f10831,f10835,f10839,f10843,f10847,f10851,f10855,f10859,f10863,f10867,f10871,f10875,f10879,f10883,f10887,f10891,f10895,f10899,f10903,f10907,f10911,f10915,f10919,f10923,f10927,f10931,f10935,f10939,f10943,f10947,f10951,f10955,f10959,f10963,f10967,f10971,f10975,f10980,f10984,f10988,f10992,f10996,f11000,f11004,f11008,f11012,f11016,f11020,f11025,f11029,f11033,f11037,f11041,f11045,f11049,f11053,f11057,f11085,f11229,f11343,f11488,f12361,f12533,f12927,f12931,f12935,f12939,f12943,f12947,f12951,f12955,f12959,f12963,f12967,f12971,f12975,f12979,f12983,f12987,f12991,f12995,f12999,f13003,f13007,f13011,f13015,f13019,f13023,f13027,f13031,f13035,f13039,f13043,f13047,f13051,f13055,f13059,f13063,f13067,f13071,f13075,f13079,f13083,f13087,f13091,f13095,f13099,f13103,f13107,f13111,f13115,f13119,f13123,f13127,f13131,f13135,f14502,f14506,f14510,f14514,f14541,f14545,f14549,f14553,f14557,f14561,f14565,f14569,f14573,f14577,f14607,f14611,f14615,f14619,f14623,f14627,f14631,f14635,f14639,f14643,f14648,f14652,f14656,f14660,f14664,f14668,f14672,f14676,f14680,f14684,f14689,f14693,f14697,f14701,f14705,f14709,f14713,f14717,f14721,f14725,f14730,f14734,f14738,f14742,f14746,f14750,f14754,f14758,f14762,f14766,f14779,f16398,f16405,f16406,f16414,f16419,f16424,f16428,f16432,f16436,f16441,f16445,f16449,f16453,f16457,f16461,f16465,f16469,f16473,f16477,f16482,f16486,f16490,f16494,f16498,f16502,f16506,f16510,f16514,f16518,f16523,f16527,f16531,f16535,f16539,f16543,f16547,f16551,f16555,f16559,f16582,f16586,f16590,f16594,f16598,f16602,f16606,f16610,f16614,f16655,f16773,f17004,f17148,f17236,f17303,f17307,f17311,f17315,f17319,f17323,f17327,f17331,f17336,f17340,f17344,f17348,f17352,f17356,f17360,f17364,f17368,f17372,f17376,f17381,f17385,f17389,f17393,f17397,f17401,f17405,f17409,f17413,f17417,f17421,f17426,f17430,f17434,f17438,f17442,f17446,f17450,f17454,f17458,f17462,f17466,f17471,f17475,f17479,f17623,f17808,f18200,f18614,f18624,f18628,f18632,f18636,f18640,f18644,f18648,f18652,f18656,f18660,f18664,f18668,f18672,f18676,f18680,f18684,f18688,f18692,f18696,f18701,f18705,f18709,f18713,f18717,f18721,f18725,f18729,f18733,f18737,f18741,f18749,f18753,f18757,f18761,f18765,f18769,f18773,f18777,f18781,f18785,f18790,f19235,f19396,f19594,f19598,f19602,f19606,f19610,f19614,f19618,f19622,f19626,f19630,f19634,f19638,f19642,f19646,f19650,f19654,f19658,f19662,f19666,f19670,f19674,f19678,f19682,f19686,f19690,f19694,f19698,f19702,f19706,f19710,f19714,f19718,f19722,f19775,f20239,f20389,f21092,f21096,f21101,f21105,f21109,f21113,f21117,f21121,f21125,f21129,f21133,f21137,f21141,f21145,f21149,f21153,f21157,f21161,f21165,f21169,f21173,f21177,f21181,f21185,f21189,f21193,f21197,f21201,f21205,f21209,f21213,f21217,f21221,f21225,f21229,f21233,f21237,f21376,f21438,f21826,f22018,f22022,f22026,f22030,f22034,f22038,f22042,f22046,f22050,f22054,f22058,f22062,f22066,f22070,f22074,f22078,f22082,f22086,f22090,f22094,f22098,f22102,f22106,f22110,f22114,f22118,f22122,f22126,f22130,f22134,f22138,f22142,f22146,f22150,f22154,f22158,f22289,f22653,f22852,f22970,f22974,f22978,f22982,f22986,f22990,f22994,f22998,f23002,f23006,f23010,f23014,f23018,f23022,f23026,f23030,f23034,f23038,f23042,f23046,f23050,f23054,f23058,f23062,f23066,f23070,f23074,f23078,f23082,f23378,f23689,f23694,f23800,f23805,f24132,f24136,f24140,f24144,f24148,f24152,f24156,f24160,f24164,f24168,f24212,f24216,f24220,f24224,f24228,f24232,f24236,f24240,f24244,f24248,f24274,f24278,f24282,f24286,f24290,f24294,f24298,f24302,f24306,f24310,f24319,f24323,f24327,f24331,f24335,f24339,f24343,f24347,f24351,f26387,f26391,f26427,f26431,f26435,f26439,f26443,f26447,f26451,f26455,f26459,f26463,f26467,f26471,f26475,f26479,f26483,f26487,f26491,f26495,f26499,f26503,f26507,f26543,f26547,f26551,f26555,f26559,f26563,f26567,f26571,f26575,f26579,f26586,f26590,f26594,f26598,f26602,f26606,f26610,f26614,f26618,f26622,f26631,f26635,f26639,f26643,f26647,f26651,f26655,f26659,f28848,f28852,f28856,f28860,f28864,f28868,f28872,f28876,f28880,f28884,f28888,f28892,f28896,f28900,f28904,f28908,f28912,f28916,f28920,f28924,f28928,f28932,f28936,f28940,f28944,f28948,f28952,f28956,f28960,f28964,f29944,f29948,f29953,f29957,f29961,f29965,f29969,f29973,f29977,f30566,f30570,f30574,f30578,f30583,f30587,f30591,f30595,f30599,f30603,f30607,f30611,f30615,f30619,f30624,f30628,f30997,f31001,f31007,f31011,f31015,f31019,f31023,f31027,f31031,f31394,f31409,f31415,f31419,f31423,f31427,f31431,f31435,f31439,f31443,f31447,f31451,f31648,f31652,f31656,f31660,f31940,f32207,f32211,f32215,f32220,f32224,f32228,f32232,f32324,f32328,f32332,f32336,f32340,f32344,f32348,f32352,f32356,f32562,f32566,f32570,f32574,f32579,f32599,f32603,f32721,f32725,f32729,f32733,f32737,f32741,f32745,f32749,f32887,f33585,f33589,f33593,f33597,f33601,f33876,f33880,f33884,f33888,f33892,f33967,f33971,f33975,f33979,f33983,f33990,f33994,f33998,f34002,f34006,f34010,f34014,f34018,f34197,f35895,f35906,f35910,f35914,f35918,f35922,f35926,f35930,f35931,f35935,f35939,f35943,f35947,f35951,f35955,f37228,f37232,f37236,f37692,f37696,f37702,f37706,f37782,f37858,f37864,f37871,f37876,f37880,f37959,f37993,f38003,f38016,f38395,f38427,f38808,f38814,f38819,f38828,f38838,f38928,f38937]) ).
fof(f38937,plain,
( spl47_1268
| ~ spl47_786
| ~ spl47_787 ),
inference(avatar_split_clause,[],[f32593,f16402,f16396,f32596]) ).
fof(f32596,plain,
( spl47_1268
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1268])]) ).
fof(f16396,plain,
( spl47_786
<=> ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_786])]) ).
fof(f16402,plain,
( spl47_787
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_787])]) ).
fof(f32593,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK27)
| ~ spl47_786
| ~ spl47_787 ),
inference(trivial_inequality_removal,[],[f32585]) ).
fof(f32585,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK27)
| ~ spl47_786
| ~ spl47_787 ),
inference(superposition,[],[f16397,f16404]) ).
fof(f16404,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK27)
| ~ spl47_787 ),
inference(avatar_component_clause,[],[f16402]) ).
fof(f16397,plain,
( ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1) )
| ~ spl47_786 ),
inference(avatar_component_clause,[],[f16396]) ).
fof(f38928,plain,
( spl47_290
| ~ spl47_288
| ~ spl47_786 ),
inference(avatar_split_clause,[],[f16409,f16396,f7377,f7388]) ).
fof(f7388,plain,
( spl47_290
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_290])]) ).
fof(f7377,plain,
( spl47_288
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_288])]) ).
fof(f16409,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK29)
| ~ spl47_288
| ~ spl47_786 ),
inference(trivial_inequality_removal,[],[f16408]) ).
fof(f16408,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK29)
| ~ spl47_288
| ~ spl47_786 ),
inference(superposition,[],[f16397,f7379]) ).
fof(f7379,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK29)
| ~ spl47_288 ),
inference(avatar_component_clause,[],[f7377]) ).
fof(f38838,plain,
( spl47_786
| ~ spl47_219 ),
inference(avatar_split_clause,[],[f5904,f7059,f16396]) ).
fof(f7059,plain,
( spl47_219
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_219])]) ).
fof(f5904,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) ),
inference(forward_demodulation,[],[f5523,f5502]) ).
fof(f5502,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(definition_unfolding,[],[f4065,f4118]) ).
fof(f4118,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f1242]) ).
fof(f1242,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rectify,[],[f318]) ).
fof(f318,axiom,
! [X7] : c_Nat_OSuc(X7) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(f4065,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Nat_OSuc(v_n____),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Nat_OSuc(v_n____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n) ).
fof(f5523,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ),
inference(definition_unfolding,[],[f4214,f4118]) ).
fof(f4214,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____)))) ),
inference(cnf_transformation,[],[f2392]) ).
fof(f2392,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____)))) ),
inference(flattening,[],[f2391]) ).
fof(f2391,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____)))) ),
inference(ennf_transformation,[],[f1338]) ).
fof(f1338,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____))))
=> ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0)
=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____))))
=> ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3)
=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bx_O_A_091_124_Ap_Advd_Aq_A_094_ASuc_An_059_Apoly_Ap_Ax_A_061_A0_059_Apoly_Aq_Ax_A_126_061_A0_A_124_093_A_061_061_062_AFalse_096) ).
fof(f38828,plain,
( ~ spl47_289
| spl47_786 ),
inference(avatar_split_clause,[],[f4082,f16396,f7381]) ).
fof(f7381,plain,
( spl47_289
<=> sP3 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_289])]) ).
fof(f4082,plain,
! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)
| ~ sP3 ),
inference(cnf_transformation,[],[f3535]) ).
fof(f3535,plain,
( ( sP3
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK29)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK29) ) )
& ( ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1) )
| ~ sP3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f3533,f3534]) ).
fof(f3534,plain,
( ? [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) )
=> ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK29)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK29) ) ),
introduced(choice_axiom,[]) ).
fof(f3533,plain,
( ( sP3
| ? [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) ) )
& ( ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1) )
| ~ sP3 ) ),
inference(rectify,[],[f3532]) ).
fof(f3532,plain,
( ( sP3
| ? [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) ) )
& ( ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) )
| ~ sP3 ) ),
inference(nnf_transformation,[],[f3480]) ).
fof(f3480,plain,
( sP3
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f38819,plain,
( spl47_1338
| ~ spl47_316
| ~ spl47_1332 ),
inference(avatar_split_clause,[],[f38017,f37987,f7494,f38817]) ).
fof(f38817,plain,
( spl47_1338
<=> ! [X0] : c_Polynomial_Osmult(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1338])]) ).
fof(f7494,plain,
( spl47_316
<=> ! [X0,X1] :
( c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X0) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_316])]) ).
fof(f37987,plain,
( spl47_1332
<=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1332])]) ).
fof(f38017,plain,
( ! [X0] : c_Polynomial_Osmult(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0) = X0
| ~ spl47_316
| ~ spl47_1332 ),
inference(resolution,[],[f37988,f7495]) ).
fof(f7495,plain,
( ! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X0) = X0 )
| ~ spl47_316 ),
inference(avatar_component_clause,[],[f7494]) ).
fof(f37988,plain,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ spl47_1332 ),
inference(avatar_component_clause,[],[f37987]) ).
fof(f38814,plain,
( ~ spl47_286
| spl47_786 ),
inference(avatar_split_clause,[],[f4074,f16396,f7367]) ).
fof(f7367,plain,
( spl47_286
<=> sP1 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_286])]) ).
fof(f4074,plain,
! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)
| ~ sP1 ),
inference(cnf_transformation,[],[f3529]) ).
fof(f3529,plain,
( ( sP1
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK28)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK28) ) )
& ( ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1) )
| ~ sP1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f3527,f3528]) ).
fof(f3528,plain,
( ? [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) )
=> ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK28)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK28) ) ),
introduced(choice_axiom,[]) ).
fof(f3527,plain,
( ( sP1
| ? [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) ) )
& ( ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1) )
| ~ sP1 ) ),
inference(rectify,[],[f3526]) ).
fof(f3526,plain,
( ( sP1
| ? [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) ) )
& ( ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) )
| ~ sP1 ) ),
inference(nnf_transformation,[],[f3477]) ).
fof(f3477,plain,
( sP1
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f38808,plain,
( spl47_1231
| ~ spl47_786
| ~ spl47_1230 ),
inference(avatar_split_clause,[],[f31403,f31391,f16396,f31406]) ).
fof(f31406,plain,
( spl47_1231
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK30) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1231])]) ).
fof(f31391,plain,
( spl47_1230
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK30) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1230])]) ).
fof(f31403,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK30)
| ~ spl47_786
| ~ spl47_1230 ),
inference(trivial_inequality_removal,[],[f31395]) ).
fof(f31395,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK30)
| ~ spl47_786
| ~ spl47_1230 ),
inference(superposition,[],[f16397,f31393]) ).
fof(f31393,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK30)
| ~ spl47_1230 ),
inference(avatar_component_clause,[],[f31391]) ).
fof(f38427,plain,
( ~ spl47_134
| spl47_1337
| ~ spl47_150
| ~ spl47_1036 ),
inference(avatar_split_clause,[],[f22876,f22140,f6777,f38425,f6701]) ).
fof(f6701,plain,
( spl47_134
<=> class_Orderings_Oord(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_134])]) ).
fof(f38425,plain,
( spl47_1337
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_Nat_Onat),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1337])]) ).
fof(f6777,plain,
( spl47_150
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_150])]) ).
fof(f22140,plain,
( spl47_1036
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,sK46(X0,X1,X3)),hAPP(X0,sK46(X0,X1,X3)))
| ~ class_Orderings_Oord(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1036])]) ).
fof(f22876,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_Nat_Onat),X1,X1)
| ~ class_Orderings_Oord(tc_Nat_Onat) )
| ~ spl47_150
| ~ spl47_1036 ),
inference(resolution,[],[f22141,f6778]) ).
fof(f6778,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0)
| ~ spl47_150 ),
inference(avatar_component_clause,[],[f6777]) ).
fof(f22141,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,sK46(X0,X1,X3)),hAPP(X0,sK46(X0,X1,X3)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ~ class_Orderings_Oord(X3) )
| ~ spl47_1036 ),
inference(avatar_component_clause,[],[f22140]) ).
fof(f38395,plain,
( ~ spl47_133
| spl47_1336
| ~ spl47_149
| ~ spl47_1036 ),
inference(avatar_split_clause,[],[f22875,f22140,f6773,f38393,f6696]) ).
fof(f6696,plain,
( spl47_133
<=> class_Orderings_Oord(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_133])]) ).
fof(f38393,plain,
( spl47_1336
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_Int_Oint),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1336])]) ).
fof(f6773,plain,
( spl47_149
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_149])]) ).
fof(f22875,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_Int_Oint),X1,X1)
| ~ class_Orderings_Oord(tc_Int_Oint) )
| ~ spl47_149
| ~ spl47_1036 ),
inference(resolution,[],[f22141,f6774]) ).
fof(f6774,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0)
| ~ spl47_149 ),
inference(avatar_component_clause,[],[f6773]) ).
fof(f38016,plain,
( ~ spl47_126
| ~ spl47_214
| spl47_1332 ),
inference(avatar_split_clause,[],[f37994,f37987,f7035,f6661]) ).
fof(f6661,plain,
( spl47_126
<=> class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_126])]) ).
fof(f7035,plain,
( spl47_214
<=> ! [X0] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_214])]) ).
fof(f37994,plain,
( ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ~ spl47_214
| spl47_1332 ),
inference(resolution,[],[f37989,f7036]) ).
fof(f7036,plain,
( ! [X0] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) )
| ~ spl47_214 ),
inference(avatar_component_clause,[],[f7035]) ).
fof(f37989,plain,
( ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| spl47_1332 ),
inference(avatar_component_clause,[],[f37987]) ).
fof(f38003,plain,
( ~ spl47_56
| spl47_1334
| spl47_1335
| ~ spl47_219
| ~ spl47_1053 ),
inference(avatar_split_clause,[],[f32580,f23004,f7059,f38000,f37996,f6311]) ).
fof(f6311,plain,
( spl47_56
<=> class_Rings_Oidom(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_56])]) ).
fof(f37996,plain,
( spl47_1334
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1334])]) ).
fof(f38000,plain,
( spl47_1335
<=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1335])]) ).
fof(f23004,plain,
( spl47_1053
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
| ~ class_Rings_Oidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1053])]) ).
fof(f32580,plain,
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),c_Polynomial_Odegree(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ~ class_Rings_Oidom(tc_Complex_Ocomplex)
| ~ spl47_219
| ~ spl47_1053 ),
inference(resolution,[],[f7061,f23005]) ).
fof(f23005,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| ~ class_Rings_Oidom(X2) )
| ~ spl47_1053 ),
inference(avatar_component_clause,[],[f23004]) ).
fof(f7061,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ~ spl47_219 ),
inference(avatar_component_clause,[],[f7059]) ).
fof(f37993,plain,
( ~ spl47_1332
| spl47_1333
| ~ spl47_219
| ~ spl47_1067 ),
inference(avatar_split_clause,[],[f32582,f23060,f7059,f37991,f37987]) ).
fof(f37991,plain,
( spl47_1333
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1333])]) ).
fof(f23060,plain,
( spl47_1067
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1067])]) ).
fof(f32582,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),X0))
| ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ spl47_219
| ~ spl47_1067 ),
inference(resolution,[],[f7061,f23061]) ).
fof(f23061,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) )
| ~ spl47_1067 ),
inference(avatar_component_clause,[],[f23060]) ).
fof(f37959,plain,
spl47_1331,
inference(avatar_split_clause,[],[f5885,f37957]) ).
fof(f37957,plain,
( spl47_1331
<=> ! [X5,X3,X4,X0,X6,X2] :
( c_Polynomial_Opdivmod__rel(X6,c_Polynomial_OpCons(X6,X0,X5),X4,c_Polynomial_OpCons(X6,c_Rings_Oinverse__class_Odivide(X6,hAPP(c_Polynomial_Ocoeff(X6,c_Polynomial_OpCons(X6,X0,X2)),c_Polynomial_Odegree(X6,X4)),hAPP(c_Polynomial_Ocoeff(X6,X4),c_Polynomial_Odegree(X6,X4))),X3),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X6),c_Polynomial_OpCons(X6,X0,X2),c_Polynomial_Osmult(X6,c_Rings_Oinverse__class_Odivide(X6,hAPP(c_Polynomial_Ocoeff(X6,c_Polynomial_OpCons(X6,X0,X2)),c_Polynomial_Odegree(X6,X4)),hAPP(c_Polynomial_Ocoeff(X6,X4),c_Polynomial_Odegree(X6,X4))),X4)))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) = X4
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
| ~ class_Fields_Ofield(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1331])]) ).
fof(f5885,plain,
! [X2,X3,X0,X6,X4,X5] :
( c_Polynomial_Opdivmod__rel(X6,c_Polynomial_OpCons(X6,X0,X5),X4,c_Polynomial_OpCons(X6,c_Rings_Oinverse__class_Odivide(X6,hAPP(c_Polynomial_Ocoeff(X6,c_Polynomial_OpCons(X6,X0,X2)),c_Polynomial_Odegree(X6,X4)),hAPP(c_Polynomial_Ocoeff(X6,X4),c_Polynomial_Odegree(X6,X4))),X3),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X6),c_Polynomial_OpCons(X6,X0,X2),c_Polynomial_Osmult(X6,c_Rings_Oinverse__class_Odivide(X6,hAPP(c_Polynomial_Ocoeff(X6,c_Polynomial_OpCons(X6,X0,X2)),c_Polynomial_Odegree(X6,X4)),hAPP(c_Polynomial_Ocoeff(X6,X4),c_Polynomial_Odegree(X6,X4))),X4)))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) = X4
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
| ~ class_Fields_Ofield(X6) ),
inference(equality_resolution,[],[f5495]) ).
fof(f5495,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( c_Polynomial_Opdivmod__rel(X6,c_Polynomial_OpCons(X6,X0,X5),X4,c_Polynomial_OpCons(X6,X1,X3),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X6),c_Polynomial_OpCons(X6,X0,X2),c_Polynomial_Osmult(X6,X1,X4)))
| c_Rings_Oinverse__class_Odivide(X6,hAPP(c_Polynomial_Ocoeff(X6,c_Polynomial_OpCons(X6,X0,X2)),c_Polynomial_Odegree(X6,X4)),hAPP(c_Polynomial_Ocoeff(X6,X4),c_Polynomial_Odegree(X6,X4))) != X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) = X4
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
| ~ class_Fields_Ofield(X6) ),
inference(cnf_transformation,[],[f3466]) ).
fof(f3466,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( c_Polynomial_Opdivmod__rel(X6,c_Polynomial_OpCons(X6,X0,X5),X4,c_Polynomial_OpCons(X6,X1,X3),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X6),c_Polynomial_OpCons(X6,X0,X2),c_Polynomial_Osmult(X6,X1,X4)))
| c_Rings_Oinverse__class_Odivide(X6,hAPP(c_Polynomial_Ocoeff(X6,c_Polynomial_OpCons(X6,X0,X2)),c_Polynomial_Odegree(X6,X4)),hAPP(c_Polynomial_Ocoeff(X6,X4),c_Polynomial_Odegree(X6,X4))) != X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) = X4
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
| ~ class_Fields_Ofield(X6) ),
inference(flattening,[],[f3465]) ).
fof(f3465,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( c_Polynomial_Opdivmod__rel(X6,c_Polynomial_OpCons(X6,X0,X5),X4,c_Polynomial_OpCons(X6,X1,X3),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X6),c_Polynomial_OpCons(X6,X0,X2),c_Polynomial_Osmult(X6,X1,X4)))
| c_Rings_Oinverse__class_Odivide(X6,hAPP(c_Polynomial_Ocoeff(X6,c_Polynomial_OpCons(X6,X0,X2)),c_Polynomial_Odegree(X6,X4)),hAPP(c_Polynomial_Ocoeff(X6,X4),c_Polynomial_Odegree(X6,X4))) != X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) = X4
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
| ~ class_Fields_Ofield(X6) ),
inference(ennf_transformation,[],[f2255]) ).
fof(f2255,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( class_Fields_Ofield(X6)
=> ( c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) != X4
=> ( c_Rings_Oinverse__class_Odivide(X6,hAPP(c_Polynomial_Ocoeff(X6,c_Polynomial_OpCons(X6,X0,X2)),c_Polynomial_Odegree(X6,X4)),hAPP(c_Polynomial_Ocoeff(X6,X4),c_Polynomial_Odegree(X6,X4))) = X1
=> c_Polynomial_Opdivmod__rel(X6,c_Polynomial_OpCons(X6,X0,X5),X4,c_Polynomial_OpCons(X6,X1,X3),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X6),c_Polynomial_OpCons(X6,X0,X2),c_Polynomial_Osmult(X6,X1,X4))) ) ) ) ),
inference(rectify,[],[f900]) ).
fof(f900,axiom,
! [X4,X17,X34,X13,X10,X6,X5] :
( class_Fields_Ofield(X5)
=> ( c_Polynomial_Opdivmod__rel(X5,X6,X10,X13,X34)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) != X10
=> ( c_Rings_Oinverse__class_Odivide(X5,hAPP(c_Polynomial_Ocoeff(X5,c_Polynomial_OpCons(X5,X4,X34)),c_Polynomial_Odegree(X5,X10)),hAPP(c_Polynomial_Ocoeff(X5,X10),c_Polynomial_Odegree(X5,X10))) = X17
=> c_Polynomial_Opdivmod__rel(X5,c_Polynomial_OpCons(X5,X4,X6),X10,c_Polynomial_OpCons(X5,X17,X13),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5),c_Polynomial_OpCons(X5,X4,X34),c_Polynomial_Osmult(X5,X17,X10))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__pCons) ).
fof(f37880,plain,
spl47_1330,
inference(avatar_split_clause,[],[f5494,f37878]) ).
fof(f37878,plain,
( spl47_1330
<=> ! [X2,X3,X4,X0,X5,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1330])]) ).
fof(f5494,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4),X3) ),
inference(cnf_transformation,[],[f3464]) ).
fof(f3464,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4),X3) ),
inference(flattening,[],[f3463]) ).
fof(f3463,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4),X3) ),
inference(ennf_transformation,[],[f2254]) ).
fof(f2254,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4),X3)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X4) ) ) ) ) ) ),
inference(rectify,[],[f718]) ).
fof(f718,axiom,
! [X67,X68,X69,X34,X13,X17] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X69),X68),X67) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17),X13),X34)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X69),X68),X67),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X34,X17)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X67)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X69)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X69,X17)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X68,X13) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
fof(f37876,plain,
spl47_1329,
inference(avatar_split_clause,[],[f5493,f37874]) ).
fof(f37874,plain,
( spl47_1329
<=> ! [X2,X3,X4,X0,X5,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1329])]) ).
fof(f5493,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4),X3) ),
inference(cnf_transformation,[],[f3462]) ).
fof(f3462,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4),X3) ),
inference(flattening,[],[f3461]) ).
fof(f3461,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4),X3) ),
inference(ennf_transformation,[],[f2253]) ).
fof(f2253,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4),X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X1) ) ) ) ) ) ),
inference(rectify,[],[f720]) ).
fof(f720,axiom,
! [X67,X68,X69,X34,X13,X17] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X69),X68),X67) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17),X13),X34)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X69),X68),X67))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X67,X69)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X34)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X69)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X69,X17)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X13,X68) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).
fof(f37871,plain,
spl47_1328,
inference(avatar_split_clause,[],[f5176,f37869]) ).
fof(f37869,plain,
( spl47_1328
<=> ! [X0,X3,X2,X1] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X1,X0),X2) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X0,X2)),c_Polynomial_Osmult(X3,c_Rings_Oinverse__class_Odivide(X3,hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_OpCons(X3,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X0,X2))),c_Polynomial_Odegree(X3,X2)),hAPP(c_Polynomial_Ocoeff(X3,X2),c_Polynomial_Odegree(X3,X2))),X2))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X2
| ~ class_Fields_Ofield(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1328])]) ).
fof(f5176,plain,
! [X2,X3,X0,X1] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X1,X0),X2) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X0,X2)),c_Polynomial_Osmult(X3,c_Rings_Oinverse__class_Odivide(X3,hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_OpCons(X3,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X0,X2))),c_Polynomial_Odegree(X3,X2)),hAPP(c_Polynomial_Ocoeff(X3,X2),c_Polynomial_Odegree(X3,X2))),X2))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X2
| ~ class_Fields_Ofield(X3) ),
inference(cnf_transformation,[],[f3105]) ).
fof(f3105,plain,
! [X0,X1,X2,X3] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X1,X0),X2) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X0,X2)),c_Polynomial_Osmult(X3,c_Rings_Oinverse__class_Odivide(X3,hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_OpCons(X3,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X0,X2))),c_Polynomial_Odegree(X3,X2)),hAPP(c_Polynomial_Ocoeff(X3,X2),c_Polynomial_Odegree(X3,X2))),X2))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X2
| ~ class_Fields_Ofield(X3) ),
inference(flattening,[],[f3104]) ).
fof(f3104,plain,
! [X0,X1,X2,X3] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X1,X0),X2) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X0,X2)),c_Polynomial_Osmult(X3,c_Rings_Oinverse__class_Odivide(X3,hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_OpCons(X3,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X0,X2))),c_Polynomial_Odegree(X3,X2)),hAPP(c_Polynomial_Ocoeff(X3,X2),c_Polynomial_Odegree(X3,X2))),X2))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X2
| ~ class_Fields_Ofield(X3) ),
inference(ennf_transformation,[],[f2019]) ).
fof(f2019,plain,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != X2
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X1,X0),X2) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X0,X2)),c_Polynomial_Osmult(X3,c_Rings_Oinverse__class_Odivide(X3,hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_OpCons(X3,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X0,X2))),c_Polynomial_Odegree(X3,X2)),hAPP(c_Polynomial_Ocoeff(X3,X2),c_Polynomial_Odegree(X3,X2))),X2)) ) ),
inference(rectify,[],[f984]) ).
fof(f984,axiom,
! [X6,X4,X10,X5] :
( class_Fields_Ofield(X5)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) != X10
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X5),c_Polynomial_OpCons(X5,X4,X6),X10) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5),c_Polynomial_OpCons(X5,X4,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X5),X6,X10)),c_Polynomial_Osmult(X5,c_Rings_Oinverse__class_Odivide(X5,hAPP(c_Polynomial_Ocoeff(X5,c_Polynomial_OpCons(X5,X4,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X5),X6,X10))),c_Polynomial_Odegree(X5,X10)),hAPP(c_Polynomial_Ocoeff(X5,X10),c_Polynomial_Odegree(X5,X10))),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pCons) ).
fof(f37864,plain,
spl47_1327,
inference(avatar_split_clause,[],[f5397,f37862]) ).
fof(f37862,plain,
( spl47_1327
<=> ! [X4,X0,X3,X2,X1] :
( c_Groups_Ominus__class_Ominus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ominus__class_Ominus(X4,X3,X1)),c_Groups_Ominus__class_Ominus(X4,X2,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ominus__class_Ominus(X4,X3,X1)),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),c_Groups_Ominus__class_Ominus(X4,X2,X0)))
| ~ class_RealVector_Oreal__normed__algebra(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1327])]) ).
fof(f5397,plain,
! [X2,X3,X0,X1,X4] :
( c_Groups_Ominus__class_Ominus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ominus__class_Ominus(X4,X3,X1)),c_Groups_Ominus__class_Ominus(X4,X2,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ominus__class_Ominus(X4,X3,X1)),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),c_Groups_Ominus__class_Ominus(X4,X2,X0)))
| ~ class_RealVector_Oreal__normed__algebra(X4) ),
inference(cnf_transformation,[],[f3370]) ).
fof(f3370,plain,
! [X0,X1,X2,X3,X4] :
( c_Groups_Ominus__class_Ominus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ominus__class_Ominus(X4,X3,X1)),c_Groups_Ominus__class_Ominus(X4,X2,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ominus__class_Ominus(X4,X3,X1)),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),c_Groups_Ominus__class_Ominus(X4,X2,X0)))
| ~ class_RealVector_Oreal__normed__algebra(X4) ),
inference(ennf_transformation,[],[f2192]) ).
fof(f2192,plain,
! [X0,X1,X2,X3,X4] :
( class_RealVector_Oreal__normed__algebra(X4)
=> c_Groups_Ominus__class_Ominus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ominus__class_Ominus(X4,X3,X1)),c_Groups_Ominus__class_Ominus(X4,X2,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ominus__class_Ominus(X4,X3,X1)),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),c_Groups_Ominus__class_Ominus(X4,X2,X0))) ),
inference(rectify,[],[f843]) ).
fof(f843,axiom,
! [X17,X4,X10,X6,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17)) = c_Groups_Oplus__class_Oplus(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X6,X4)),c_Groups_Ominus__class_Ominus(X5,X10,X17)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X6,X4)),X17)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ominus__class_Ominus(X5,X10,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oprod__diff__prod) ).
fof(f37858,plain,
spl47_1326,
inference(avatar_split_clause,[],[f5474,f37856]) ).
fof(f37856,plain,
( spl47_1326
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X1)),X0) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,X3,X1),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,X4,X2),X0)),X1))
| ~ class_RealVector_Oreal__field(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1326])]) ).
fof(f5474,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X1)),X0) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,X3,X1),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,X4,X2),X0)),X1))
| ~ class_RealVector_Oreal__field(X5) ),
inference(cnf_transformation,[],[f3443]) ).
fof(f3443,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X1)),X0) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,X3,X1),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,X4,X2),X0)),X1))
| ~ class_RealVector_Oreal__field(X5) ),
inference(ennf_transformation,[],[f2240]) ).
fof(f2240,plain,
! [X0,X1,X2,X3,X4,X5] :
( class_RealVector_Oreal__field(X5)
=> c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X1)),X0) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,X3,X1),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,X4,X2),X0)),X1)) ),
inference(rectify,[],[f983]) ).
fof(f983,axiom,
! [X35,X46,X16,X17,X4,X5] :
( class_RealVector_Oreal__field(X5)
=> c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X16),X46)),X35) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,X17,X46),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,X4,X16),X35)),X46)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__mult__lemma) ).
fof(f37782,plain,
( spl47_1325
| ~ spl47_307
| ~ spl47_1302 ),
inference(avatar_split_clause,[],[f36296,f34190,f7457,f37780]) ).
fof(f37780,plain,
( spl47_1325
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1325])]) ).
fof(f7457,plain,
( spl47_307
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,X0)
| ~ class_Divides_Osemiring__div(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_307])]) ).
fof(f34190,plain,
( spl47_1302
<=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1302])]) ).
fof(f36296,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,X0)
| ~ spl47_307
| ~ spl47_1302 ),
inference(resolution,[],[f34191,f7458]) ).
fof(f7458,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X1)
| c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,X0) )
| ~ spl47_307 ),
inference(avatar_component_clause,[],[f7457]) ).
fof(f34191,plain,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ spl47_1302 ),
inference(avatar_component_clause,[],[f34190]) ).
fof(f37706,plain,
spl47_1324,
inference(avatar_split_clause,[],[f5477,f37704]) ).
fof(f37704,plain,
( spl47_1324
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X0),X2)),X3)
| c_Groups_Oone__class_Oone(X5) != c_Groups_Oplus__class_Oplus(X5,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X1)
| ~ c_Orderings_Oord__class_Oless(X5,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X5,X4,X3)
| ~ class_Rings_Olinordered__semiring__1__strict(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1324])]) ).
fof(f5477,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X0),X2)),X3)
| c_Groups_Oone__class_Oone(X5) != c_Groups_Oplus__class_Oplus(X5,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X1)
| ~ c_Orderings_Oord__class_Oless(X5,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X5,X4,X3)
| ~ class_Rings_Olinordered__semiring__1__strict(X5) ),
inference(cnf_transformation,[],[f3449]) ).
fof(f3449,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X0),X2)),X3)
| c_Groups_Oone__class_Oone(X5) != c_Groups_Oplus__class_Oplus(X5,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X1)
| ~ c_Orderings_Oord__class_Oless(X5,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X5,X4,X3)
| ~ class_Rings_Olinordered__semiring__1__strict(X5) ),
inference(flattening,[],[f3448]) ).
fof(f3448,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X0),X2)),X3)
| c_Groups_Oone__class_Oone(X5) != c_Groups_Oplus__class_Oplus(X5,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X1)
| ~ c_Orderings_Oord__class_Oless(X5,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X5,X4,X3)
| ~ class_Rings_Olinordered__semiring__1__strict(X5) ),
inference(ennf_transformation,[],[f2243]) ).
fof(f2243,plain,
! [X0,X1,X2,X3,X4,X5] :
( class_Rings_Olinordered__semiring__1__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X3)
=> ( c_Orderings_Oord__class_Oless(X5,X2,X3)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X1)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X0)
=> ( c_Groups_Oone__class_Oone(X5) = c_Groups_Oplus__class_Oplus(X5,X1,X0)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X0),X2)),X3) ) ) ) ) ) ),
inference(rectify,[],[f637]) ).
fof(f637,axiom,
! [X59,X60,X10,X4,X6,X5] :
( class_Rings_Olinordered__semiring__1__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X6,X4)
=> ( c_Orderings_Oord__class_Oless(X5,X10,X4)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X60)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X59)
=> ( c_Groups_Oone__class_Oone(X5) = c_Groups_Oplus__class_Oplus(X5,X60,X59)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X60),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X59),X10)),X4) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__lt) ).
fof(f37702,plain,
spl47_1323,
inference(avatar_split_clause,[],[f5476,f37700]) ).
fof(f37700,plain,
( spl47_1323
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X0),X2)),X3)
| c_Groups_Oone__class_Oone(X5) != c_Groups_Oplus__class_Oplus(X5,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X5,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X5,X4,X3)
| ~ class_Rings_Olinordered__semiring__1(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1323])]) ).
fof(f5476,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X0),X2)),X3)
| c_Groups_Oone__class_Oone(X5) != c_Groups_Oplus__class_Oplus(X5,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X5,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X5,X4,X3)
| ~ class_Rings_Olinordered__semiring__1(X5) ),
inference(cnf_transformation,[],[f3447]) ).
fof(f3447,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X0),X2)),X3)
| c_Groups_Oone__class_Oone(X5) != c_Groups_Oplus__class_Oplus(X5,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X5,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X5,X4,X3)
| ~ class_Rings_Olinordered__semiring__1(X5) ),
inference(flattening,[],[f3446]) ).
fof(f3446,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X0),X2)),X3)
| c_Groups_Oone__class_Oone(X5) != c_Groups_Oplus__class_Oplus(X5,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X5,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X5,X4,X3)
| ~ class_Rings_Olinordered__semiring__1(X5) ),
inference(ennf_transformation,[],[f2242]) ).
fof(f2242,plain,
! [X0,X1,X2,X3,X4,X5] :
( class_Rings_Olinordered__semiring__1(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X3)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X2,X3)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X1)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X0)
=> ( c_Groups_Oone__class_Oone(X5) = c_Groups_Oplus__class_Oplus(X5,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X0),X2)),X3) ) ) ) ) ) ),
inference(rectify,[],[f633]) ).
fof(f633,axiom,
! [X59,X60,X10,X4,X6,X5] :
( class_Rings_Olinordered__semiring__1(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X6,X4)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X10,X4)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X60)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X59)
=> ( c_Groups_Oone__class_Oone(X5) = c_Groups_Oplus__class_Oplus(X5,X60,X59)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X60),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X59),X10)),X4) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__le) ).
fof(f37696,plain,
spl47_1322,
inference(avatar_split_clause,[],[f5399,f37694]) ).
fof(f37694,plain,
( spl47_1322
<=> ! [X4,X0,X3,X2,X1] :
( c_Groups_Oplus__class_Oplus(X4,c_Rings_Oinverse__class_Odivide(X4,X1,X3),c_Rings_Oinverse__class_Odivide(X4,X0,X2)) = c_Rings_Oinverse__class_Odivide(X4,c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2))
| c_Groups_Ozero__class_Ozero(X4) = X2
| c_Groups_Ozero__class_Ozero(X4) = X3
| ~ class_Fields_Ofield(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1322])]) ).
fof(f5399,plain,
! [X2,X3,X0,X1,X4] :
( c_Groups_Oplus__class_Oplus(X4,c_Rings_Oinverse__class_Odivide(X4,X1,X3),c_Rings_Oinverse__class_Odivide(X4,X0,X2)) = c_Rings_Oinverse__class_Odivide(X4,c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2))
| c_Groups_Ozero__class_Ozero(X4) = X2
| c_Groups_Ozero__class_Ozero(X4) = X3
| ~ class_Fields_Ofield(X4) ),
inference(cnf_transformation,[],[f3374]) ).
fof(f3374,plain,
! [X0,X1,X2,X3,X4] :
( c_Groups_Oplus__class_Oplus(X4,c_Rings_Oinverse__class_Odivide(X4,X1,X3),c_Rings_Oinverse__class_Odivide(X4,X0,X2)) = c_Rings_Oinverse__class_Odivide(X4,c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2))
| c_Groups_Ozero__class_Ozero(X4) = X2
| c_Groups_Ozero__class_Ozero(X4) = X3
| ~ class_Fields_Ofield(X4) ),
inference(flattening,[],[f3373]) ).
fof(f3373,plain,
! [X0,X1,X2,X3,X4] :
( c_Groups_Oplus__class_Oplus(X4,c_Rings_Oinverse__class_Odivide(X4,X1,X3),c_Rings_Oinverse__class_Odivide(X4,X0,X2)) = c_Rings_Oinverse__class_Odivide(X4,c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2))
| c_Groups_Ozero__class_Ozero(X4) = X2
| c_Groups_Ozero__class_Ozero(X4) = X3
| ~ class_Fields_Ofield(X4) ),
inference(ennf_transformation,[],[f2194]) ).
fof(f2194,plain,
! [X0,X1,X2,X3,X4] :
( class_Fields_Ofield(X4)
=> ( c_Groups_Ozero__class_Ozero(X4) != X3
=> ( c_Groups_Ozero__class_Ozero(X4) != X2
=> c_Groups_Oplus__class_Oplus(X4,c_Rings_Oinverse__class_Odivide(X4,X1,X3),c_Rings_Oinverse__class_Odivide(X4,X0,X2)) = c_Rings_Oinverse__class_Odivide(X4,c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2)) ) ) ),
inference(rectify,[],[f969]) ).
fof(f969,axiom,
! [X48,X6,X26,X10,X5] :
( class_Fields_Ofield(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X10
=> ( c_Groups_Ozero__class_Ozero(X5) != X26
=> c_Groups_Oplus__class_Oplus(X5,c_Rings_Oinverse__class_Odivide(X5,X6,X10),c_Rings_Oinverse__class_Odivide(X5,X48,X26)) = c_Rings_Oinverse__class_Odivide(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X26)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__eq) ).
fof(f37692,plain,
spl47_1321,
inference(avatar_split_clause,[],[f5398,f37690]) ).
fof(f37690,plain,
( spl47_1321
<=> ! [X4,X0,X3,X2,X1] :
( c_Groups_Ominus__class_Ominus(X4,c_Rings_Oinverse__class_Odivide(X4,X1,X3),c_Rings_Oinverse__class_Odivide(X4,X0,X2)) = c_Rings_Oinverse__class_Odivide(X4,c_Groups_Ominus__class_Ominus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2))
| c_Groups_Ozero__class_Ozero(X4) = X2
| c_Groups_Ozero__class_Ozero(X4) = X3
| ~ class_Fields_Ofield(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1321])]) ).
fof(f5398,plain,
! [X2,X3,X0,X1,X4] :
( c_Groups_Ominus__class_Ominus(X4,c_Rings_Oinverse__class_Odivide(X4,X1,X3),c_Rings_Oinverse__class_Odivide(X4,X0,X2)) = c_Rings_Oinverse__class_Odivide(X4,c_Groups_Ominus__class_Ominus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2))
| c_Groups_Ozero__class_Ozero(X4) = X2
| c_Groups_Ozero__class_Ozero(X4) = X3
| ~ class_Fields_Ofield(X4) ),
inference(cnf_transformation,[],[f3372]) ).
fof(f3372,plain,
! [X0,X1,X2,X3,X4] :
( c_Groups_Ominus__class_Ominus(X4,c_Rings_Oinverse__class_Odivide(X4,X1,X3),c_Rings_Oinverse__class_Odivide(X4,X0,X2)) = c_Rings_Oinverse__class_Odivide(X4,c_Groups_Ominus__class_Ominus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2))
| c_Groups_Ozero__class_Ozero(X4) = X2
| c_Groups_Ozero__class_Ozero(X4) = X3
| ~ class_Fields_Ofield(X4) ),
inference(flattening,[],[f3371]) ).
fof(f3371,plain,
! [X0,X1,X2,X3,X4] :
( c_Groups_Ominus__class_Ominus(X4,c_Rings_Oinverse__class_Odivide(X4,X1,X3),c_Rings_Oinverse__class_Odivide(X4,X0,X2)) = c_Rings_Oinverse__class_Odivide(X4,c_Groups_Ominus__class_Ominus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2))
| c_Groups_Ozero__class_Ozero(X4) = X2
| c_Groups_Ozero__class_Ozero(X4) = X3
| ~ class_Fields_Ofield(X4) ),
inference(ennf_transformation,[],[f2193]) ).
fof(f2193,plain,
! [X0,X1,X2,X3,X4] :
( class_Fields_Ofield(X4)
=> ( c_Groups_Ozero__class_Ozero(X4) != X3
=> ( c_Groups_Ozero__class_Ozero(X4) != X2
=> c_Groups_Ominus__class_Ominus(X4,c_Rings_Oinverse__class_Odivide(X4,X1,X3),c_Rings_Oinverse__class_Odivide(X4,X0,X2)) = c_Rings_Oinverse__class_Odivide(X4,c_Groups_Ominus__class_Ominus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2)) ) ) ),
inference(rectify,[],[f970]) ).
fof(f970,axiom,
! [X48,X6,X26,X10,X5] :
( class_Fields_Ofield(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X10
=> ( c_Groups_Ozero__class_Ozero(X5) != X26
=> c_Groups_Ominus__class_Ominus(X5,c_Rings_Oinverse__class_Odivide(X5,X6,X10),c_Rings_Oinverse__class_Odivide(X5,X48,X26)) = c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X48),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X26)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__frac__eq) ).
fof(f37236,plain,
spl47_1320,
inference(avatar_split_clause,[],[f5457,f37234]) ).
fof(f37234,plain,
( spl47_1320
<=> ! [X4,X0,X3,X2,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1320])]) ).
fof(f5457,plain,
! [X2,X3,X0,X1,X4] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(cnf_transformation,[],[f3431]) ).
fof(f3431,plain,
! [X0,X1,X2,X3,X4] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(ennf_transformation,[],[f2230]) ).
fof(f2230,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0) ),
inference(rectify,[],[f864]) ).
fof(f864,axiom,
! [X7,X21,X60,X32,X33] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X32)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X60),X21),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X60),X7)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,X33)),X60),X21),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).
fof(f37232,plain,
( spl47_1319
| ~ spl47_308
| ~ spl47_1302 ),
inference(avatar_split_clause,[],[f36295,f34190,f7461,f37230]) ).
fof(f37230,plain,
( spl47_1319
<=> ! [X0] : c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1319])]) ).
fof(f7461,plain,
( spl47_308
<=> ! [X0,X1] :
( c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Divides_Osemiring__div(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_308])]) ).
fof(f36295,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = X0
| ~ spl47_308
| ~ spl47_1302 ),
inference(resolution,[],[f34191,f7462]) ).
fof(f7462,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 )
| ~ spl47_308 ),
inference(avatar_component_clause,[],[f7461]) ).
fof(f37228,plain,
spl47_1318,
inference(avatar_split_clause,[],[f5456,f37226]) ).
fof(f37226,plain,
( spl47_1318
<=> ! [X4,X0,X3,X2,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1318])]) ).
fof(f5456,plain,
! [X2,X3,X0,X1,X4] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(cnf_transformation,[],[f3430]) ).
fof(f3430,plain,
! [X0,X1,X2,X3,X4] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(ennf_transformation,[],[f2229]) ).
fof(f2229,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0)) ),
inference(rectify,[],[f867]) ).
fof(f867,axiom,
! [X7,X21,X60,X33,X32] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32,X33)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X60),X21),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X60),X7)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,X32)),X60),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).
fof(f35955,plain,
spl47_1317,
inference(avatar_split_clause,[],[f6011,f35953]) ).
fof(f35953,plain,
( spl47_1317
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Oorder(X2,X0,X1)))),X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Rings_Oidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1317])]) ).
fof(f6011,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Oorder(X2,X0,X1)))),X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Rings_Oidom(X2) ),
inference(forward_demodulation,[],[f5620,f4240]) ).
fof(f4240,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
inference(cnf_transformation,[],[f1356]) ).
fof(f1356,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
inference(rectify,[],[f392]) ).
fof(f392,axiom,
! [X7,X21] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X7) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(f5620,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(X2,X0,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Rings_Oidom(X2) ),
inference(definition_unfolding,[],[f4809,f4118]) ).
fof(f4809,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Nat_OSuc(c_Polynomial_Oorder(X2,X0,X1)))),X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f2781]) ).
fof(f2781,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Nat_OSuc(c_Polynomial_Oorder(X2,X0,X1)))),X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Rings_Oidom(X2) ),
inference(flattening,[],[f2780]) ).
fof(f2780,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Nat_OSuc(c_Polynomial_Oorder(X2,X0,X1)))),X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Rings_Oidom(X2) ),
inference(ennf_transformation,[],[f1755]) ).
fof(f1755,plain,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Nat_OSuc(c_Polynomial_Oorder(X2,X0,X1)))),X1)) ) ),
inference(rectify,[],[f389]) ).
fof(f389,axiom,
! [X4,X8,X5] :
( class_Rings_Oidom(X5)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) != X8
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X5)),c_Polynomial_OpCons(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),c_Polynomial_OpCons(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))))),c_Nat_OSuc(c_Polynomial_Oorder(X5,X4,X8)))),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__2) ).
fof(f35951,plain,
spl47_1316,
inference(avatar_split_clause,[],[f6010,f35949]) ).
fof(f35949,plain,
( spl47_1316
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ominus__class_Ominus(X2,X1,X0)),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Rings_Ocomm__ring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1316])]) ).
fof(f6010,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ominus__class_Ominus(X2,X1,X0)),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(forward_demodulation,[],[f6009,f4114]) ).
fof(f4114,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f1238]) ).
fof(f1238,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f311]) ).
fof(f311,axiom,
! [X21] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X21,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(f6009,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ominus__class_Ominus(X2,X1,X0)),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(forward_demodulation,[],[f6008,f4240]) ).
fof(f6008,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ominus__class_Ominus(X2,X1,X0)),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(forward_demodulation,[],[f5619,f4240]) ).
fof(f5619,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ominus__class_Ominus(X2,X1,X0)),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(definition_unfolding,[],[f4750,f4118,f4118,f4118,f4118]) ).
fof(f4750,plain,
! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ominus__class_Ominus(X2,X1,X0)),c_Groups_Oplus__class_Oplus(X2,X1,X0))
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(cnf_transformation,[],[f2707]) ).
fof(f2707,plain,
! [X0,X1,X2] :
( c_Groups_Ominus__class_Ominus(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ominus__class_Ominus(X2,X1,X0)),c_Groups_Oplus__class_Oplus(X2,X1,X0))
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(ennf_transformation,[],[f1710]) ).
fof(f1710,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__ring__1(X2)
=> c_Groups_Ominus__class_Ominus(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ominus__class_Ominus(X2,X1,X0)),c_Groups_Oplus__class_Oplus(X2,X1,X0)) ),
inference(rectify,[],[f883]) ).
fof(f883,axiom,
! [X10,X6,X5] :
( class_Rings_Ocomm__ring__1(X5)
=> c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X10),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X6,X10)),c_Groups_Oplus__class_Oplus(X5,X6,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__diff) ).
fof(f35947,plain,
spl47_1315,
inference(avatar_split_clause,[],[f5469,f35945]) ).
fof(f35945,plain,
( spl47_1315
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1315])]) ).
fof(f5469,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(cnf_transformation,[],[f3902]) ).
fof(f3902,plain,
! [X0,X1,X2,X3,X4] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(nnf_transformation,[],[f3437]) ).
fof(f3437,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(ennf_transformation,[],[f2236]) ).
fof(f2236,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0) ) ),
inference(rectify,[],[f875]) ).
fof(f875,axiom,
! [X11,X14,X85,X80,X81] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X81,X80)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X80),X85),X14),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X81),X85),X11))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X80,X81)),X85),X14),X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff1) ).
fof(f35943,plain,
spl47_1314,
inference(avatar_split_clause,[],[f5468,f35941]) ).
fof(f35941,plain,
( spl47_1314
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1314])]) ).
fof(f5468,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(cnf_transformation,[],[f3902]) ).
fof(f35939,plain,
spl47_1313,
inference(avatar_split_clause,[],[f5467,f35937]) ).
fof(f35937,plain,
( spl47_1313
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1313])]) ).
fof(f5467,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(cnf_transformation,[],[f3901]) ).
fof(f3901,plain,
! [X0,X1,X2,X3,X4] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(nnf_transformation,[],[f3436]) ).
fof(f3436,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(ennf_transformation,[],[f2235]) ).
fof(f2235,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0)) ) ),
inference(rectify,[],[f876]) ).
fof(f876,axiom,
! [X11,X14,X85,X81,X80] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X80,X81)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X80),X85),X14),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X81),X85),X11))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X81,X80)),X85),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff2) ).
fof(f35935,plain,
spl47_1312,
inference(avatar_split_clause,[],[f5466,f35933]) ).
fof(f35933,plain,
( spl47_1312
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1312])]) ).
fof(f5466,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(cnf_transformation,[],[f3901]) ).
fof(f35931,plain,
( ~ spl47_7
| ~ spl47_157
| spl47_1302 ),
inference(avatar_split_clause,[],[f35706,f34190,f6807,f6066]) ).
fof(f6066,plain,
( spl47_7
<=> class_Fields_Ofield(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_7])]) ).
fof(f6807,plain,
( spl47_157
<=> ! [X0] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0))
| ~ class_Fields_Ofield(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_157])]) ).
fof(f35706,plain,
( ~ class_Fields_Ofield(tc_Complex_Ocomplex)
| ~ spl47_157
| spl47_1302 ),
inference(resolution,[],[f34192,f6808]) ).
fof(f6808,plain,
( ! [X0] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0))
| ~ class_Fields_Ofield(X0) )
| ~ spl47_157 ),
inference(avatar_component_clause,[],[f6807]) ).
fof(f34192,plain,
( ~ class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| spl47_1302 ),
inference(avatar_component_clause,[],[f34190]) ).
fof(f35930,plain,
spl47_1311,
inference(avatar_split_clause,[],[f5465,f35928]) ).
fof(f35928,plain,
( spl47_1311
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1311])]) ).
fof(f5465,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(cnf_transformation,[],[f3900]) ).
fof(f3900,plain,
! [X0,X1,X2,X3,X4] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(nnf_transformation,[],[f3435]) ).
fof(f3435,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(ennf_transformation,[],[f2234]) ).
fof(f2234,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0) ) ),
inference(rectify,[],[f863]) ).
fof(f863,axiom,
! [X11,X14,X85,X80,X81] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X81,X80)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X80),X85),X14),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X81),X85),X11))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X80,X81)),X85),X14),X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).
fof(f35926,plain,
spl47_1310,
inference(avatar_split_clause,[],[f5464,f35924]) ).
fof(f35924,plain,
( spl47_1310
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1310])]) ).
fof(f5464,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(cnf_transformation,[],[f3900]) ).
fof(f35922,plain,
spl47_1309,
inference(avatar_split_clause,[],[f5463,f35920]) ).
fof(f35920,plain,
( spl47_1309
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1309])]) ).
fof(f5463,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(cnf_transformation,[],[f3899]) ).
fof(f3899,plain,
! [X0,X1,X2,X3,X4] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(nnf_transformation,[],[f3434]) ).
fof(f3434,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(ennf_transformation,[],[f2233]) ).
fof(f2233,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0)) ) ),
inference(rectify,[],[f866]) ).
fof(f866,axiom,
! [X11,X14,X85,X81,X80] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X80,X81)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X80),X85),X14),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X81),X85),X11))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X81,X80)),X85),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).
fof(f35918,plain,
spl47_1308,
inference(avatar_split_clause,[],[f5462,f35916]) ).
fof(f35916,plain,
( spl47_1308
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1308])]) ).
fof(f5462,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(cnf_transformation,[],[f3899]) ).
fof(f35914,plain,
spl47_1307,
inference(avatar_split_clause,[],[f5392,f35912]) ).
fof(f35912,plain,
( spl47_1307
<=> ! [X5,X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X4,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),X1)),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Odvd(X3)
| ~ class_Rings_Ocomm__ring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1307])]) ).
fof(f5392,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X4,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),X1)),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Odvd(X3)
| ~ class_Rings_Ocomm__ring(X3) ),
inference(cnf_transformation,[],[f3877]) ).
fof(f3877,plain,
! [X0,X1,X2,X3] :
( ! [X4,X5] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X4,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),X1)),X0))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),X1)),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X4,X0))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Odvd(X3)
| ~ class_Rings_Ocomm__ring(X3) ),
inference(nnf_transformation,[],[f3366]) ).
fof(f3366,plain,
! [X0,X1,X2,X3] :
( ! [X4,X5] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X4,X0)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),X1)),X0))) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Odvd(X3)
| ~ class_Rings_Ocomm__ring(X3) ),
inference(flattening,[],[f3365]) ).
fof(f3365,plain,
! [X0,X1,X2,X3] :
( ! [X4,X5] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X4,X0)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),X1)),X0))) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Odvd(X3)
| ~ class_Rings_Ocomm__ring(X3) ),
inference(ennf_transformation,[],[f2185]) ).
fof(f2185,plain,
! [X0,X1,X2,X3] :
( ( class_Rings_Odvd(X3)
& class_Rings_Ocomm__ring(X3) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
=> ! [X4,X5] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X4,X0)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),X1)),X0))) ) ) ),
inference(rectify,[],[f853]) ).
fof(f853,axiom,
! [X63,X83,X52,X5] :
( ( class_Rings_Odvd(X5)
& class_Rings_Ocomm__ring(X5) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X52),X83))
=> ! [X2,X45] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X52),c_Groups_Oplus__class_Oplus(X5,X2,X63)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X52),c_Groups_Oplus__class_Oplus(X5,c_Groups_Ominus__class_Ominus(X5,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X45),X83)),X63))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__period_I3_J) ).
fof(f35910,plain,
spl47_1306,
inference(avatar_split_clause,[],[f5391,f35908]) ).
fof(f35908,plain,
( spl47_1306
<=> ! [X2,X3,X4,X0,X5,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),X1)),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X4,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Odvd(X3)
| ~ class_Rings_Ocomm__ring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1306])]) ).
fof(f5391,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),X1)),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X4,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Odvd(X3)
| ~ class_Rings_Ocomm__ring(X3) ),
inference(cnf_transformation,[],[f3877]) ).
fof(f35906,plain,
spl47_1305,
inference(avatar_split_clause,[],[f4904,f35904]) ).
fof(f35904,plain,
( spl47_1305
<=> ! [X2,X0,X1] :
( hAPP(c_Polynomial_Ocoeff(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Polynomial_Ocoeff(X2,X1),c_Polynomial_Odegree(X2,X1))),hAPP(c_Polynomial_Ocoeff(X2,X0),c_Polynomial_Odegree(X2,X0)))
| ~ class_Rings_Ocomm__semiring__0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1305])]) ).
fof(f4904,plain,
! [X2,X0,X1] :
( hAPP(c_Polynomial_Ocoeff(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Polynomial_Ocoeff(X2,X1),c_Polynomial_Odegree(X2,X1))),hAPP(c_Polynomial_Ocoeff(X2,X0),c_Polynomial_Odegree(X2,X0)))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(cnf_transformation,[],[f2876]) ).
fof(f2876,plain,
! [X0,X1,X2] :
( hAPP(c_Polynomial_Ocoeff(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Polynomial_Ocoeff(X2,X1),c_Polynomial_Odegree(X2,X1))),hAPP(c_Polynomial_Ocoeff(X2,X0),c_Polynomial_Odegree(X2,X0)))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(ennf_transformation,[],[f1824]) ).
fof(f1824,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__0(X2)
=> hAPP(c_Polynomial_Ocoeff(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Polynomial_Ocoeff(X2,X1),c_Polynomial_Odegree(X2,X1))),hAPP(c_Polynomial_Ocoeff(X2,X0),c_Polynomial_Odegree(X2,X0))) ),
inference(rectify,[],[f879]) ).
fof(f879,axiom,
! [X13,X8,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> hAPP(c_Polynomial_Ocoeff(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X8),X13)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X5,X8),c_Polynomial_Odegree(X5,X13))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Polynomial_Ocoeff(X5,X8),c_Polynomial_Odegree(X5,X8))),hAPP(c_Polynomial_Ocoeff(X5,X13),c_Polynomial_Odegree(X5,X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__mult__degree__sum) ).
fof(f35895,plain,
spl47_1304,
inference(avatar_split_clause,[],[f4751,f35893]) ).
fof(f35893,plain,
( spl47_1304
<=> ! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Polynomial_Osynthetic__div(X2,X0,X1)),c_Polynomial_OpCons(X2,hAPP(c_Polynomial_Opoly(X2,X0),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)))) = X0
| ~ class_Rings_Ocomm__ring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1304])]) ).
fof(f4751,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Polynomial_Osynthetic__div(X2,X0,X1)),c_Polynomial_OpCons(X2,hAPP(c_Polynomial_Opoly(X2,X0),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)))) = X0
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(cnf_transformation,[],[f2708]) ).
fof(f2708,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Polynomial_Osynthetic__div(X2,X0,X1)),c_Polynomial_OpCons(X2,hAPP(c_Polynomial_Opoly(X2,X0),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)))) = X0
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(ennf_transformation,[],[f1711]) ).
fof(f1711,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__ring__1(X2)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Polynomial_Osynthetic__div(X2,X0,X1)),c_Polynomial_OpCons(X2,hAPP(c_Polynomial_Opoly(X2,X0),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)))) = X0 ),
inference(rectify,[],[f462]) ).
fof(f462,axiom,
! [X8,X16,X5] :
( class_Rings_Ocomm__ring__1(X5)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),c_Polynomial_OpCons(X5,c_Groups_Ouminus__class_Ouminus(X5,X16),c_Polynomial_OpCons(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))))),c_Polynomial_Osynthetic__div(X5,X8,X16)),c_Polynomial_OpCons(X5,hAPP(c_Polynomial_Opoly(X5,X8),X16),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)))) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__correct_H) ).
fof(f34197,plain,
( ~ spl47_1302
| spl47_1303
| ~ spl47_219
| ~ spl47_748 ),
inference(avatar_split_clause,[],[f16399,f14617,f7059,f34194,f34190]) ).
fof(f34194,plain,
( spl47_1303
<=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)),v_p) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1303])]) ).
fof(f14617,plain,
( spl47_748
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| ~ class_Divides_Osemiring__div(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_748])]) ).
fof(f16399,plain,
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)),v_p)
| ~ class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ spl47_219
| ~ spl47_748 ),
inference(resolution,[],[f7061,f14618]) ).
fof(f14618,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,X0,X1)
| ~ class_Divides_Osemiring__div(X2) )
| ~ spl47_748 ),
inference(avatar_component_clause,[],[f14617]) ).
fof(f34018,plain,
spl47_1301,
inference(avatar_split_clause,[],[f5485,f34016]) ).
fof(f34016,plain,
( spl47_1301
<=> ! [X2,X3,X4,X0,X5,X1] :
( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0)
| ~ class_Rings_Oordered__ring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1301])]) ).
fof(f5485,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0)
| ~ class_Rings_Oordered__ring(X5) ),
inference(cnf_transformation,[],[f3907]) ).
fof(f3907,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0) )
& ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0)
| ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)) ) )
| ~ class_Rings_Oordered__ring(X5) ),
inference(nnf_transformation,[],[f3453]) ).
fof(f3453,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0) )
| ~ class_Rings_Oordered__ring(X5) ),
inference(ennf_transformation,[],[f2247]) ).
fof(f2247,plain,
! [X0,X1,X2,X3,X4,X5] :
( class_Rings_Oordered__ring(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0) ) ),
inference(rectify,[],[f850]) ).
fof(f850,axiom,
! [X52,X29,X24,X82,X12,X5] :
( class_Rings_Oordered__ring(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X82),X24),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X29),X82),X52))
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X12,X29)),X82),X24),X52) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff1) ).
fof(f34014,plain,
spl47_1300,
inference(avatar_split_clause,[],[f5484,f34012]) ).
fof(f34012,plain,
( spl47_1300
<=> ! [X5,X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0)
| ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| ~ class_Rings_Oordered__ring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1300])]) ).
fof(f5484,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0)
| ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| ~ class_Rings_Oordered__ring(X5) ),
inference(cnf_transformation,[],[f3907]) ).
fof(f34010,plain,
spl47_1299,
inference(avatar_split_clause,[],[f5483,f34008]) ).
fof(f34008,plain,
( spl47_1299
<=> ! [X2,X3,X4,X0,X5,X1] :
( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| ~ c_Orderings_Oord__class_Oless(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0))
| ~ class_Rings_Oordered__ring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1299])]) ).
fof(f5483,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| ~ c_Orderings_Oord__class_Oless(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0))
| ~ class_Rings_Oordered__ring(X5) ),
inference(cnf_transformation,[],[f3906]) ).
fof(f3906,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| ~ c_Orderings_Oord__class_Oless(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0)) )
& ( c_Orderings_Oord__class_Oless(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0))
| ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)) ) )
| ~ class_Rings_Oordered__ring(X5) ),
inference(nnf_transformation,[],[f3452]) ).
fof(f3452,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
<=> c_Orderings_Oord__class_Oless(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0)) )
| ~ class_Rings_Oordered__ring(X5) ),
inference(ennf_transformation,[],[f2246]) ).
fof(f2246,plain,
! [X0,X1,X2,X3,X4,X5] :
( class_Rings_Oordered__ring(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
<=> c_Orderings_Oord__class_Oless(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0)) ) ),
inference(rectify,[],[f851]) ).
fof(f851,axiom,
! [X52,X29,X24,X82,X12,X5] :
( class_Rings_Oordered__ring(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X82),X24),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X29),X82),X52))
<=> c_Orderings_Oord__class_Oless(X5,X24,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X29,X12)),X82),X52)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff2) ).
fof(f34006,plain,
spl47_1298,
inference(avatar_split_clause,[],[f5482,f34004]) ).
fof(f34004,plain,
( spl47_1298
<=> ! [X5,X4,X2,X0,X3,X1] :
( c_Orderings_Oord__class_Oless(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0))
| ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| ~ class_Rings_Oordered__ring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1298])]) ).
fof(f5482,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Orderings_Oord__class_Oless(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0))
| ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| ~ class_Rings_Oordered__ring(X5) ),
inference(cnf_transformation,[],[f3906]) ).
fof(f34002,plain,
spl47_1297,
inference(avatar_split_clause,[],[f5481,f34000]) ).
fof(f34000,plain,
( spl47_1297
<=> ! [X2,X3,X4,X0,X5,X1] :
( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0)
| ~ class_Rings_Oordered__ring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1297])]) ).
fof(f5481,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0)
| ~ class_Rings_Oordered__ring(X5) ),
inference(cnf_transformation,[],[f3905]) ).
fof(f3905,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0) )
& ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)) ) )
| ~ class_Rings_Oordered__ring(X5) ),
inference(nnf_transformation,[],[f3451]) ).
fof(f3451,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
<=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0) )
| ~ class_Rings_Oordered__ring(X5) ),
inference(ennf_transformation,[],[f2245]) ).
fof(f2245,plain,
! [X0,X1,X2,X3,X4,X5] :
( class_Rings_Oordered__ring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
<=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0) ) ),
inference(rectify,[],[f849]) ).
fof(f849,axiom,
! [X52,X29,X24,X82,X12,X5] :
( class_Rings_Oordered__ring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X82),X24),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X29),X82),X52))
<=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X12,X29)),X82),X24),X52) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff1) ).
fof(f33998,plain,
spl47_1296,
inference(avatar_split_clause,[],[f5480,f33996]) ).
fof(f33996,plain,
( spl47_1296
<=> ! [X5,X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| ~ class_Rings_Oordered__ring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1296])]) ).
fof(f5480,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| ~ class_Rings_Oordered__ring(X5) ),
inference(cnf_transformation,[],[f3905]) ).
fof(f33994,plain,
spl47_1295,
inference(avatar_split_clause,[],[f5479,f33992]) ).
fof(f33992,plain,
( spl47_1295
<=> ! [X2,X3,X4,X0,X5,X1] :
( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0))
| ~ class_Rings_Oordered__ring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1295])]) ).
fof(f5479,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0))
| ~ class_Rings_Oordered__ring(X5) ),
inference(cnf_transformation,[],[f3904]) ).
fof(f3904,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0)) )
& ( c_Orderings_Oord__class_Oless__eq(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)) ) )
| ~ class_Rings_Oordered__ring(X5) ),
inference(nnf_transformation,[],[f3450]) ).
fof(f3450,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
<=> c_Orderings_Oord__class_Oless__eq(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0)) )
| ~ class_Rings_Oordered__ring(X5) ),
inference(ennf_transformation,[],[f2244]) ).
fof(f2244,plain,
! [X0,X1,X2,X3,X4,X5] :
( class_Rings_Oordered__ring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
<=> c_Orderings_Oord__class_Oless__eq(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0)) ) ),
inference(rectify,[],[f848]) ).
fof(f848,axiom,
! [X52,X29,X24,X82,X12,X5] :
( class_Rings_Oordered__ring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X82),X24),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X29),X82),X52))
<=> c_Orderings_Oord__class_Oless__eq(X5,X24,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X29,X12)),X82),X52)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff2) ).
fof(f33990,plain,
spl47_1294,
inference(avatar_split_clause,[],[f5478,f33988]) ).
fof(f33988,plain,
( spl47_1294
<=> ! [X5,X4,X2,X0,X3,X1] :
( c_Orderings_Oord__class_Oless__eq(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| ~ class_Rings_Oordered__ring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1294])]) ).
fof(f5478,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(X5,X2,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X1,X4)),X3),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0))
| ~ class_Rings_Oordered__ring(X5) ),
inference(cnf_transformation,[],[f3904]) ).
fof(f33983,plain,
spl47_1293,
inference(avatar_split_clause,[],[f5473,f33981]) ).
fof(f33981,plain,
( spl47_1293
<=> ! [X2,X4,X0,X3,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X3),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1293])]) ).
fof(f5473,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X3),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X0)) ),
inference(cnf_transformation,[],[f3442]) ).
fof(f3442,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X3),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X0)) ),
inference(flattening,[],[f3441]) ).
fof(f3441,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X3),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X0)) ),
inference(ennf_transformation,[],[f2239]) ).
fof(f2239,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X3),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X0))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X1) ) ) ) ),
inference(rectify,[],[f721]) ).
fof(f721,axiom,
! [X34,X13,X67,X68,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17),X68),X67),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17),X13),X34))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X67)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X67,X17)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X34,X17)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X68,X13) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).
fof(f33979,plain,
spl47_1292,
inference(avatar_split_clause,[],[f5472,f33977]) ).
fof(f33977,plain,
( spl47_1292
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X3),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1292])]) ).
fof(f5472,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X3),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X0)) ),
inference(cnf_transformation,[],[f3440]) ).
fof(f3440,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X3),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X0)) ),
inference(flattening,[],[f3439]) ).
fof(f3439,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X3),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X0)) ),
inference(ennf_transformation,[],[f2238]) ).
fof(f2238,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X3),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X1),X0))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X0)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3) ) ) ) ),
inference(rectify,[],[f719]) ).
fof(f719,axiom,
! [X34,X13,X67,X68,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17),X68),X67),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17),X13),X34))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X34,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,X34)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,X67)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X13,X68) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
fof(f33975,plain,
spl47_1291,
inference(avatar_split_clause,[],[f5458,f33973]) ).
fof(f33973,plain,
( spl47_1291
<=> ! [X4,X0,X3,X2,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1) = X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1291])]) ).
fof(f5458,plain,
! [X2,X3,X0,X1,X4] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1) = X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(cnf_transformation,[],[f3897]) ).
fof(f3897,plain,
! [X0,X1,X2,X3,X4] :
( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1) != X0 )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1) = X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(nnf_transformation,[],[f3432]) ).
fof(f3432,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0)
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1) = X0 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(ennf_transformation,[],[f2231]) ).
fof(f2231,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0)
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1) = X0 ) ),
inference(rectify,[],[f865]) ).
fof(f865,axiom,
! [X11,X14,X85,X80,X81] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X81,X80)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X80),X85),X14) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X81),X85),X11)
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X80,X81)),X85),X14) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).
fof(f33971,plain,
spl47_1290,
inference(avatar_split_clause,[],[f5433,f33969]) ).
fof(f33969,plain,
( spl47_1290
<=> ! [X4,X0,X3,X2,X1] :
( X0 = X2
| X1 = X3
| c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) != c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1290])]) ).
fof(f5433,plain,
! [X2,X3,X0,X1,X4] :
( X0 = X2
| X1 = X3
| c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) != c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4) ),
inference(cnf_transformation,[],[f3892]) ).
fof(f3892,plain,
! [X0,X1,X2,X3,X4] :
( ( ( c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2))
| ( X0 != X2
& X1 != X3 ) )
& ( X0 = X2
| X1 = X3
| c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) != c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2)) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4) ),
inference(flattening,[],[f3891]) ).
fof(f3891,plain,
! [X0,X1,X2,X3,X4] :
( ( ( c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2))
| ( X0 != X2
& X1 != X3 ) )
& ( X0 = X2
| X1 = X3
| c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) != c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2)) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4) ),
inference(nnf_transformation,[],[f3408]) ).
fof(f3408,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2))
<=> ( X0 = X2
| X1 = X3 ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4) ),
inference(ennf_transformation,[],[f2213]) ).
fof(f2213,plain,
! [X0,X1,X2,X3,X4] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4)
=> ( c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2))
<=> ( X0 = X2
| X1 = X3 ) ) ),
inference(rectify,[],[f488]) ).
fof(f488,axiom,
! [X30,X15,X25,X49,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X49),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X30)) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X49),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X25))
<=> ( X25 = X30
| X15 = X49 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__eq) ).
fof(f33967,plain,
spl47_1289,
inference(avatar_split_clause,[],[f5424,f33965]) ).
fof(f33965,plain,
( spl47_1289
<=> ! [X2,X4,X0,X3,X1] :
( c_Groups_Ominus__class_Ominus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),c_Groups_Ominus__class_Ominus(X4,X2,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ominus__class_Ominus(X4,X3,X1)),X0))
| ~ class_Rings_Oring(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1289])]) ).
fof(f5424,plain,
! [X2,X3,X0,X1,X4] :
( c_Groups_Ominus__class_Ominus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),c_Groups_Ominus__class_Ominus(X4,X2,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ominus__class_Ominus(X4,X3,X1)),X0))
| ~ class_Rings_Oring(X4) ),
inference(cnf_transformation,[],[f3395]) ).
fof(f3395,plain,
! [X0,X1,X2,X3,X4] :
( c_Groups_Ominus__class_Ominus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),c_Groups_Ominus__class_Ominus(X4,X2,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ominus__class_Ominus(X4,X3,X1)),X0))
| ~ class_Rings_Oring(X4) ),
inference(ennf_transformation,[],[f2205]) ).
fof(f2205,plain,
! [X0,X1,X2,X3,X4] :
( class_Rings_Oring(X4)
=> c_Groups_Ominus__class_Ominus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),c_Groups_Ominus__class_Ominus(X4,X2,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ominus__class_Ominus(X4,X3,X1)),X0)) ),
inference(rectify,[],[f837]) ).
fof(f837,axiom,
! [X17,X4,X10,X6,X5] :
( class_Rings_Oring(X5)
=> c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17)) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),c_Groups_Ominus__class_Ominus(X5,X10,X17)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X6,X4)),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__diff__mult) ).
fof(f33892,plain,
spl47_1288,
inference(avatar_split_clause,[],[f5646,f33890]) ).
fof(f33890,plain,
( spl47_1288
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Olinordered__semidom(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1288])]) ).
fof(f5646,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(definition_unfolding,[],[f5289,f4118,f4118]) ).
fof(f5289,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X1)) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Nat_OSuc(X1))
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(cnf_transformation,[],[f3228]) ).
fof(f3228,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X1)) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Nat_OSuc(X1))
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(flattening,[],[f3227]) ).
fof(f3227,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X1)) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Nat_OSuc(X1))
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(ennf_transformation,[],[f2089]) ).
fof(f2089,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X1)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Nat_OSuc(X1))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> X0 = X2 ) ) ) ),
inference(rectify,[],[f120]) ).
fof(f120,axiom,
! [X17,X7,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Nat_OSuc(X7)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X17),c_Nat_OSuc(X7))
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X17)
=> X4 = X17 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__base) ).
fof(f33888,plain,
( spl47_1287
| ~ spl47_219
| ~ spl47_815 ),
inference(avatar_split_clause,[],[f32581,f16525,f7059,f33886]) ).
fof(f33886,plain,
( spl47_1287
<=> ! [X0] :
( sP18(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)),v_p,tc_Complex_Ocomplex,X0)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1287])]) ).
fof(f16525,plain,
( spl47_815
<=> ! [X0,X3,X2,X1] :
( sP18(X0,X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
| c_Groups_Ozero__class_Ozero(X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_815])]) ).
fof(f32581,plain,
( ! [X0] :
( sP18(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)),v_p,tc_Complex_Ocomplex,X0)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
| ~ spl47_219
| ~ spl47_815 ),
inference(resolution,[],[f7061,f16526]) ).
fof(f16526,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
| sP18(X0,X1,X2,X3)
| c_Groups_Ozero__class_Ozero(X2) = X3 )
| ~ spl47_815 ),
inference(avatar_component_clause,[],[f16525]) ).
fof(f33884,plain,
spl47_1286,
inference(avatar_split_clause,[],[f5500,f33882]) ).
fof(f33882,plain,
( spl47_1286
<=> ! [X1,X6,X2,X0,X4,X5,X3,X7] :
( c_Polynomial_Opdivmod__rel(X7,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X5),X2),X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X5),X0),X3))
| ~ c_Polynomial_Opdivmod__rel(X7,X4,X2,X1,X0)
| ~ c_Polynomial_Opdivmod__rel(X7,X6,X5,X4,X3)
| ~ class_Fields_Ofield(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1286])]) ).
fof(f5500,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( c_Polynomial_Opdivmod__rel(X7,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X5),X2),X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X5),X0),X3))
| ~ c_Polynomial_Opdivmod__rel(X7,X4,X2,X1,X0)
| ~ c_Polynomial_Opdivmod__rel(X7,X6,X5,X4,X3)
| ~ class_Fields_Ofield(X7) ),
inference(cnf_transformation,[],[f3474]) ).
fof(f3474,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( c_Polynomial_Opdivmod__rel(X7,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X5),X2),X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X5),X0),X3))
| ~ c_Polynomial_Opdivmod__rel(X7,X4,X2,X1,X0)
| ~ c_Polynomial_Opdivmod__rel(X7,X6,X5,X4,X3)
| ~ class_Fields_Ofield(X7) ),
inference(flattening,[],[f3473]) ).
fof(f3473,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( c_Polynomial_Opdivmod__rel(X7,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X5),X2),X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X5),X0),X3))
| ~ c_Polynomial_Opdivmod__rel(X7,X4,X2,X1,X0)
| ~ c_Polynomial_Opdivmod__rel(X7,X6,X5,X4,X3)
| ~ class_Fields_Ofield(X7) ),
inference(ennf_transformation,[],[f2259]) ).
fof(f2259,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( class_Fields_Ofield(X7)
=> ( c_Polynomial_Opdivmod__rel(X7,X6,X5,X4,X3)
=> ( c_Polynomial_Opdivmod__rel(X7,X4,X2,X1,X0)
=> c_Polynomial_Opdivmod__rel(X7,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X5),X2),X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X5),X0),X3)) ) ) ),
inference(rectify,[],[f740]) ).
fof(f740,axiom,
! [X67,X68,X26,X34,X13,X10,X6,X5] :
( class_Fields_Ofield(X5)
=> ( c_Polynomial_Opdivmod__rel(X5,X6,X10,X13,X34)
=> ( c_Polynomial_Opdivmod__rel(X5,X13,X26,X68,X67)
=> c_Polynomial_Opdivmod__rel(X5,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X10),X26),X68,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X10),X67),X34)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__mult) ).
fof(f33880,plain,
spl47_1285,
inference(avatar_split_clause,[],[f5492,f33878]) ).
fof(f33878,plain,
( spl47_1285
<=> ! [X2,X4,X0,X5,X3,X1] :
( c_Polynomial_Opoly__rec(X2,X5,X3,X4,c_Polynomial_OpCons(X5,X1,X0)) = hAPP(hAPP(hAPP(X4,X1),X0),c_Polynomial_Opoly__rec(X2,X5,X3,X4,X0))
| hAPP(hAPP(hAPP(X4,c_Groups_Ozero__class_Ozero(X5)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X3) != X3
| ~ class_Groups_Ozero(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1285])]) ).
fof(f5492,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Polynomial_Opoly__rec(X2,X5,X3,X4,c_Polynomial_OpCons(X5,X1,X0)) = hAPP(hAPP(hAPP(X4,X1),X0),c_Polynomial_Opoly__rec(X2,X5,X3,X4,X0))
| hAPP(hAPP(hAPP(X4,c_Groups_Ozero__class_Ozero(X5)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X3) != X3
| ~ class_Groups_Ozero(X5) ),
inference(cnf_transformation,[],[f3460]) ).
fof(f3460,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Polynomial_Opoly__rec(X2,X5,X3,X4,c_Polynomial_OpCons(X5,X1,X0)) = hAPP(hAPP(hAPP(X4,X1),X0),c_Polynomial_Opoly__rec(X2,X5,X3,X4,X0))
| hAPP(hAPP(hAPP(X4,c_Groups_Ozero__class_Ozero(X5)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X3) != X3
| ~ class_Groups_Ozero(X5) ),
inference(flattening,[],[f3459]) ).
fof(f3459,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Polynomial_Opoly__rec(X2,X5,X3,X4,c_Polynomial_OpCons(X5,X1,X0)) = hAPP(hAPP(hAPP(X4,X1),X0),c_Polynomial_Opoly__rec(X2,X5,X3,X4,X0))
| hAPP(hAPP(hAPP(X4,c_Groups_Ozero__class_Ozero(X5)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X3) != X3
| ~ class_Groups_Ozero(X5) ),
inference(ennf_transformation,[],[f2252]) ).
fof(f2252,plain,
! [X0,X1,X2,X3,X4,X5] :
( class_Groups_Ozero(X5)
=> ( hAPP(hAPP(hAPP(X4,c_Groups_Ozero__class_Ozero(X5)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X3) = X3
=> c_Polynomial_Opoly__rec(X2,X5,X3,X4,c_Polynomial_OpCons(X5,X1,X0)) = hAPP(hAPP(hAPP(X4,X1),X0),c_Polynomial_Opoly__rec(X2,X5,X3,X4,X0)) ) ),
inference(rectify,[],[f102]) ).
fof(f102,axiom,
! [X9,X12,X5,X30,X1,X31] :
( class_Groups_Ozero(X31)
=> ( hAPP(hAPP(hAPP(X1,c_Groups_Ozero__class_Ozero(X31)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X31))),X30) = X30
=> c_Polynomial_Opoly__rec(X5,X31,X30,X1,c_Polynomial_OpCons(X31,X12,X9)) = hAPP(hAPP(hAPP(X1,X12),X9),c_Polynomial_Opoly__rec(X5,X31,X30,X1,X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__rec__pCons) ).
fof(f33876,plain,
spl47_1284,
inference(avatar_split_clause,[],[f4815,f33874]) ).
fof(f33874,plain,
( spl47_1284
<=> ! [X2,X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
| hAPP(c_Polynomial_Ocoeff(X2,X1),c_Polynomial_Odegree(X2,X1)) != hAPP(c_Polynomial_Ocoeff(X2,X0),c_Polynomial_Odegree(X2,X0))
| ~ class_Rings_Oidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1284])]) ).
fof(f4815,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
| hAPP(c_Polynomial_Ocoeff(X2,X1),c_Polynomial_Odegree(X2,X1)) != hAPP(c_Polynomial_Ocoeff(X2,X0),c_Polynomial_Odegree(X2,X0))
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f2791]) ).
fof(f2791,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
| hAPP(c_Polynomial_Ocoeff(X2,X1),c_Polynomial_Odegree(X2,X1)) != hAPP(c_Polynomial_Ocoeff(X2,X0),c_Polynomial_Odegree(X2,X0))
| ~ class_Rings_Oidom(X2) ),
inference(flattening,[],[f2790]) ).
fof(f2790,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
| hAPP(c_Polynomial_Ocoeff(X2,X1),c_Polynomial_Odegree(X2,X1)) != hAPP(c_Polynomial_Ocoeff(X2,X0),c_Polynomial_Odegree(X2,X0))
| ~ class_Rings_Oidom(X2) ),
inference(ennf_transformation,[],[f1760]) ).
fof(f1760,plain,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( hAPP(c_Polynomial_Ocoeff(X2,X1),c_Polynomial_Odegree(X2,X1)) = hAPP(c_Polynomial_Ocoeff(X2,X0),c_Polynomial_Odegree(X2,X0))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X0),X1))
=> X0 = X1 ) ) ) ),
inference(rectify,[],[f756]) ).
fof(f756,axiom,
! [X13,X8,X5] :
( class_Rings_Oidom(X5)
=> ( hAPP(c_Polynomial_Ocoeff(X5,X8),c_Polynomial_Odegree(X5,X8)) = hAPP(c_Polynomial_Ocoeff(X5,X13),c_Polynomial_Odegree(X5,X13))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),X8),X13))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),X13),X8))
=> X8 = X13 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__dvd__antisym) ).
fof(f33601,plain,
spl47_1283,
inference(avatar_split_clause,[],[f6034,f33599]) ).
fof(f33599,plain,
( spl47_1283
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X1))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1283])]) ).
fof(f6034,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X1))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),X3)) ),
inference(forward_demodulation,[],[f5470,f4626]) ).
fof(f4626,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0),
inference(cnf_transformation,[],[f1615]) ).
fof(f1615,plain,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0),
inference(rectify,[],[f674]) ).
fof(f674,axiom,
! [X64,X61,X62] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X62,X61),X64) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X62,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X61,X64)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(f5470,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),X3)) ),
inference(cnf_transformation,[],[f3903]) ).
fof(f3903,plain,
! [X0,X1,X2,X3,X4] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X1))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),X3)) ),
inference(nnf_transformation,[],[f3438]) ).
fof(f3438,plain,
! [X0,X1,X2,X3,X4] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X1))) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),X3)) ),
inference(ennf_transformation,[],[f2237]) ).
fof(f2237,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),X3))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X1))) ) ),
inference(rectify,[],[f669]) ).
fof(f669,axiom,
! [X24,X63,X15,X52,X12] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X12),X52))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X12),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,X63)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X12),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X52)),X63))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__period) ).
fof(f33597,plain,
spl47_1282,
inference(avatar_split_clause,[],[f6033,f33595]) ).
fof(f33595,plain,
( spl47_1282
<=> ! [X4,X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X1))))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1282])]) ).
fof(f6033,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X1))))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),X3)) ),
inference(forward_demodulation,[],[f5471,f4626]) ).
fof(f5471,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4),X3)) ),
inference(cnf_transformation,[],[f3903]) ).
fof(f33593,plain,
spl47_1281,
inference(avatar_split_clause,[],[f6026,f33591]) ).
fof(f33591,plain,
( spl47_1281
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,sK40(X1,X2))))
| hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2))))
| ~ hBOOL(hAPP(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1281])]) ).
fof(f6026,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,sK40(X1,X2))))
| hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2))))
| ~ hBOOL(hAPP(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(forward_demodulation,[],[f5010,f4239]) ).
fof(f4239,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0),
inference(cnf_transformation,[],[f1355]) ).
fof(f1355,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0),
inference(rectify,[],[f672]) ).
fof(f672,axiom,
! [X48,X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X48,X26) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,X48),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).
fof(f5010,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2))))
| ~ hBOOL(hAPP(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sK40(X1,X2),X2)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(cnf_transformation,[],[f3766]) ).
fof(f3766,plain,
! [X0,X1,X2] :
( ! [X3] :
( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2))))
| ~ hBOOL(hAPP(X1,X3)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ( ~ hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sK40(X1,X2),X2)))
& hBOOL(hAPP(X1,sK40(X1,X2))) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40])],[f3764,f3765]) ).
fof(f3765,plain,
! [X1,X2] :
( ? [X4] :
( ~ hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,X2)))
& hBOOL(hAPP(X1,X4)) )
=> ( ~ hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sK40(X1,X2),X2)))
& hBOOL(hAPP(X1,sK40(X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f3764,plain,
! [X0,X1,X2] :
( ! [X3] :
( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2))))
| ~ hBOOL(hAPP(X1,X3)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ? [X4] :
( ~ hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,X2)))
& hBOOL(hAPP(X1,X4)) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(rectify,[],[f2996]) ).
fof(f2996,plain,
! [X0,X1,X2] :
( ! [X4] :
( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2))))
| ~ hBOOL(hAPP(X1,X4)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ? [X3] :
( ~ hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X2)))
& hBOOL(hAPP(X1,X3)) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(flattening,[],[f2995]) ).
fof(f2995,plain,
! [X0,X1,X2] :
( ! [X4] :
( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2))))
| ~ hBOOL(hAPP(X1,X4)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ? [X3] :
( ~ hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X2)))
& hBOOL(hAPP(X1,X3)) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(ennf_transformation,[],[f1908]) ).
fof(f1908,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
=> ( ! [X3] :
( hBOOL(hAPP(X1,X3))
=> hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X2))) )
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
=> ! [X4] :
( hBOOL(hAPP(X1,X4))
=> hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2)))) ) ) ) ),
inference(rectify,[],[f752]) ).
fof(f752,axiom,
! [X44,X39,X52] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X52)
=> ( ! [X2] :
( hBOOL(hAPP(X39,X2))
=> hBOOL(hAPP(X39,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X52))) )
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X44)
=> ! [X2] :
( hBOOL(hAPP(X39,X2))
=> hBOOL(hAPP(X39,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X44),X52)))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incr__mult__lemma) ).
fof(f33589,plain,
spl47_1280,
inference(avatar_split_clause,[],[f5486,f33587]) ).
fof(f33587,plain,
( spl47_1280
<=> ! [X5,X4,X0,X3,X2,X1] :
( c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2) = X0
| c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2) != c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)
| ~ class_Rings_Oring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1280])]) ).
fof(f5486,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2) = X0
| c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2) != c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)
| ~ class_Rings_Oring(X5) ),
inference(cnf_transformation,[],[f3908]) ).
fof(f3908,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)
| c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2) != X0 )
& ( c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2) = X0
| c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2) != c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0) ) )
| ~ class_Rings_Oring(X5) ),
inference(nnf_transformation,[],[f3454]) ).
fof(f3454,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)
<=> c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2) = X0 )
| ~ class_Rings_Oring(X5) ),
inference(ennf_transformation,[],[f2248]) ).
fof(f2248,plain,
! [X0,X1,X2,X3,X4,X5] :
( class_Rings_Oring(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)
<=> c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2) = X0 ) ),
inference(rectify,[],[f838]) ).
fof(f838,axiom,
! [X52,X29,X24,X82,X12,X5] :
( class_Rings_Oring(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X82),X24) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X29),X82),X52)
<=> c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X12,X29)),X82),X24) = X52 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff1) ).
fof(f33585,plain,
spl47_1279,
inference(avatar_split_clause,[],[f5449,f33583]) ).
fof(f33583,plain,
( spl47_1279
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ class_Rings_Ocomm__semiring__1(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1279])]) ).
fof(f5449,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ class_Rings_Ocomm__semiring__1(X4) ),
inference(cnf_transformation,[],[f3418]) ).
fof(f3418,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ class_Rings_Ocomm__semiring__1(X4) ),
inference(ennf_transformation,[],[f2222]) ).
fof(f2222,plain,
! [X0,X1,X2,X3,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
inference(rectify,[],[f503]) ).
fof(f503,axiom,
! [X53,X54,X55,X56,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X56),X55)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X54),X53)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X56),X54)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X55),X53)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(f32887,plain,
( ~ spl47_1278
| ~ spl47_219
| ~ spl47_356 ),
inference(avatar_split_clause,[],[f16400,f7822,f7059,f32884]) ).
fof(f32884,plain,
( spl47_1278
<=> sP11(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)),v_p,c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1278])]) ).
fof(f7822,plain,
( spl47_356
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_356])]) ).
fof(f16400,plain,
( ~ sP11(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)),v_p,c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
| ~ spl47_219
| ~ spl47_356 ),
inference(resolution,[],[f7061,f7823]) ).
fof(f7823,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP11(X0,X1,X2) )
| ~ spl47_356 ),
inference(avatar_component_clause,[],[f7822]) ).
fof(f32749,plain,
spl47_1277,
inference(avatar_split_clause,[],[f5648,f32747]) ).
fof(f32747,plain,
( spl47_1277
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ class_Groups_Omonoid__mult(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1277])]) ).
fof(f5648,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ class_Groups_Omonoid__mult(X3) ),
inference(definition_unfolding,[],[f5305,f4118]) ).
fof(f5305,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ class_Groups_Omonoid__mult(X3) ),
inference(cnf_transformation,[],[f3248]) ).
fof(f3248,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ class_Groups_Omonoid__mult(X3) ),
inference(flattening,[],[f3247]) ).
fof(f3247,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ class_Groups_Omonoid__mult(X3) ),
inference(ennf_transformation,[],[f2103]) ).
fof(f2103,plain,
! [X0,X1,X2,X3] :
( class_Groups_Omonoid__mult(X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))),X0) ) ),
inference(rectify,[],[f885]) ).
fof(f885,axiom,
! [X10,X7,X8,X5] :
( class_Groups_Omonoid__mult(X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X8,X7)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X10),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X7),X8)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X10),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X8))),X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__realpow__diff) ).
fof(f32745,plain,
spl47_1276,
inference(avatar_split_clause,[],[f5428,f32743]) ).
fof(f32743,plain,
( spl47_1276
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X2)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ class_Rings_Olinordered__semiring__strict(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1276])]) ).
fof(f5428,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X2)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ class_Rings_Olinordered__semiring__strict(X4) ),
inference(cnf_transformation,[],[f3403]) ).
fof(f3403,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X2)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ class_Rings_Olinordered__semiring__strict(X4) ),
inference(flattening,[],[f3402]) ).
fof(f3402,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X2)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ class_Rings_Olinordered__semiring__strict(X4) ),
inference(ennf_transformation,[],[f2209]) ).
fof(f2209,plain,
! [X0,X1,X2,X3,X4] :
( class_Rings_Olinordered__semiring__strict(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X3,X2)
=> ( c_Orderings_Oord__class_Oless(X4,X1,X0)
=> ( c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
=> c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ) ) ) ) ),
inference(rectify,[],[f614]) ).
fof(f614,axiom,
! [X46,X16,X17,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X17)
=> ( c_Orderings_Oord__class_Oless(X5,X16,X46)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X17)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X16)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X46)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono) ).
fof(f32741,plain,
spl47_1275,
inference(avatar_split_clause,[],[f5427,f32739]) ).
fof(f32739,plain,
( spl47_1275
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ class_Rings_Olinordered__semiring__strict(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1275])]) ).
fof(f5427,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ class_Rings_Olinordered__semiring__strict(X4) ),
inference(cnf_transformation,[],[f3401]) ).
fof(f3401,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ class_Rings_Olinordered__semiring__strict(X4) ),
inference(flattening,[],[f3400]) ).
fof(f3400,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ class_Rings_Olinordered__semiring__strict(X4) ),
inference(ennf_transformation,[],[f2208]) ).
fof(f2208,plain,
! [X0,X1,X2,X3,X4] :
( class_Rings_Olinordered__semiring__strict(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X3,X2)
=> ( c_Orderings_Oord__class_Oless(X4,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
=> c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ) ) ) ) ),
inference(rectify,[],[f613]) ).
fof(f613,axiom,
! [X46,X16,X17,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X17)
=> ( c_Orderings_Oord__class_Oless(X5,X16,X46)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X16)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X46)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).
fof(f32737,plain,
spl47_1274,
inference(avatar_split_clause,[],[f5426,f32735]) ).
fof(f32735,plain,
( spl47_1274
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ class_Rings_Olinordered__semiring__strict(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1274])]) ).
fof(f5426,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ class_Rings_Olinordered__semiring__strict(X4) ),
inference(cnf_transformation,[],[f3399]) ).
fof(f3399,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ class_Rings_Olinordered__semiring__strict(X4) ),
inference(flattening,[],[f3398]) ).
fof(f3398,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ class_Rings_Olinordered__semiring__strict(X4) ),
inference(ennf_transformation,[],[f2207]) ).
fof(f2207,plain,
! [X0,X1,X2,X3,X4] :
( class_Rings_Olinordered__semiring__strict(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X3,X2)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
=> ( c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X1)
=> c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ) ) ) ) ),
inference(rectify,[],[f612]) ).
fof(f612,axiom,
! [X46,X16,X17,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X17)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X16,X46)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X16)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X46)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).
fof(f32733,plain,
spl47_1273,
inference(avatar_split_clause,[],[f5425,f32731]) ).
fof(f32731,plain,
( spl47_1273
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ class_Rings_Olinordered__semiring__strict(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1273])]) ).
fof(f5425,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ class_Rings_Olinordered__semiring__strict(X4) ),
inference(cnf_transformation,[],[f3397]) ).
fof(f3397,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ class_Rings_Olinordered__semiring__strict(X4) ),
inference(flattening,[],[f3396]) ).
fof(f3396,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ class_Rings_Olinordered__semiring__strict(X4) ),
inference(ennf_transformation,[],[f2206]) ).
fof(f2206,plain,
! [X0,X1,X2,X3,X4] :
( class_Rings_Olinordered__semiring__strict(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
=> ( c_Orderings_Oord__class_Oless(X4,X1,X0)
=> ( c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X3)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
=> c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ) ) ) ) ),
inference(rectify,[],[f611]) ).
fof(f611,axiom,
! [X46,X16,X17,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X17)
=> ( c_Orderings_Oord__class_Oless(X5,X16,X46)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X16)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X46)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).
fof(f32729,plain,
spl47_1272,
inference(avatar_split_clause,[],[f5420,f32727]) ).
fof(f32727,plain,
( spl47_1272
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ class_Rings_Oordered__semiring(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1272])]) ).
fof(f5420,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless__eq(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ class_Rings_Oordered__semiring(X4) ),
inference(cnf_transformation,[],[f3388]) ).
fof(f3388,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ class_Rings_Oordered__semiring(X4) ),
inference(flattening,[],[f3387]) ).
fof(f3387,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ class_Rings_Oordered__semiring(X4) ),
inference(ennf_transformation,[],[f2201]) ).
fof(f2201,plain,
! [X0,X1,X2,X3,X4] :
( class_Rings_Oordered__semiring(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X3)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
=> c_Orderings_Oord__class_Oless__eq(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ) ) ) ) ),
inference(rectify,[],[f560]) ).
fof(f560,axiom,
! [X46,X16,X17,X4,X5] :
( class_Rings_Oordered__semiring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X17)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X16,X46)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X16)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X46)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono_H) ).
fof(f32725,plain,
spl47_1271,
inference(avatar_split_clause,[],[f5419,f32723]) ).
fof(f32723,plain,
( spl47_1271
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ class_Rings_Oordered__semiring(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1271])]) ).
fof(f5419,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless__eq(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ class_Rings_Oordered__semiring(X4) ),
inference(cnf_transformation,[],[f3386]) ).
fof(f3386,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ class_Rings_Oordered__semiring(X4) ),
inference(flattening,[],[f3385]) ).
fof(f3385,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ class_Rings_Oordered__semiring(X4) ),
inference(ennf_transformation,[],[f2200]) ).
fof(f2200,plain,
! [X0,X1,X2,X3,X4] :
( class_Rings_Oordered__semiring(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
=> c_Orderings_Oord__class_Oless__eq(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ) ) ) ) ),
inference(rectify,[],[f561]) ).
fof(f561,axiom,
! [X46,X16,X17,X4,X5] :
( class_Rings_Oordered__semiring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X17)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X16,X46)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X17)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X16)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X46)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono) ).
fof(f32721,plain,
spl47_1270,
inference(avatar_split_clause,[],[f5173,f32719]) ).
fof(f32719,plain,
( spl47_1270
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1270])]) ).
fof(f5173,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(cnf_transformation,[],[f3101]) ).
fof(f3101,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(flattening,[],[f3100]) ).
fof(f3100,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(ennf_transformation,[],[f2017]) ).
fof(f2017,plain,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( c_Groups_Ozero__class_Ozero(X3) != X2
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)) ) ) ),
inference(rectify,[],[f925]) ).
fof(f925,axiom,
! [X21,X7,X4,X5] :
( class_Fields_Ofield(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X4
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X21)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X7)) = c_Rings_Oinverse__class_Odivide(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X21),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__diff) ).
fof(f32603,plain,
spl47_1269,
inference(avatar_split_clause,[],[f6018,f32601]) ).
fof(f32601,plain,
( spl47_1269
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| X0 = X1
| ~ class_Rings_Oidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1269])]) ).
fof(f6018,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| X0 = X1
| ~ class_Rings_Oidom(X2) ),
inference(forward_demodulation,[],[f6017,f4114]) ).
fof(f6017,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| X0 = X1
| ~ class_Rings_Oidom(X2) ),
inference(forward_demodulation,[],[f6016,f4240]) ).
fof(f6016,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| X0 = X1
| ~ class_Rings_Oidom(X2) ),
inference(forward_demodulation,[],[f5624,f4240]) ).
fof(f5624,plain,
! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| X0 = X1
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Oidom(X2) ),
inference(definition_unfolding,[],[f4841,f4118,f4118,f4118,f4118]) ).
fof(f4841,plain,
! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| X0 = X1
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f3734]) ).
fof(f3734,plain,
! [X0,X1,X2] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ( c_Groups_Ouminus__class_Ouminus(X2,X0) != X1
& X0 != X1 ) )
& ( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| X0 = X1
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) )
| ~ class_Rings_Oidom(X2) ),
inference(flattening,[],[f3733]) ).
fof(f3733,plain,
! [X0,X1,X2] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ( c_Groups_Ouminus__class_Ouminus(X2,X0) != X1
& X0 != X1 ) )
& ( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| X0 = X1
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) )
| ~ class_Rings_Oidom(X2) ),
inference(nnf_transformation,[],[f2803]) ).
fof(f2803,plain,
! [X0,X1,X2] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> ( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| X0 = X1 ) )
| ~ class_Rings_Oidom(X2) ),
inference(ennf_transformation,[],[f1772]) ).
fof(f1772,plain,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> ( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| X0 = X1 ) ) ),
inference(rectify,[],[f441]) ).
fof(f441,axiom,
! [X25,X15,X5] :
( class_Rings_Oidom(X5)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X15),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X25),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> ( c_Groups_Ouminus__class_Ouminus(X5,X25) = X15
| X15 = X25 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__disj) ).
fof(f32599,plain,
( ~ spl47_1268
| spl47_145 ),
inference(avatar_split_clause,[],[f3912,f6756,f32596]) ).
fof(f6756,plain,
( spl47_145
<=> sP0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_145])]) ).
fof(f3912,plain,
( sP0
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK27) ),
inference(cnf_transformation,[],[f3521]) ).
fof(f3521,plain,
( ( sP0
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK27)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK27) ) )
& ( ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1) )
| ~ sP0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f3519,f3520]) ).
fof(f3520,plain,
( ? [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) )
=> ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK27)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK27) ) ),
introduced(choice_axiom,[]) ).
fof(f3519,plain,
( ( sP0
| ? [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) ) )
& ( ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1) )
| ~ sP0 ) ),
inference(rectify,[],[f3518]) ).
fof(f3518,plain,
( ( sP0
| ? [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) ) )
& ( ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) )
| ~ sP0 ) ),
inference(nnf_transformation,[],[f3475]) ).
fof(f3475,plain,
( sP0
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f32579,plain,
( spl47_1267
| spl47_220
| spl47_219
| ~ spl47_1261 ),
inference(avatar_split_clause,[],[f32534,f32350,f7059,f7064,f32576]) ).
fof(f32576,plain,
( spl47_1267
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK43(v_q,v_p)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1267])]) ).
fof(f7064,plain,
( spl47_220
<=> c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_220])]) ).
fof(f32350,plain,
( spl47_1261
<=> ! [X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,X2)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X2),sK43(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1261])]) ).
fof(f32534,plain,
( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK43(v_q,v_p))
| spl47_219
| ~ spl47_1261 ),
inference(resolution,[],[f32351,f7060]) ).
fof(f7060,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| spl47_219 ),
inference(avatar_component_clause,[],[f7059]) ).
fof(f32351,plain,
( ! [X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,X2)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X2),sK43(X1,X2)) )
| ~ spl47_1261 ),
inference(avatar_component_clause,[],[f32350]) ).
fof(f32574,plain,
spl47_1266,
inference(avatar_split_clause,[],[f5647,f32572]) ).
fof(f32572,plain,
( spl47_1266
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Rings_Olinordered__semidom(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1266])]) ).
fof(f5647,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(definition_unfolding,[],[f5290,f4118,f4118]) ).
fof(f5290,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Nat_OSuc(X1)))
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(cnf_transformation,[],[f3230]) ).
fof(f3230,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Nat_OSuc(X1)))
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(flattening,[],[f3229]) ).
fof(f3229,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Nat_OSuc(X1)))
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(ennf_transformation,[],[f2090]) ).
fof(f2090,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Nat_OSuc(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),c_Nat_OSuc(X1)))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ) ) ),
inference(rectify,[],[f121]) ).
fof(f121,axiom,
! [X17,X7,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Nat_OSuc(X7)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X17),c_Nat_OSuc(X7)))
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X17)
=> c_Orderings_Oord__class_Oless__eq(X5,X4,X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__base) ).
fof(f32570,plain,
spl47_1265,
inference(avatar_split_clause,[],[f5451,f32568]) ).
fof(f32568,plain,
( spl47_1265
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X3),X2))
| ~ class_Rings_Ocomm__semiring__1(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1265])]) ).
fof(f5451,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X3),X2))
| ~ class_Rings_Ocomm__semiring__1(X4) ),
inference(cnf_transformation,[],[f3422]) ).
fof(f3422,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X3),X2))
| ~ class_Rings_Ocomm__semiring__1(X4) ),
inference(flattening,[],[f3421]) ).
fof(f3421,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X3),X2))
| ~ class_Rings_Ocomm__semiring__1(X4) ),
inference(ennf_transformation,[],[f2224]) ).
fof(f2224,plain,
! [X0,X1,X2,X3,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X3),X2))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X1),X0))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))) ) ) ),
inference(rectify,[],[f529]) ).
fof(f529,axiom,
! [X46,X16,X17,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X4),X17))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X16),X46))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X46))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__dvd__mono) ).
fof(f32566,plain,
spl47_1264,
inference(avatar_split_clause,[],[f5287,f32564]) ).
fof(f32564,plain,
( spl47_1264
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)
| ~ class_Rings_Olinordered__semidom(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1264])]) ).
fof(f5287,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(cnf_transformation,[],[f3224]) ).
fof(f3224,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(flattening,[],[f3223]) ).
fof(f3223,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(ennf_transformation,[],[f2087]) ).
fof(f2087,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
=> X0 = X2 ) ) ) ) ),
inference(rectify,[],[f130]) ).
fof(f130,axiom,
! [X17,X7,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X17),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X17)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
=> X4 = X17 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).
fof(f32562,plain,
spl47_1263,
inference(avatar_split_clause,[],[f5250,f32560]) ).
fof(f32560,plain,
( spl47_1263
<=> ! [X0,X3,X2,X1] :
( hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Polynomial_Omonom(X3,c_Groups_Oone__class_Oone(X3),X2)),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)),hAPP(c_Polynomial_Opoly(X3,X1),X0))
| ~ class_Rings_Ocomm__ring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1263])]) ).
fof(f5250,plain,
! [X2,X3,X0,X1] :
( hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Polynomial_Omonom(X3,c_Groups_Oone__class_Oone(X3),X2)),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)),hAPP(c_Polynomial_Opoly(X3,X1),X0))
| ~ class_Rings_Ocomm__ring__1(X3) ),
inference(cnf_transformation,[],[f3168]) ).
fof(f3168,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Polynomial_Omonom(X3,c_Groups_Oone__class_Oone(X3),X2)),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)),hAPP(c_Polynomial_Opoly(X3,X1),X0))
| ~ class_Rings_Ocomm__ring__1(X3) ),
inference(ennf_transformation,[],[f2057]) ).
fof(f2057,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__ring__1(X3)
=> hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Polynomial_Omonom(X3,c_Groups_Oone__class_Oone(X3),X2)),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
inference(rectify,[],[f591]) ).
fof(f591,axiom,
! [X6,X8,X7,X5] :
( class_Rings_Ocomm__ring__1(X5)
=> hAPP(c_Polynomial_Opoly(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),c_Polynomial_Omonom(X5,c_Groups_Oone__class_Oone(X5),X7)),X8)),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X7)),hAPP(c_Polynomial_Opoly(X5,X8),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__replicate__append) ).
fof(f32356,plain,
spl47_1262,
inference(avatar_split_clause,[],[f5882,f32354]) ).
fof(f32354,plain,
( spl47_1262
<=> ! [X5,X4,X3,X2,X1] :
( c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2))
| ~ class_Rings_Oring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1262])]) ).
fof(f5882,plain,
! [X2,X3,X1,X4,X5] :
( c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2))
| ~ class_Rings_Oring(X5) ),
inference(equality_resolution,[],[f5487]) ).
fof(f5487,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X3),X2) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),X0)
| c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X4,X1)),X3),X2) != X0
| ~ class_Rings_Oring(X5) ),
inference(cnf_transformation,[],[f3908]) ).
fof(f32352,plain,
spl47_1261,
inference(avatar_split_clause,[],[f5806,f32350]) ).
fof(f5806,plain,
! [X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,X2)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X2),sK43(X1,X2)) ),
inference(equality_resolution,[],[f5060]) ).
fof(f5060,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X0)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Polynomial_Odegree(tc_Complex_Ocomplex,X2) != X0
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X2),sK43(X1,X2)) ),
inference(cnf_transformation,[],[f3782]) ).
fof(f3782,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X0)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Polynomial_Odegree(tc_Complex_Ocomplex,X2) != X0
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),sK43(X1,X2))
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X2),sK43(X1,X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK43])],[f3050,f3781]) ).
fof(f3781,plain,
! [X1,X2] :
( ? [X3] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),X3)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X2),X3) )
=> ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),sK43(X1,X2))
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X2),sK43(X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3050,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X0)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Polynomial_Odegree(tc_Complex_Ocomplex,X2) != X0
| ? [X3] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),X3)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X2),X3) ) ),
inference(flattening,[],[f3049]) ).
fof(f3049,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X0)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Polynomial_Odegree(tc_Complex_Ocomplex,X2) != X0
| ? [X3] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),X3)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X2),X3) ) ),
inference(ennf_transformation,[],[f1939]) ).
fof(f1939,plain,
! [X0,X1,X2] :
( ! [X3] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X2),X3)
=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),X3) )
=> ( c_Polynomial_Odegree(tc_Complex_Ocomplex,X2) = X0
=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X0))) ) ) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X7,X13,X8] :
( ! [X2] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X8),X2)
=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X13),X2) )
=> ( c_Polynomial_Odegree(tc_Complex_Ocomplex,X8) = X7
=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X7
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X8),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X13),X7))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nullstellensatz__lemma) ).
fof(f32348,plain,
spl47_1260,
inference(avatar_split_clause,[],[f5805,f32346]) ).
fof(f32346,plain,
( spl47_1260
<=> ! [X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,X2)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),sK43(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1260])]) ).
fof(f5805,plain,
! [X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),c_Polynomial_Odegree(tc_Complex_Ocomplex,X2))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,X2)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),sK43(X1,X2)) ),
inference(equality_resolution,[],[f5061]) ).
fof(f5061,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X0)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Polynomial_Odegree(tc_Complex_Ocomplex,X2) != X0
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),sK43(X1,X2)) ),
inference(cnf_transformation,[],[f3782]) ).
fof(f32344,plain,
spl47_1259,
inference(avatar_split_clause,[],[f5491,f32342]) ).
fof(f32342,plain,
( spl47_1259
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_Polynomial_Opoly__rec(X4,X5,X3,X2,c_Polynomial_OpCons(X5,X1,X0)) = hAPP(hAPP(hAPP(X2,X1),X0),c_If(X4,c_fequal(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X3,c_Polynomial_Opoly__rec(X4,X5,X3,X2,X0)))
| ~ class_Groups_Ozero(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1259])]) ).
fof(f5491,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Polynomial_Opoly__rec(X4,X5,X3,X2,c_Polynomial_OpCons(X5,X1,X0)) = hAPP(hAPP(hAPP(X2,X1),X0),c_If(X4,c_fequal(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X3,c_Polynomial_Opoly__rec(X4,X5,X3,X2,X0)))
| ~ class_Groups_Ozero(X5) ),
inference(cnf_transformation,[],[f3458]) ).
fof(f3458,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Polynomial_Opoly__rec(X4,X5,X3,X2,c_Polynomial_OpCons(X5,X1,X0)) = hAPP(hAPP(hAPP(X2,X1),X0),c_If(X4,c_fequal(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X3,c_Polynomial_Opoly__rec(X4,X5,X3,X2,X0)))
| ~ class_Groups_Ozero(X5) ),
inference(ennf_transformation,[],[f2251]) ).
fof(f2251,plain,
! [X0,X1,X2,X3,X4,X5] :
( class_Groups_Ozero(X5)
=> c_Polynomial_Opoly__rec(X4,X5,X3,X2,c_Polynomial_OpCons(X5,X1,X0)) = hAPP(hAPP(hAPP(X2,X1),X0),c_If(X4,c_fequal(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X3,c_Polynomial_Opoly__rec(X4,X5,X3,X2,X0))) ),
inference(rectify,[],[f90]) ).
fof(f90,axiom,
! [X9,X12,X1,X30,X5,X31] :
( class_Groups_Ozero(X31)
=> c_Polynomial_Opoly__rec(X5,X31,X30,X1,c_Polynomial_OpCons(X31,X12,X9)) = hAPP(hAPP(hAPP(X1,X12),X9),c_If(X5,c_fequal(X9,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X31))),X30,c_Polynomial_Opoly__rec(X5,X31,X30,X1,X9))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__rec_Osimps) ).
fof(f32340,plain,
spl47_1258,
inference(avatar_split_clause,[],[f5432,f32338]) ).
fof(f32338,plain,
( spl47_1258
<=> ! [X4,X0,X3,X2,X1] :
( c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Oplus__class_Oplus(X4,X3,X1)),X2),X0)
| ~ class_Rings_Osemiring(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1258])]) ).
fof(f5432,plain,
! [X2,X3,X0,X1,X4] :
( c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Oplus__class_Oplus(X4,X3,X1)),X2),X0)
| ~ class_Rings_Osemiring(X4) ),
inference(cnf_transformation,[],[f3407]) ).
fof(f3407,plain,
! [X0,X1,X2,X3,X4] :
( c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Oplus__class_Oplus(X4,X3,X1)),X2),X0)
| ~ class_Rings_Osemiring(X4) ),
inference(ennf_transformation,[],[f2212]) ).
fof(f2212,plain,
! [X0,X1,X2,X3,X4] :
( class_Rings_Osemiring(X4)
=> c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Oplus__class_Oplus(X4,X3,X1)),X2),X0) ),
inference(rectify,[],[f520]) ).
fof(f520,axiom,
! [X16,X17,X57,X4,X5] :
( class_Rings_Osemiring(X5)
=> c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X57),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X57),X16)) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oplus__class_Oplus(X5,X4,X17)),X57),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_combine__common__factor) ).
fof(f32336,plain,
spl47_1257,
inference(avatar_split_clause,[],[f5401,f32334]) ).
fof(f32334,plain,
( spl47_1257
<=> ! [X4,X0,X3,X2,X1] :
( c_Rings_Oinverse__class_Odivide(X4,X1,X3) = c_Rings_Oinverse__class_Odivide(X4,X0,X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)
| c_Groups_Ozero__class_Ozero(X4) = X2
| c_Groups_Ozero__class_Ozero(X4) = X3
| ~ class_Fields_Ofield(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1257])]) ).
fof(f5401,plain,
! [X2,X3,X0,X1,X4] :
( c_Rings_Oinverse__class_Odivide(X4,X1,X3) = c_Rings_Oinverse__class_Odivide(X4,X0,X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)
| c_Groups_Ozero__class_Ozero(X4) = X2
| c_Groups_Ozero__class_Ozero(X4) = X3
| ~ class_Fields_Ofield(X4) ),
inference(cnf_transformation,[],[f3879]) ).
fof(f3879,plain,
! [X0,X1,X2,X3,X4] :
( ( ( c_Rings_Oinverse__class_Odivide(X4,X1,X3) = c_Rings_Oinverse__class_Odivide(X4,X0,X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)
| c_Rings_Oinverse__class_Odivide(X4,X1,X3) != c_Rings_Oinverse__class_Odivide(X4,X0,X2) ) )
| c_Groups_Ozero__class_Ozero(X4) = X2
| c_Groups_Ozero__class_Ozero(X4) = X3
| ~ class_Fields_Ofield(X4) ),
inference(nnf_transformation,[],[f3376]) ).
fof(f3376,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Rings_Oinverse__class_Odivide(X4,X1,X3) = c_Rings_Oinverse__class_Odivide(X4,X0,X2)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3) )
| c_Groups_Ozero__class_Ozero(X4) = X2
| c_Groups_Ozero__class_Ozero(X4) = X3
| ~ class_Fields_Ofield(X4) ),
inference(flattening,[],[f3375]) ).
fof(f3375,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Rings_Oinverse__class_Odivide(X4,X1,X3) = c_Rings_Oinverse__class_Odivide(X4,X0,X2)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3) )
| c_Groups_Ozero__class_Ozero(X4) = X2
| c_Groups_Ozero__class_Ozero(X4) = X3
| ~ class_Fields_Ofield(X4) ),
inference(ennf_transformation,[],[f2195]) ).
fof(f2195,plain,
! [X0,X1,X2,X3,X4] :
( class_Fields_Ofield(X4)
=> ( c_Groups_Ozero__class_Ozero(X4) != X3
=> ( c_Groups_Ozero__class_Ozero(X4) != X2
=> ( c_Rings_Oinverse__class_Odivide(X4,X1,X3) = c_Rings_Oinverse__class_Odivide(X4,X0,X2)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3) ) ) ) ),
inference(rectify,[],[f943]) ).
fof(f943,axiom,
! [X49,X15,X30,X25,X5] :
( class_Fields_Ofield(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X25
=> ( c_Groups_Ozero__class_Ozero(X5) != X30
=> ( c_Rings_Oinverse__class_Odivide(X5,X15,X25) = c_Rings_Oinverse__class_Odivide(X5,X49,X30)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X49),X25) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X30) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__eq__eq) ).
fof(f32332,plain,
spl47_1256,
inference(avatar_split_clause,[],[f5400,f32330]) ).
fof(f32330,plain,
( spl47_1256
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)
| c_Rings_Oinverse__class_Odivide(X4,X1,X3) != c_Rings_Oinverse__class_Odivide(X4,X0,X2)
| c_Groups_Ozero__class_Ozero(X4) = X2
| c_Groups_Ozero__class_Ozero(X4) = X3
| ~ class_Fields_Ofield(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1256])]) ).
fof(f5400,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X0),X3)
| c_Rings_Oinverse__class_Odivide(X4,X1,X3) != c_Rings_Oinverse__class_Odivide(X4,X0,X2)
| c_Groups_Ozero__class_Ozero(X4) = X2
| c_Groups_Ozero__class_Ozero(X4) = X3
| ~ class_Fields_Ofield(X4) ),
inference(cnf_transformation,[],[f3879]) ).
fof(f32328,plain,
spl47_1255,
inference(avatar_split_clause,[],[f5009,f32326]) ).
fof(f32326,plain,
( spl47_1255
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2))))
| ~ hBOOL(hAPP(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| hBOOL(hAPP(X1,sK40(X1,X2)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1255])]) ).
fof(f5009,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2))))
| ~ hBOOL(hAPP(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| hBOOL(hAPP(X1,sK40(X1,X2)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(cnf_transformation,[],[f3766]) ).
fof(f32324,plain,
( spl47_1254
| ~ spl47_240
| ~ spl47_303
| ~ spl47_1033 ),
inference(avatar_split_clause,[],[f31575,f22128,f7441,f7149,f32322]) ).
fof(f32322,plain,
( spl47_1254
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK35(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1254])]) ).
fof(f7149,plain,
( spl47_240
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_240])]) ).
fof(f7441,plain,
( spl47_303
<=> ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_303])]) ).
fof(f22128,plain,
( spl47_1033
<=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK35(X0,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1033])]) ).
fof(f31575,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK35(X0,X0)
| ~ spl47_240
| ~ spl47_303
| ~ spl47_1033 ),
inference(forward_demodulation,[],[f31458,f7150]) ).
fof(f7150,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0)
| ~ spl47_240 ),
inference(avatar_component_clause,[],[f7149]) ).
fof(f31458,plain,
( ! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0) = sK35(X0,X0)
| ~ spl47_303
| ~ spl47_1033 ),
inference(superposition,[],[f7442,f22129]) ).
fof(f22129,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK35(X0,X0)) = X0
| ~ spl47_1033 ),
inference(avatar_component_clause,[],[f22128]) ).
fof(f7442,plain,
( ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1) = X0
| ~ spl47_303 ),
inference(avatar_component_clause,[],[f7441]) ).
fof(f32232,plain,
spl47_1253,
inference(avatar_split_clause,[],[f5875,f32230]) ).
fof(f32230,plain,
( spl47_1253
<=> ! [X4,X0,X3,X2] :
( c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1253])]) ).
fof(f5875,plain,
! [X2,X3,X0,X4] :
( c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4) ),
inference(equality_resolution,[],[f5434]) ).
fof(f5434,plain,
! [X2,X3,X0,X1,X4] :
( c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X0)) = c_Groups_Oplus__class_Oplus(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X2))
| X1 != X3
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4) ),
inference(cnf_transformation,[],[f3892]) ).
fof(f32228,plain,
spl47_1252,
inference(avatar_split_clause,[],[f5335,f32226]) ).
fof(f32226,plain,
( spl47_1252
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1252])]) ).
fof(f5335,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f3279]) ).
fof(f3279,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f2131]) ).
fof(f2131,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X1),X0)) ),
inference(rectify,[],[f546]) ).
fof(f546,axiom,
! [X34,X13,X8,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),X8,X13)),X34) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X8),X34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X13),X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__add__left) ).
fof(f32224,plain,
spl47_1251,
inference(avatar_split_clause,[],[f5334,f32222]) ).
fof(f32222,plain,
( spl47_1251
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_OpCons(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X1),X0)))
| ~ class_Rings_Ocomm__semiring__0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1251])]) ).
fof(f5334,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_OpCons(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X1),X0)))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f3278]) ).
fof(f3278,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_OpCons(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X1),X0)))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f2130]) ).
fof(f2130,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_OpCons(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X1),X0))) ),
inference(rectify,[],[f635]) ).
fof(f635,axiom,
! [X13,X8,X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),c_Polynomial_OpCons(X5,X4,X8)),X13) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),c_Polynomial_Osmult(X5,X4,X13),c_Polynomial_OpCons(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X8),X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pCons__left) ).
fof(f32220,plain,
spl47_1250,
inference(avatar_split_clause,[],[f5333,f32218]) ).
fof(f32218,plain,
( spl47_1250
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_OpCons(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X1,X2),c_Polynomial_OpCons(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0)))
| ~ class_Rings_Ocomm__semiring__0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1250])]) ).
fof(f5333,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_OpCons(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X1,X2),c_Polynomial_OpCons(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0)))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f3277]) ).
fof(f3277,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_OpCons(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X1,X2),c_Polynomial_OpCons(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0)))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f2129]) ).
fof(f2129,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_OpCons(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X1,X2),c_Polynomial_OpCons(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0))) ),
inference(rectify,[],[f636]) ).
fof(f636,axiom,
! [X13,X4,X8,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X8),c_Polynomial_OpCons(X5,X4,X13)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),c_Polynomial_Osmult(X5,X4,X8),c_Polynomial_OpCons(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X8),X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pCons__right) ).
fof(f32215,plain,
( spl47_1249
| ~ spl47_253
| ~ spl47_1033 ),
inference(avatar_split_clause,[],[f31457,f22128,f7201,f32213]) ).
fof(f32213,plain,
( spl47_1249
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK35(X0,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1249])]) ).
fof(f7201,plain,
( spl47_253
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_253])]) ).
fof(f31457,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK35(X0,X0),X0)
| ~ spl47_253
| ~ spl47_1033 ),
inference(superposition,[],[f7202,f22129]) ).
fof(f7202,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ spl47_253 ),
inference(avatar_component_clause,[],[f7201]) ).
fof(f32211,plain,
spl47_1248,
inference(avatar_split_clause,[],[f5044,f32209]) ).
fof(f32209,plain,
( spl47_1248
<=> ! [X4,X0,X2,X1] :
( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),sK41(X0,X1,X2))))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,X4,c_Groups_Ozero__class_Ozero(X2))))
| ~ class_Rings_Osemiring__0(X2)
| ~ class_Rings_Odvd(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1248])]) ).
fof(f5044,plain,
! [X2,X0,X1,X4] :
( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),sK41(X0,X1,X2))))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,X4,c_Groups_Ozero__class_Ozero(X2))))
| ~ class_Rings_Osemiring__0(X2)
| ~ class_Rings_Odvd(X2) ),
inference(cnf_transformation,[],[f3776]) ).
fof(f3776,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),sK41(X0,X1,X2))))
| ! [X4] :
( ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,X4,c_Groups_Ozero__class_Ozero(X2)))) ) )
& ( ( hBOOL(hAPP(X1,sK42(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,sK42(X0,X1,X2),c_Groups_Ozero__class_Ozero(X2)))) )
| ! [X6] : ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X6))) ) )
| ~ class_Rings_Osemiring__0(X2)
| ~ class_Rings_Odvd(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK41,sK42])],[f3773,f3775,f3774]) ).
fof(f3774,plain,
! [X0,X1,X2] :
( ? [X3] : hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X3)))
=> hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),sK41(X0,X1,X2)))) ),
introduced(choice_axiom,[]) ).
fof(f3775,plain,
! [X0,X1,X2] :
( ? [X5] :
( hBOOL(hAPP(X1,X5))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,X5,c_Groups_Ozero__class_Ozero(X2)))) )
=> ( hBOOL(hAPP(X1,sK42(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,sK42(X0,X1,X2),c_Groups_Ozero__class_Ozero(X2)))) ) ),
introduced(choice_axiom,[]) ).
fof(f3773,plain,
! [X0,X1,X2] :
( ( ( ? [X3] : hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X3)))
| ! [X4] :
( ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,X4,c_Groups_Ozero__class_Ozero(X2)))) ) )
& ( ? [X5] :
( hBOOL(hAPP(X1,X5))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,X5,c_Groups_Ozero__class_Ozero(X2)))) )
| ! [X6] : ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X6))) ) )
| ~ class_Rings_Osemiring__0(X2)
| ~ class_Rings_Odvd(X2) ),
inference(rectify,[],[f3772]) ).
fof(f3772,plain,
! [X0,X1,X2] :
( ( ( ? [X3] : hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X3)))
| ! [X4] :
( ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,X4,c_Groups_Ozero__class_Ozero(X2)))) ) )
& ( ? [X4] :
( hBOOL(hAPP(X1,X4))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,X4,c_Groups_Ozero__class_Ozero(X2)))) )
| ! [X3] : ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X3))) ) )
| ~ class_Rings_Osemiring__0(X2)
| ~ class_Rings_Odvd(X2) ),
inference(nnf_transformation,[],[f3038]) ).
fof(f3038,plain,
! [X0,X1,X2] :
( ( ? [X3] : hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X3)))
<=> ? [X4] :
( hBOOL(hAPP(X1,X4))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,X4,c_Groups_Ozero__class_Ozero(X2)))) ) )
| ~ class_Rings_Osemiring__0(X2)
| ~ class_Rings_Odvd(X2) ),
inference(flattening,[],[f3037]) ).
fof(f3037,plain,
! [X0,X1,X2] :
( ( ? [X3] : hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X3)))
<=> ? [X4] :
( hBOOL(hAPP(X1,X4))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,X4,c_Groups_Ozero__class_Ozero(X2)))) ) )
| ~ class_Rings_Osemiring__0(X2)
| ~ class_Rings_Odvd(X2) ),
inference(ennf_transformation,[],[f1933]) ).
fof(f1933,plain,
! [X0,X1,X2] :
( ( class_Rings_Osemiring__0(X2)
& class_Rings_Odvd(X2) )
=> ( ? [X3] : hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X3)))
<=> ? [X4] :
( hBOOL(hAPP(X1,X4))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,X4,c_Groups_Ozero__class_Ozero(X2)))) ) ) ),
inference(rectify,[],[f638]) ).
fof(f638,axiom,
! [X47,X39,X5] :
( ( class_Rings_Osemiring__0(X5)
& class_Rings_Odvd(X5) )
=> ( ? [X2] : hBOOL(hAPP(X39,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X47),X2)))
<=> ? [X2] :
( hBOOL(hAPP(X39,X2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X47),c_Groups_Oplus__class_Oplus(X5,X2,c_Groups_Ozero__class_Ozero(X5)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unity__coeff__ex) ).
fof(f32207,plain,
spl47_1247,
inference(avatar_split_clause,[],[f4864,f32205]) ).
fof(f32205,plain,
( spl47_1247
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1247])]) ).
fof(f4864,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(cnf_transformation,[],[f2834]) ).
fof(f2834,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(flattening,[],[f2833]) ).
fof(f2833,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(ennf_transformation,[],[f1792]) ).
fof(f1792,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Oone__class_Oone(X2))
=> c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ) ) ),
inference(rectify,[],[f634]) ).
fof(f634,axiom,
! [X7,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> ( c_Orderings_Oord__class_Oless(X5,X4,c_Groups_Oone__class_Oone(X5))
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less) ).
fof(f31940,plain,
( spl47_1246
| ~ spl47_251
| ~ spl47_1033 ),
inference(avatar_split_clause,[],[f31455,f22128,f7193,f31938]) ).
fof(f31938,plain,
( spl47_1246
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,sK35(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1246])]) ).
fof(f7193,plain,
( spl47_251
<=> ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_251])]) ).
fof(f31455,plain,
( ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,sK35(X0,X0))
| ~ spl47_251
| ~ spl47_1033 ),
inference(superposition,[],[f7194,f22129]) ).
fof(f7194,plain,
( ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0)
| ~ spl47_251 ),
inference(avatar_component_clause,[],[f7193]) ).
fof(f31660,plain,
spl47_1245,
inference(avatar_split_clause,[],[f5452,f31658]) ).
fof(f31658,plain,
( spl47_1245
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X0)),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X2)),X1))
| ~ class_Rings_Ocomm__semiring__1(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1245])]) ).
fof(f5452,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X0)),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X2)),X1))
| ~ class_Rings_Ocomm__semiring__1(X4) ),
inference(cnf_transformation,[],[f3424]) ).
fof(f3424,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X0)),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X2)),X1))
| ~ class_Rings_Ocomm__semiring__1(X4) ),
inference(flattening,[],[f3423]) ).
fof(f3423,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X0)),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X2)),X1))
| ~ class_Rings_Ocomm__semiring__1(X4) ),
inference(ennf_transformation,[],[f2225]) ).
fof(f2225,plain,
! [X0,X1,X2,X3,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X2)),X1))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X0)),X1)) ) ) ),
inference(rectify,[],[f111]) ).
fof(f111,axiom,
! [X21,X17,X7,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7)),X17))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X7)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X21)),X17)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__dvd) ).
fof(f31656,plain,
spl47_1244,
inference(avatar_split_clause,[],[f5450,f31654]) ).
fof(f31654,plain,
( spl47_1244
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X2),X0)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X3),X2))
| ~ class_Rings_Ocomm__semiring__1(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1244])]) ).
fof(f5450,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X2),X0)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X3),X2))
| ~ class_Rings_Ocomm__semiring__1(X4) ),
inference(cnf_transformation,[],[f3420]) ).
fof(f3420,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X2),X0)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X3),X2))
| ~ class_Rings_Ocomm__semiring__1(X4) ),
inference(flattening,[],[f3419]) ).
fof(f3419,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X2),X0)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X3),X2))
| ~ class_Rings_Ocomm__semiring__1(X4) ),
inference(ennf_transformation,[],[f2223]) ).
fof(f2223,plain,
! [X0,X1,X2,X3,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),X3),X2))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X2),X0))) ) ) ),
inference(rectify,[],[f112]) ).
fof(f112,axiom,
! [X21,X7,X10,X6,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X6),X10))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X21)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X7)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X10),X21))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power__le) ).
fof(f31652,plain,
spl47_1243,
inference(avatar_split_clause,[],[f5353,f31650]) ).
fof(f31650,plain,
( spl47_1243
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1243])]) ).
fof(f5353,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3299]) ).
fof(f3299,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2149]) ).
fof(f2149,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ),
inference(rectify,[],[f511]) ).
fof(f511,axiom,
! [X13,X10,X6,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X10)),X13) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X13)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X10),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(f31648,plain,
spl47_1242,
inference(avatar_split_clause,[],[f5295,f31646]) ).
fof(f31646,plain,
( spl47_1242
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))
| ~ class_Groups_Ocomm__monoid__mult(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1242])]) ).
fof(f5295,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))
| ~ class_Groups_Ocomm__monoid__mult(X3) ),
inference(cnf_transformation,[],[f3236]) ).
fof(f3236,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))
| ~ class_Groups_Ocomm__monoid__mult(X3) ),
inference(ennf_transformation,[],[f2095]) ).
fof(f2095,plain,
! [X0,X1,X2,X3] :
( class_Groups_Ocomm__monoid__mult(X3)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ),
inference(rectify,[],[f534]) ).
fof(f534,axiom,
! [X7,X17,X4,X5] :
( class_Groups_Ocomm__monoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17)),X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X17),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult__distrib) ).
fof(f31451,plain,
spl47_1241,
inference(avatar_split_clause,[],[f5277,f31449]) ).
fof(f31449,plain,
( spl47_1241
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2))
| ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Oone__class_Oone(X3))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ class_Rings_Olinordered__semidom(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1241])]) ).
fof(f5277,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2))
| ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Oone__class_Oone(X3))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(cnf_transformation,[],[f3210]) ).
fof(f3210,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2))
| ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Oone__class_Oone(X3))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(flattening,[],[f3209]) ).
fof(f3209,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2))
| ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Oone__class_Oone(X3))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(ennf_transformation,[],[f2080]) ).
fof(f2080,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> ( c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Oone__class_Oone(X3))
=> c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)) ) ) ) ),
inference(rectify,[],[f205]) ).
fof(f205,axiom,
! [X4,X36,X7,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X36)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> ( c_Orderings_Oord__class_Oless(X5,X4,c_Groups_Oone__class_Oone(X5))
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X36),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).
fof(f31447,plain,
spl47_1240,
inference(avatar_split_clause,[],[f5275,f31445]) ).
fof(f31445,plain,
( spl47_1240
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Rings_Olinordered__semidom(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1240])]) ).
fof(f5275,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(cnf_transformation,[],[f3206]) ).
fof(f3206,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(flattening,[],[f3205]) ).
fof(f3205,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(ennf_transformation,[],[f2078]) ).
fof(f2078,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
=> c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ) ) ) ),
inference(rectify,[],[f249]) ).
fof(f249,axiom,
! [X7,X17,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X17)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X17),X7)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__mono) ).
fof(f31443,plain,
spl47_1239,
inference(avatar_split_clause,[],[f5274,f31441]) ).
fof(f31441,plain,
( spl47_1239
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Oone__class_Oone(X3))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ class_Rings_Olinordered__semidom(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1239])]) ).
fof(f5274,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Oone__class_Oone(X3))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(cnf_transformation,[],[f3204]) ).
fof(f3204,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Oone__class_Oone(X3))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(flattening,[],[f3203]) ).
fof(f3203,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Oone__class_Oone(X3))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(ennf_transformation,[],[f2077]) ).
fof(f2077,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Oone__class_Oone(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)) ) ) ) ),
inference(rectify,[],[f131]) ).
fof(f131,axiom,
! [X4,X36,X7,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X36)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,c_Groups_Oone__class_Oone(X5))
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X36),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__decreasing) ).
fof(f31439,plain,
spl47_1238,
inference(avatar_split_clause,[],[f5265,f31437]) ).
fof(f31437,plain,
( spl47_1238
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)))
| ~ class_Rings_Oidom(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1238])]) ).
fof(f5265,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)))
| ~ class_Rings_Oidom(X3) ),
inference(cnf_transformation,[],[f3864]) ).
fof(f3864,plain,
! [X0,X1,X2,X3] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
& c_Groups_Ozero__class_Ozero(X3) != X2 ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))) ) )
| ~ class_Rings_Oidom(X3) ),
inference(flattening,[],[f3863]) ).
fof(f3863,plain,
! [X0,X1,X2,X3] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
& c_Groups_Ozero__class_Ozero(X3) != X2 ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))) ) )
| ~ class_Rings_Oidom(X3) ),
inference(nnf_transformation,[],[f3192]) ).
fof(f3192,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| c_Groups_Ozero__class_Ozero(X3) = X2 ) )
| ~ class_Rings_Oidom(X3) ),
inference(ennf_transformation,[],[f2070]) ).
fof(f2070,plain,
! [X0,X1,X2,X3] :
( class_Rings_Oidom(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| c_Groups_Ozero__class_Ozero(X3) = X2 ) ) ),
inference(rectify,[],[f584]) ).
fof(f584,axiom,
! [X29,X12,X24,X5] :
( class_Rings_Oidom(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X29)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X12),X29))
| c_Groups_Ozero__class_Ozero(X5) = X24 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__left) ).
fof(f31435,plain,
spl47_1237,
inference(avatar_split_clause,[],[f5262,f31433]) ).
fof(f31433,plain,
( spl47_1237
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| c_Groups_Ozero__class_Ozero(X3) = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
| ~ class_Rings_Oidom(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1237])]) ).
fof(f5262,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| c_Groups_Ozero__class_Ozero(X3) = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
| ~ class_Rings_Oidom(X3) ),
inference(cnf_transformation,[],[f3862]) ).
fof(f3862,plain,
! [X0,X1,X2,X3] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
& c_Groups_Ozero__class_Ozero(X3) != X1 ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| c_Groups_Ozero__class_Ozero(X3) = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))) ) )
| ~ class_Rings_Oidom(X3) ),
inference(flattening,[],[f3861]) ).
fof(f3861,plain,
! [X0,X1,X2,X3] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
& c_Groups_Ozero__class_Ozero(X3) != X1 ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| c_Groups_Ozero__class_Ozero(X3) = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))) ) )
| ~ class_Rings_Oidom(X3) ),
inference(nnf_transformation,[],[f3191]) ).
fof(f3191,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| c_Groups_Ozero__class_Ozero(X3) = X1 ) )
| ~ class_Rings_Oidom(X3) ),
inference(ennf_transformation,[],[f2069]) ).
fof(f2069,plain,
! [X0,X1,X2,X3] :
( class_Rings_Oidom(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| c_Groups_Ozero__class_Ozero(X3) = X1 ) ) ),
inference(rectify,[],[f585]) ).
fof(f585,axiom,
! [X29,X24,X12,X5] :
( class_Rings_Oidom(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X29),X24)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X12),X29))
| c_Groups_Ozero__class_Ozero(X5) = X24 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__right) ).
fof(f31431,plain,
spl47_1236,
inference(avatar_split_clause,[],[f5172,f31429]) ).
fof(f31429,plain,
( spl47_1236
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Rings_Oinverse__class_Odivide(X3,X1,X2)),X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1236])]) ).
fof(f5172,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Rings_Oinverse__class_Odivide(X3,X1,X2)),X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(cnf_transformation,[],[f3099]) ).
fof(f3099,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Rings_Oinverse__class_Odivide(X3,X1,X2)),X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(flattening,[],[f3098]) ).
fof(f3098,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Rings_Oinverse__class_Odivide(X3,X1,X2)),X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(ennf_transformation,[],[f2016]) ).
fof(f2016,plain,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( c_Groups_Ozero__class_Ozero(X3) != X2
=> hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Rings_Oinverse__class_Odivide(X3,X1,X2)),X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)) ) ),
inference(rectify,[],[f914]) ).
fof(f914,axiom,
! [X7,X4,X17,X5] :
( class_Fields_Ofield(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X17
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Rings_Oinverse__class_Odivide(X5,X4,X17)),X7) = c_Rings_Oinverse__class_Odivide(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X17),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__power__divide) ).
fof(f31427,plain,
spl47_1235,
inference(avatar_split_clause,[],[f5123,f31425]) ).
fof(f31425,plain,
( spl47_1235
<=> ! [X0,X3,X2,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1)),X2),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1235])]) ).
fof(f5123,plain,
! [X2,X3,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1)),X2),X0),
inference(cnf_transformation,[],[f1961]) ).
fof(f1961,plain,
! [X0,X1,X2,X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1)),X2),X0),
inference(rectify,[],[f726]) ).
fof(f726,axiom,
! [X20,X33,X60,X32] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X60),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X60),X20)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X33)),X60),X20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
fof(f31423,plain,
spl47_1234,
inference(avatar_split_clause,[],[f4812,f31421]) ).
fof(f31421,plain,
( spl47_1234
<=> ! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Rings_Oidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1234])]) ).
fof(f4812,plain,
! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f2785]) ).
fof(f2785,plain,
! [X0,X1,X2] :
( c_Polynomial_Odegree(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Rings_Oidom(X2) ),
inference(flattening,[],[f2784]) ).
fof(f2784,plain,
! [X0,X1,X2] :
( c_Polynomial_Odegree(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Rings_Oidom(X2) ),
inference(ennf_transformation,[],[f1757]) ).
fof(f1757,plain,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
=> c_Polynomial_Odegree(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0)) ) ) ),
inference(rectify,[],[f627]) ).
fof(f627,axiom,
! [X13,X8,X5] :
( class_Rings_Oidom(X5)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) != X8
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) != X13
=> c_Polynomial_Odegree(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X8),X13)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X5,X8),c_Polynomial_Odegree(X5,X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__mult__eq) ).
fof(f31419,plain,
spl47_1233,
inference(avatar_split_clause,[],[f4805,f31417]) ).
fof(f31417,plain,
( spl47_1233
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Polynomial_Oorder(X2,X1,X0))),X0))
| ~ class_Rings_Oidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1233])]) ).
fof(f4805,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Polynomial_Oorder(X2,X1,X0))),X0))
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f2776]) ).
fof(f2776,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Polynomial_Oorder(X2,X1,X0))),X0))
| ~ class_Rings_Oidom(X2) ),
inference(ennf_transformation,[],[f1752]) ).
fof(f1752,plain,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),c_Polynomial_Oorder(X2,X1,X0))),X0)) ),
inference(rectify,[],[f461]) ).
fof(f461,axiom,
! [X8,X4,X5] :
( class_Rings_Oidom(X5)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X5)),c_Polynomial_OpCons(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),c_Polynomial_OpCons(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))))),c_Polynomial_Oorder(X5,X4,X8))),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__1) ).
fof(f31415,plain,
spl47_1232,
inference(avatar_split_clause,[],[f4730,f31413]) ).
fof(f31413,plain,
( spl47_1232
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oone__class_Oone(X2))),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ class_Rings_Oring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1232])]) ).
fof(f4730,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oone__class_Oone(X2))),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ class_Rings_Oring__1(X2) ),
inference(cnf_transformation,[],[f2682]) ).
fof(f2682,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oone__class_Oone(X2))),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ class_Rings_Oring__1(X2) ),
inference(ennf_transformation,[],[f1692]) ).
fof(f1692,plain,
! [X0,X1,X2] :
( class_Rings_Oring__1(X2)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oone__class_Oone(X2))),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(rectify,[],[f625]) ).
fof(f625,axiom,
! [X7,X4,X5] :
( class_Rings_Oring__1(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Ouminus__class_Ouminus(X5,X4)),X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Oone__class_Oone(X5))),X7)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus) ).
fof(f31409,plain,
( ~ spl47_1231
| spl47_220
| spl47_219 ),
inference(avatar_split_clause,[],[f4087,f7059,f7064,f31406]) ).
fof(f4087,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK30) ),
inference(cnf_transformation,[],[f3537]) ).
fof(f3537,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK30)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK30) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f2309,f3536]) ).
fof(f3536,plain,
( ? [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) )
=> ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK30)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK30) ) ),
introduced(choice_axiom,[]) ).
fof(f2309,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) ) ),
inference(flattening,[],[f2308]) ).
fof(f2308,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) ) ),
inference(ennf_transformation,[],[f1211]) ).
fof(f1211,plain,
( ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0)
=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) )
=> ( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
( ! [X2] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X2) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X2) )
=> ( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_091_124_AALL_Ax_O_Apoly_Ap_Ax_A_061_A0_A_N_N_062_Apoly_Aq_Ax_A_061_A0_059_Adegree_Ap_A_061_Adegree_Ap_059_Adegree_Ap_A_126_061_A0_A_124_093_061_061_062_Ap_Advd_Aq_A_094_Adegree_Ap_096) ).
fof(f31394,plain,
( spl47_1230
| spl47_220
| spl47_219 ),
inference(avatar_split_clause,[],[f4086,f7059,f7064,f31391]) ).
fof(f4086,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK30) ),
inference(cnf_transformation,[],[f3537]) ).
fof(f31031,plain,
spl47_1229,
inference(avatar_split_clause,[],[f6031,f31029]) ).
fof(f31029,plain,
( spl47_1229
<=> ! [X4,X3,X2,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4))),X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1229])]) ).
fof(f6031,plain,
! [X2,X3,X1,X4] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4))),X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(forward_demodulation,[],[f5880,f5123]) ).
fof(f5880,plain,
! [X2,X3,X1,X4] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(equality_resolution,[],[f5459]) ).
fof(f5459,plain,
! [X2,X3,X0,X1,X4] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2),X1) != X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(cnf_transformation,[],[f3897]) ).
fof(f31027,plain,
spl47_1228,
inference(avatar_split_clause,[],[f5396,f31025]) ).
fof(f31025,plain,
( spl47_1228
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Rings_Oinverse__class_Odivide(X4,X3,X2)),c_Rings_Oinverse__class_Odivide(X4,X1,X0)) = c_Rings_Oinverse__class_Odivide(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ class_Fields_Ofield__inverse__zero(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1228])]) ).
fof(f5396,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Rings_Oinverse__class_Odivide(X4,X3,X2)),c_Rings_Oinverse__class_Odivide(X4,X1,X0)) = c_Rings_Oinverse__class_Odivide(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ class_Fields_Ofield__inverse__zero(X4) ),
inference(cnf_transformation,[],[f3369]) ).
fof(f3369,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Rings_Oinverse__class_Odivide(X4,X3,X2)),c_Rings_Oinverse__class_Odivide(X4,X1,X0)) = c_Rings_Oinverse__class_Odivide(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0))
| ~ class_Fields_Ofield__inverse__zero(X4) ),
inference(ennf_transformation,[],[f2191]) ).
fof(f2191,plain,
! [X0,X1,X2,X3,X4] :
( class_Fields_Ofield__inverse__zero(X4)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Rings_Oinverse__class_Odivide(X4,X3,X2)),c_Rings_Oinverse__class_Odivide(X4,X1,X0)) = c_Rings_Oinverse__class_Odivide(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X0)) ),
inference(rectify,[],[f928]) ).
fof(f928,axiom,
! [X48,X26,X10,X6,X5] :
( class_Fields_Ofield__inverse__zero(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Rings_Oinverse__class_Odivide(X5,X6,X10)),c_Rings_Oinverse__class_Odivide(X5,X26,X48)) = c_Rings_Oinverse__class_Odivide(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X48)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__times__eq) ).
fof(f31023,plain,
spl47_1227,
inference(avatar_split_clause,[],[f5332,f31021]) ).
fof(f31021,plain,
( spl47_1227
<=> ! [X0,X3,X2,X1] :
( c_Polynomial_Opcompose(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X0),c_Polynomial_Opcompose(X3,X1,X0)))
| ~ class_Rings_Ocomm__semiring__0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1227])]) ).
fof(f5332,plain,
! [X2,X3,X0,X1] :
( c_Polynomial_Opcompose(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X0),c_Polynomial_Opcompose(X3,X1,X0)))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f3276]) ).
fof(f3276,plain,
! [X0,X1,X2,X3] :
( c_Polynomial_Opcompose(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X0),c_Polynomial_Opcompose(X3,X1,X0)))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f2128]) ).
fof(f2128,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Polynomial_Opcompose(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_OpCons(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X0),c_Polynomial_Opcompose(X3,X1,X0))) ),
inference(rectify,[],[f640]) ).
fof(f640,axiom,
! [X13,X8,X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Polynomial_Opcompose(X5,c_Polynomial_OpCons(X5,X4,X8),X13) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),c_Polynomial_OpCons(X5,X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X13),c_Polynomial_Opcompose(X5,X8,X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pcompose__pCons) ).
fof(f31019,plain,
spl47_1226,
inference(avatar_split_clause,[],[f5018,f31017]) ).
fof(f31017,plain,
( spl47_1226
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1226])]) ).
fof(f5018,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(cnf_transformation,[],[f3770]) ).
fof(f3770,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(nnf_transformation,[],[f3002]) ).
fof(f3002,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(ennf_transformation,[],[f1913]) ).
fof(f1913,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) ) ),
inference(rectify,[],[f724]) ).
fof(f724,axiom,
! [X11,X14,X44] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X44)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X14)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X11)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X14),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel1) ).
fof(f31015,plain,
spl47_1225,
inference(avatar_split_clause,[],[f4874,f31013]) ).
fof(f31013,plain,
( spl47_1225
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ class_Groups_Omonoid__mult(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1225])]) ).
fof(f4874,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ class_Groups_Omonoid__mult(X2) ),
inference(cnf_transformation,[],[f2845]) ).
fof(f2845,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ class_Groups_Omonoid__mult(X2) ),
inference(flattening,[],[f2844]) ).
fof(f2844,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ class_Groups_Omonoid__mult(X2) ),
inference(ennf_transformation,[],[f1800]) ).
fof(f1800,plain,
! [X0,X1,X2] :
( class_Groups_Omonoid__mult(X2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X0) ) ),
inference(rectify,[],[f755]) ).
fof(f755,axiom,
! [X6,X7,X5] :
( class_Groups_Omonoid__mult(X5)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__minus__mult) ).
fof(f31011,plain,
spl47_1224,
inference(avatar_split_clause,[],[f4840,f31009]) ).
fof(f31009,plain,
( spl47_1224
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0))
| c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ class_Rings_Oidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1224])]) ).
fof(f4840,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0))
| c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f3732]) ).
fof(f3732,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0))
| c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1)) )
& ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0)) ) )
| ~ class_Rings_Oidom(X2) ),
inference(nnf_transformation,[],[f2802]) ).
fof(f2802,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0))
<=> c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1)) )
| ~ class_Rings_Oidom(X2) ),
inference(ennf_transformation,[],[f1771]) ).
fof(f1771,plain,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0))
<=> c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1)) ) ),
inference(rectify,[],[f456]) ).
fof(f456,axiom,
! [X9,X24,X5] :
( class_Rings_Oidom(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),c_Polynomial_OpCons(X5,X24,c_Polynomial_OpCons(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))))),X9))
<=> c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Polynomial_Opoly(X5,X9),c_Groups_Ouminus__class_Ouminus(X5,X24)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__iff__poly__eq__0) ).
fof(f31007,plain,
spl47_1223,
inference(avatar_split_clause,[],[f4839,f31005]) ).
fof(f31005,plain,
( spl47_1223
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0))
| ~ class_Rings_Oidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1223])]) ).
fof(f4839,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0))
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f3732]) ).
fof(f31001,plain,
spl47_1222,
inference(avatar_split_clause,[],[f4829,f30999]) ).
fof(f30999,plain,
( spl47_1222
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X1))
| ~ class_Rings_Oidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1222])]) ).
fof(f4829,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X1))
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f3725]) ).
fof(f3725,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X1)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X1))
| c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X1),X0) ) )
| ~ class_Rings_Oidom(X2) ),
inference(nnf_transformation,[],[f2798]) ).
fof(f2798,plain,
! [X0,X1,X2] :
( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X1)) )
| ~ class_Rings_Oidom(X2) ),
inference(ennf_transformation,[],[f1767]) ).
fof(f1767,plain,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X1)) ) ),
inference(rectify,[],[f455]) ).
fof(f455,axiom,
! [X24,X9,X5] :
( class_Rings_Oidom(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Polynomial_Opoly(X5,X9),X24)
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),c_Polynomial_OpCons(X5,c_Groups_Ouminus__class_Ouminus(X5,X24),c_Polynomial_OpCons(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))))),X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__0__iff__dvd) ).
fof(f30997,plain,
spl47_1221,
inference(avatar_split_clause,[],[f4828,f30995]) ).
fof(f30995,plain,
( spl47_1221
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X1))
| c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X1),X0)
| ~ class_Rings_Oidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1221])]) ).
fof(f4828,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X1))
| c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X1),X0)
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f3725]) ).
fof(f30628,plain,
spl47_1220,
inference(avatar_split_clause,[],[f5884,f30626]) ).
fof(f30626,plain,
( spl47_1220
<=> ! [X4,X0,X5,X3,X1] :
( c_Groups_Oplus__class_Oplus(X5,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X1)) != c_Groups_Oplus__class_Oplus(X5,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X0))
| X0 = X1
| c_Groups_Ozero__class_Ozero(X5) = X4
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1220])]) ).
fof(f5884,plain,
! [X3,X0,X1,X4,X5] :
( c_Groups_Oplus__class_Oplus(X5,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X1)) != c_Groups_Oplus__class_Oplus(X5,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X0))
| X0 = X1
| c_Groups_Ozero__class_Ozero(X5) = X4
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5) ),
inference(equality_resolution,[],[f5490]) ).
fof(f5490,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Groups_Oplus__class_Oplus(X5,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X1)) != c_Groups_Oplus__class_Oplus(X5,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X0))
| X0 = X1
| X2 != X3
| c_Groups_Ozero__class_Ozero(X5) = X4
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5) ),
inference(cnf_transformation,[],[f3457]) ).
fof(f3457,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Groups_Oplus__class_Oplus(X5,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X1)) != c_Groups_Oplus__class_Oplus(X5,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X0))
| X0 = X1
| X2 != X3
| c_Groups_Ozero__class_Ozero(X5) = X4
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5) ),
inference(flattening,[],[f3456]) ).
fof(f3456,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Groups_Oplus__class_Oplus(X5,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X1)) != c_Groups_Oplus__class_Oplus(X5,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X0))
| X0 = X1
| X2 != X3
| c_Groups_Ozero__class_Ozero(X5) = X4
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5) ),
inference(ennf_transformation,[],[f2250]) ).
fof(f2250,plain,
! [X0,X1,X2,X3,X4,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X4
=> ( ( X0 != X1
& X2 = X3 )
=> c_Groups_Oplus__class_Oplus(X5,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X1)) != c_Groups_Oplus__class_Oplus(X5,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X0)) ) ) ),
inference(rectify,[],[f582]) ).
fof(f582,axiom,
! [X46,X16,X17,X4,X34,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X34
=> ( ( X16 != X46
& X4 = X17 )
=> c_Groups_Oplus__class_Oplus(X5,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X34),X16)) != c_Groups_Oplus__class_Oplus(X5,X17,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X34),X46)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
fof(f30624,plain,
spl47_1219,
inference(avatar_split_clause,[],[f5443,f30622]) ).
fof(f30622,plain,
( spl47_1219
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),c_Polynomial_Omonom(X4,X3,X2)),c_Polynomial_Omonom(X4,X1,X0)) = c_Polynomial_Omonom(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ class_Rings_Ocomm__semiring__0(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1219])]) ).
fof(f5443,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),c_Polynomial_Omonom(X4,X3,X2)),c_Polynomial_Omonom(X4,X1,X0)) = c_Polynomial_Omonom(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ class_Rings_Ocomm__semiring__0(X4) ),
inference(cnf_transformation,[],[f3412]) ).
fof(f3412,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),c_Polynomial_Omonom(X4,X3,X2)),c_Polynomial_Omonom(X4,X1,X0)) = c_Polynomial_Omonom(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ class_Rings_Ocomm__semiring__0(X4) ),
inference(ennf_transformation,[],[f2217]) ).
fof(f2217,plain,
! [X0,X1,X2,X3,X4] :
( class_Rings_Ocomm__semiring__0(X4)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),c_Polynomial_Omonom(X4,X3,X2)),c_Polynomial_Omonom(X4,X1,X0)) = c_Polynomial_Omonom(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
inference(rectify,[],[f485]) ).
fof(f485,axiom,
! [X7,X17,X21,X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),c_Polynomial_Omonom(X5,X4,X21)),c_Polynomial_Omonom(X5,X17,X7)) = c_Polynomial_Omonom(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__monom) ).
fof(f30619,plain,
spl47_1218,
inference(avatar_split_clause,[],[f5352,f30617]) ).
fof(f30617,plain,
( spl47_1218
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1218])]) ).
fof(f5352,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3298]) ).
fof(f3298,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2148]) ).
fof(f2148,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)) ),
inference(rectify,[],[f600]) ).
fof(f600,axiom,
! [X13,X8,X6,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X8)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X13)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(f30615,plain,
spl47_1217,
inference(avatar_split_clause,[],[f5331,f30613]) ).
fof(f30613,plain,
( spl47_1217
<=> ! [X0,X3,X2,X1] :
( hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Polynomial_Opoly(X3,X2),X0)),hAPP(c_Polynomial_Opoly(X3,X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1217])]) ).
fof(f5331,plain,
! [X2,X3,X0,X1] :
( hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Polynomial_Opoly(X3,X2),X0)),hAPP(c_Polynomial_Opoly(X3,X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f3275]) ).
fof(f3275,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Polynomial_Opoly(X3,X2),X0)),hAPP(c_Polynomial_Opoly(X3,X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f2127]) ).
fof(f2127,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Polynomial_Opoly(X3,X2),X0)),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
inference(rectify,[],[f535]) ).
fof(f535,axiom,
! [X6,X13,X8,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> hAPP(c_Polynomial_Opoly(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X8),X13)),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Polynomial_Opoly(X5,X8),X6)),hAPP(c_Polynomial_Opoly(X5,X13),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__mult) ).
fof(f30611,plain,
spl47_1216,
inference(avatar_split_clause,[],[f5304,f30609]) ).
fof(f30609,plain,
( spl47_1216
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| ~ class_Groups_Omonoid__mult(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1216])]) ).
fof(f5304,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| ~ class_Groups_Omonoid__mult(X3) ),
inference(cnf_transformation,[],[f3246]) ).
fof(f3246,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| ~ class_Groups_Omonoid__mult(X3) ),
inference(ennf_transformation,[],[f2102]) ).
fof(f2102,plain,
! [X0,X1,X2,X3] :
( class_Groups_Omonoid__mult(X3)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)) ),
inference(rectify,[],[f599]) ).
fof(f599,axiom,
! [X7,X21,X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X7)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X21)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__add) ).
fof(f30607,plain,
spl47_1215,
inference(avatar_split_clause,[],[f5119,f30605]) ).
fof(f30605,plain,
( spl47_1215
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1215])]) ).
fof(f5119,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))) ),
inference(cnf_transformation,[],[f3820]) ).
fof(f3820,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))) ) ),
inference(flattening,[],[f3819]) ).
fof(f3819,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))) ) ),
inference(nnf_transformation,[],[f1959]) ).
fof(f1959,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 ) ),
inference(rectify,[],[f729]) ).
fof(f729,axiom,
! [X11,X14,X44] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X14)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X11)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X14),X11))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X44 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).
fof(f30603,plain,
spl47_1214,
inference(avatar_split_clause,[],[f5034,f30601]) ).
fof(f30601,plain,
( spl47_1214
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1214])]) ).
fof(f5034,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3024]) ).
fof(f3024,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(flattening,[],[f3023]) ).
fof(f3023,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(ennf_transformation,[],[f1926]) ).
fof(f1926,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
inference(rectify,[],[f722]) ).
fof(f722,axiom,
! [X67,X68,X69] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X69),X68),X67),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X67)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X69)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X68,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__neg__lemma) ).
fof(f30599,plain,
spl47_1213,
inference(avatar_split_clause,[],[f5032,f30597]) ).
fof(f30597,plain,
( spl47_1213
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1213])]) ).
fof(f5032,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f3020]) ).
fof(f3020,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(flattening,[],[f3019]) ).
fof(f3019,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(ennf_transformation,[],[f1924]) ).
fof(f1924,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0)) ) ) ),
inference(rectify,[],[f818]) ).
fof(f818,axiom,
! [X7,X21,X20] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X20),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X7)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X20),X21))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X21)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X20),X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diffD1) ).
fof(f30595,plain,
spl47_1212,
inference(avatar_split_clause,[],[f5031,f30593]) ).
fof(f30593,plain,
( spl47_1212
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1212])]) ).
fof(f5031,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f3018]) ).
fof(f3018,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(flattening,[],[f3017]) ).
fof(f3017,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(ennf_transformation,[],[f1923]) ).
fof(f1923,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ) ) ),
inference(rectify,[],[f819]) ).
fof(f819,axiom,
! [X7,X21,X20] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X20),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X7)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X20),X7))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X21)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X20),X21)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diffD) ).
fof(f30591,plain,
spl47_1211,
inference(avatar_split_clause,[],[f4962,f30589]) ).
fof(f30589,plain,
( spl47_1211
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1211])]) ).
fof(f4962,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 ),
inference(cnf_transformation,[],[f3758]) ).
fof(f3758,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X2))) ) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 ),
inference(nnf_transformation,[],[f2939]) ).
fof(f2939,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 ),
inference(ennf_transformation,[],[f1866]) ).
fof(f1866,plain,
! [X0,X1,X2] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) ) ),
inference(rectify,[],[f71]) ).
fof(f71,axiom,
! [X29,X12,X11] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X11
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X12),X11)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X29),X11)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X12),X29)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__eq__nat) ).
fof(f30587,plain,
spl47_1210,
inference(avatar_split_clause,[],[f4961,f30585]) ).
fof(f30585,plain,
( spl47_1210
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X2)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1210])]) ).
fof(f4961,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X2)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 ),
inference(cnf_transformation,[],[f3758]) ).
fof(f30583,plain,
spl47_1209,
inference(avatar_split_clause,[],[f4960,f30581]) ).
fof(f30581,plain,
( spl47_1209
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1209])]) ).
fof(f4960,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 ),
inference(cnf_transformation,[],[f3757]) ).
fof(f3757,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X2))) ) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 ),
inference(nnf_transformation,[],[f2938]) ).
fof(f2938,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 ),
inference(ennf_transformation,[],[f1865]) ).
fof(f1865,plain,
! [X0,X1,X2] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ) ),
inference(rectify,[],[f79]) ).
fof(f79,axiom,
! [X29,X12,X11] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X11
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X12),X11)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X29),X11)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X12),X29)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__eq__int) ).
fof(f30578,plain,
spl47_1208,
inference(avatar_split_clause,[],[f4959,f30576]) ).
fof(f30576,plain,
( spl47_1208
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X2)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1208])]) ).
fof(f4959,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),X2)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 ),
inference(cnf_transformation,[],[f3757]) ).
fof(f30574,plain,
spl47_1207,
inference(avatar_split_clause,[],[f4958,f30572]) ).
fof(f30572,plain,
( spl47_1207
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1207])]) ).
fof(f4958,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2 ),
inference(cnf_transformation,[],[f3756]) ).
fof(f3756,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ) )
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2 ),
inference(nnf_transformation,[],[f2937]) ).
fof(f2937,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0))) )
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2 ),
inference(ennf_transformation,[],[f1864]) ).
fof(f1864,plain,
! [X0,X1,X2] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X2
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0))) ) ),
inference(rectify,[],[f675]) ).
fof(f675,axiom,
! [X63,X14,X44] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X44
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X14),X63))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X44),X14)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X44),X63))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mono) ).
fof(f30570,plain,
spl47_1206,
inference(avatar_split_clause,[],[f4957,f30568]) ).
fof(f30568,plain,
( spl47_1206
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1206])]) ).
fof(f4957,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X2 ),
inference(cnf_transformation,[],[f3756]) ).
fof(f30566,plain,
spl47_1205,
inference(avatar_split_clause,[],[f4871,f30564]) ).
fof(f30564,plain,
( spl47_1205
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ class_Power_Opower(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1205])]) ).
fof(f4871,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ class_Power_Opower(X2) ),
inference(cnf_transformation,[],[f2841]) ).
fof(f2841,plain,
! [X0,X1,X2] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
& ( c_Groups_Oone__class_Oone(X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) )
| ~ class_Power_Opower(X2) ),
inference(ennf_transformation,[],[f1797]) ).
fof(f1797,plain,
! [X0,X1,X2] :
( class_Power_Opower(X2)
=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
=> hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
=> c_Groups_Oone__class_Oone(X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1) ) ) ),
inference(rectify,[],[f884]) ).
fof(f884,axiom,
! [X21,X7,X5] :
( class_Power_Opower(X5)
=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X7
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X21),X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X21),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X7
=> c_Groups_Oone__class_Oone(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X21),X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__num__eq__if) ).
fof(f29977,plain,
spl47_1204,
inference(avatar_split_clause,[],[f6023,f29975]) ).
fof(f29975,plain,
( spl47_1204
<=> ! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1204])]) ).
fof(f6023,plain,
! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(forward_demodulation,[],[f5638,f4240]) ).
fof(f5638,plain,
! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(definition_unfolding,[],[f4981,f4118,f4118]) ).
fof(f4981,plain,
! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2959]) ).
fof(f2959,plain,
! [X0,X1,X2] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1885]) ).
fof(f1885,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
inference(rectify,[],[f860]) ).
fof(f860,axiom,
! [X21,X33,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X33)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,X20)),X21) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X33),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).
fof(f29973,plain,
spl47_1203,
inference(avatar_split_clause,[],[f6022,f29971]) ).
fof(f29971,plain,
( spl47_1203
<=> ! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1203])]) ).
fof(f6022,plain,
! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(forward_demodulation,[],[f5637,f4240]) ).
fof(f5637,plain,
! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(definition_unfolding,[],[f4980,f4118,f4118]) ).
fof(f4980,plain,
! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),c_Nat_OSuc(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2958]) ).
fof(f2958,plain,
! [X0,X1,X2] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),c_Nat_OSuc(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1884]) ).
fof(f1884,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),c_Nat_OSuc(X1)) ),
inference(rectify,[],[f859]) ).
fof(f859,axiom,
! [X21,X33,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X33)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,X20))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X20),c_Nat_OSuc(X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).
fof(f29969,plain,
spl47_1202,
inference(avatar_split_clause,[],[f6015,f29967]) ).
fof(f29967,plain,
( spl47_1202
<=> ! [X2,X0] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ouminus__class_Ouminus(X2,X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Oidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1202])]) ).
fof(f6015,plain,
! [X2,X0] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ouminus__class_Ouminus(X2,X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Oidom(X2) ),
inference(forward_demodulation,[],[f6014,f4114]) ).
fof(f6014,plain,
! [X2,X0] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ouminus__class_Ouminus(X2,X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(X2) ),
inference(forward_demodulation,[],[f6013,f4240]) ).
fof(f6013,plain,
! [X2,X0] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ouminus__class_Ouminus(X2,X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Rings_Oidom(X2) ),
inference(forward_demodulation,[],[f5770,f4240]) ).
fof(f5770,plain,
! [X2,X0] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ouminus__class_Ouminus(X2,X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Oidom(X2) ),
inference(equality_resolution,[],[f5622]) ).
fof(f5622,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Groups_Ouminus__class_Ouminus(X2,X0) != X1
| ~ class_Rings_Oidom(X2) ),
inference(definition_unfolding,[],[f4843,f4118,f4118,f4118,f4118]) ).
fof(f4843,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| c_Groups_Ouminus__class_Ouminus(X2,X0) != X1
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f3734]) ).
fof(f29965,plain,
spl47_1201,
inference(avatar_split_clause,[],[f5330,f29963]) ).
fof(f29963,plain,
( spl47_1201
<=> ! [X0,X3,X2,X1] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)),c_Polynomial_OpCons(X3,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)))
| ~ class_Rings_Ocomm__semiring__0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1201])]) ).
fof(f5330,plain,
! [X2,X3,X0,X1] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)),c_Polynomial_OpCons(X3,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f3274]) ).
fof(f3274,plain,
! [X0,X1,X2,X3] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)),c_Polynomial_OpCons(X3,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f2126]) ).
fof(f2126,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)),c_Polynomial_OpCons(X3,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0))) ),
inference(rectify,[],[f243]) ).
fof(f243,axiom,
! [X35,X8,X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5,c_Polynomial_OpCons(X5,X4,X8),X35) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),c_Polynomial_Osmult(X5,X35,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5,X8,X35)),c_Polynomial_OpCons(X5,X4,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5,X8,X35))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__pCons) ).
fof(f29961,plain,
spl47_1200,
inference(avatar_split_clause,[],[f5042,f29959]) ).
fof(f29959,plain,
( spl47_1200
<=> ! [X0,X6,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,sK42(X0,X1,X2),c_Groups_Ozero__class_Ozero(X2))))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X6)))
| ~ class_Rings_Osemiring__0(X2)
| ~ class_Rings_Odvd(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1200])]) ).
fof(f5042,plain,
! [X2,X0,X1,X6] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),c_Groups_Oplus__class_Oplus(X2,sK42(X0,X1,X2),c_Groups_Ozero__class_Ozero(X2))))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X6)))
| ~ class_Rings_Osemiring__0(X2)
| ~ class_Rings_Odvd(X2) ),
inference(cnf_transformation,[],[f3776]) ).
fof(f29957,plain,
spl47_1199,
inference(avatar_split_clause,[],[f5033,f29955]) ).
fof(f29955,plain,
( spl47_1199
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1199])]) ).
fof(f5033,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0)) ),
inference(cnf_transformation,[],[f3022]) ).
fof(f3022,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0)) ),
inference(flattening,[],[f3021]) ).
fof(f3021,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0)) ),
inference(ennf_transformation,[],[f1925]) ).
fof(f1925,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),X0))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X2)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ) ),
inference(rectify,[],[f713]) ).
fof(f713,axiom,
! [X67,X68,X69] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X69),X68),X67))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X67,X69)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X69)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X68) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__pos__lemma) ).
fof(f29953,plain,
spl47_1198,
inference(avatar_split_clause,[],[f4885,f29951]) ).
fof(f29951,plain,
( spl47_1198
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Ocoeff(X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
| ~ class_Groups_Ozero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1198])]) ).
fof(f4885,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Ocoeff(X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f2860]) ).
fof(f2860,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Ocoeff(X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
| ~ class_Groups_Ozero(X2) ),
inference(flattening,[],[f2859]) ).
fof(f2859,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Ocoeff(X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
| ~ class_Groups_Ozero(X2) ),
inference(ennf_transformation,[],[f1810]) ).
fof(f1810,plain,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
=> ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Ocoeff(X2,X1),X0)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1 ) ) ) ),
inference(rectify,[],[f754]) ).
fof(f754,axiom,
! [X7,X8,X5] :
( class_Groups_Ozero(X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X5,X8),X7)
=> ( c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Polynomial_Ocoeff(X5,X8),X7)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5,X8),X7)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X8 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__zero__or__degree__less) ).
fof(f29948,plain,
spl47_1197,
inference(avatar_split_clause,[],[f4445,f29946]) ).
fof(f29946,plain,
( spl47_1197
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1197])]) ).
fof(f4445,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(cnf_transformation,[],[f2554]) ).
fof(f2554,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(flattening,[],[f2553]) ).
fof(f2553,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(ennf_transformation,[],[f1526]) ).
fof(f1526,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1))
=> X0 = X1 ) ) ) ),
inference(rectify,[],[f452]) ).
fof(f452,axiom,
! [X7,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X7)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X21),X7))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X7),X21))
=> X7 = X21 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__antisym__nonneg) ).
fof(f29944,plain,
spl47_1196,
inference(avatar_split_clause,[],[f4322,f29942]) ).
fof(f29942,plain,
( spl47_1196
<=> ! [X0,X1] :
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0),c_Groups_Oone__class_Oone(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Oone__class_Oone(X1))),c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Oring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1196])]) ).
fof(f4322,plain,
! [X0,X1] :
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0),c_Groups_Oone__class_Oone(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Oone__class_Oone(X1))),c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Oring__1(X1) ),
inference(cnf_transformation,[],[f2433]) ).
fof(f2433,plain,
! [X0,X1] :
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0),c_Groups_Oone__class_Oone(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Oone__class_Oone(X1))),c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Oring__1(X1) ),
inference(ennf_transformation,[],[f1418]) ).
fof(f1418,plain,
! [X0,X1] :
( class_Rings_Oring__1(X1)
=> c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0),c_Groups_Oone__class_Oone(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Oone__class_Oone(X1))),c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Oone__class_Oone(X1))) ),
inference(rectify,[],[f852]) ).
fof(f852,axiom,
! [X6,X5] :
( class_Rings_Oring__1(X5)
=> c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X6),c_Groups_Oone__class_Oone(X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oplus__class_Oplus(X5,X6,c_Groups_Oone__class_Oone(X5))),c_Groups_Ominus__class_Ominus(X5,X6,c_Groups_Oone__class_Oone(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__squared__diff__one__factored) ).
fof(f28964,plain,
spl47_1195,
inference(avatar_split_clause,[],[f5644,f28962]) ).
fof(f28962,plain,
( spl47_1195
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1195])]) ).
fof(f5644,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f5118,f4118,f4118]) ).
fof(f5118,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3818]) ).
fof(f3818,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X0)) ) ),
inference(nnf_transformation,[],[f1958]) ).
fof(f1958,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f683]) ).
fof(f683,axiom,
! [X11,X14,X44] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X44)),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X44)),X11))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
fof(f28960,plain,
spl47_1194,
inference(avatar_split_clause,[],[f5643,f28958]) ).
fof(f28958,plain,
( spl47_1194
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1194])]) ).
fof(f5643,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0)) ),
inference(definition_unfolding,[],[f5115,f4118,f4118]) ).
fof(f5115,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X0)) ),
inference(cnf_transformation,[],[f3817]) ).
fof(f3817,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X0)) ) ),
inference(nnf_transformation,[],[f1957]) ).
fof(f1957,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f688]) ).
fof(f688,axiom,
! [X11,X14,X44] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X44)),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X44)),X11))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).
fof(f28956,plain,
spl47_1193,
inference(avatar_split_clause,[],[f5627,f28954]) ).
fof(f28954,plain,
( spl47_1193
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1193])]) ).
fof(f5627,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(definition_unfolding,[],[f4863,f4118]) ).
fof(f4863,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)),c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(cnf_transformation,[],[f2832]) ).
fof(f2832,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)),c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(flattening,[],[f2831]) ).
fof(f2831,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)),c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(ennf_transformation,[],[f1791]) ).
fof(f1791,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Oone__class_Oone(X2))
=> c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)),c_Groups_Oone__class_Oone(X2)) ) ) ),
inference(rectify,[],[f244]) ).
fof(f244,axiom,
! [X7,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> ( c_Orderings_Oord__class_Oless(X5,X4,c_Groups_Oone__class_Oone(X5))
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Nat_OSuc(X7)),c_Groups_Oone__class_Oone(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).
fof(f28952,plain,
spl47_1192,
inference(avatar_split_clause,[],[f5359,f28950]) ).
fof(f28950,plain,
( spl47_1192
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1192])]) ).
fof(f5359,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3311]) ).
fof(f3311,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(flattening,[],[f3310]) ).
fof(f3310,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2155]) ).
fof(f2155,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0))) ) ) ),
inference(rectify,[],[f212]) ).
fof(f212,axiom,
! [X16,X17,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X4),X17))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X4),X16))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X4),c_Groups_Oplus__class_Oplus(X5,X17,X16))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__add) ).
fof(f28948,plain,
spl47_1191,
inference(avatar_split_clause,[],[f5357,f28946]) ).
fof(f28946,plain,
( spl47_1191
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1191])]) ).
fof(f5357,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3307]) ).
fof(f3307,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(flattening,[],[f3306]) ).
fof(f3306,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2153]) ).
fof(f2153,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))) ) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X7,X10,X6,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X6),X10))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X7)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X10),X7))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power__same) ).
fof(f28944,plain,
spl47_1190,
inference(avatar_split_clause,[],[f5350,f28942]) ).
fof(f28942,plain,
( spl47_1190
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Oplus__class_Oplus(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1190])]) ).
fof(f5350,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Oplus__class_Oplus(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3296]) ).
fof(f3296,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Oplus__class_Oplus(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2146]) ).
fof(f2146,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Oplus__class_Oplus(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
inference(rectify,[],[f490]) ).
fof(f490,axiom,
! [X16,X17,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oplus__class_Oplus(X5,X4,X17)),X16) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(f28940,plain,
spl47_1189,
inference(avatar_split_clause,[],[f5349,f28938]) ).
fof(f28938,plain,
( spl47_1189
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1189])]) ).
fof(f5349,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3295]) ).
fof(f3295,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2145]) ).
fof(f2145,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(rectify,[],[f492]) ).
fof(f492,axiom,
! [X26,X10,X6,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),c_Groups_Oplus__class_Oplus(X5,X10,X26)) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(f28936,plain,
spl47_1188,
inference(avatar_split_clause,[],[f5293,f28934]) ).
fof(f28934,plain,
( spl47_1188
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Oplus__class_Oplus(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ class_Rings_Ocomm__semiring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1188])]) ).
fof(f5293,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Oplus__class_Oplus(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ class_Rings_Ocomm__semiring(X3) ),
inference(cnf_transformation,[],[f3233]) ).
fof(f3233,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Oplus__class_Oplus(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ class_Rings_Ocomm__semiring(X3) ),
inference(ennf_transformation,[],[f2093]) ).
fof(f2093,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Oplus__class_Oplus(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
inference(rectify,[],[f519]) ).
fof(f519,axiom,
! [X16,X17,X4,X5] :
( class_Rings_Ocomm__semiring(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oplus__class_Oplus(X5,X4,X17)),X16) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
fof(f28932,plain,
spl47_1187,
inference(avatar_split_clause,[],[f5267,f28930]) ).
fof(f28930,plain,
( spl47_1187
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| ~ class_Rings_Oidom(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1187])]) ).
fof(f5267,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| ~ class_Rings_Oidom(X3) ),
inference(cnf_transformation,[],[f3864]) ).
fof(f28928,plain,
spl47_1186,
inference(avatar_split_clause,[],[f5264,f28926]) ).
fof(f28926,plain,
( spl47_1186
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| ~ class_Rings_Oidom(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1186])]) ).
fof(f5264,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| ~ class_Rings_Oidom(X3) ),
inference(cnf_transformation,[],[f3862]) ).
fof(f28924,plain,
spl47_1185,
inference(avatar_split_clause,[],[f5251,f28922]) ).
fof(f28922,plain,
( spl47_1185
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Ominus__class_Ominus(X3,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Ocomm__ring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1185])]) ).
fof(f5251,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Ominus__class_Ominus(X3,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Ocomm__ring__1(X3) ),
inference(cnf_transformation,[],[f3170]) ).
fof(f3170,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Ominus__class_Ominus(X3,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Ocomm__ring__1(X3) ),
inference(flattening,[],[f3169]) ).
fof(f3169,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Ominus__class_Ominus(X3,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Ocomm__ring__1(X3) ),
inference(ennf_transformation,[],[f2058]) ).
fof(f2058,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__ring__1(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Groups_Ominus__class_Ominus(X3,X1,X0))) ) ) ),
inference(rectify,[],[f769]) ).
fof(f769,axiom,
! [X26,X10,X6,X5] :
( class_Rings_Ocomm__ring__1(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X6),X10))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X6),X26))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X6),c_Groups_Ominus__class_Ominus(X5,X10,X26))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diff) ).
fof(f28920,plain,
spl47_1184,
inference(avatar_split_clause,[],[f5234,f28918]) ).
fof(f28918,plain,
( spl47_1184
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Divides_Odiv__class_Omod(X3,X1,X0)))
| ~ class_Divides_Osemiring__div(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1184])]) ).
fof(f5234,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Divides_Odiv__class_Omod(X3,X1,X0)))
| ~ class_Divides_Osemiring__div(X3) ),
inference(cnf_transformation,[],[f3152]) ).
fof(f3152,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Divides_Odiv__class_Omod(X3,X1,X0)))
| ~ class_Divides_Osemiring__div(X3) ),
inference(flattening,[],[f3151]) ).
fof(f3151,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Divides_Odiv__class_Omod(X3,X1,X0)))
| ~ class_Divides_Osemiring__div(X3) ),
inference(ennf_transformation,[],[f2045]) ).
fof(f2045,plain,
! [X0,X1,X2,X3] :
( class_Divides_Osemiring__div(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),c_Divides_Odiv__class_Omod(X3,X1,X0)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1)) ) ) ),
inference(rectify,[],[f995]) ).
fof(f995,axiom,
! [X7,X21,X20,X5] :
( class_Divides_Osemiring__div(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X20),c_Divides_Odiv__class_Omod(X5,X21,X7)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X20),X7))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X20),X21)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mod__imp__dvd) ).
fof(f28916,plain,
spl47_1183,
inference(avatar_split_clause,[],[f5171,f28914]) ).
fof(f28914,plain,
( spl47_1183
<=> ! [X0,X3,X2,X1] :
( c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X2)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1183])]) ).
fof(f5171,plain,
! [X2,X3,X0,X1] :
( c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X2)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(cnf_transformation,[],[f3097]) ).
fof(f3097,plain,
! [X0,X1,X2,X3] :
( c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X2)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(flattening,[],[f3096]) ).
fof(f3096,plain,
! [X0,X1,X2,X3] :
( c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X2)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(ennf_transformation,[],[f2015]) ).
fof(f2015,plain,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( c_Groups_Ozero__class_Ozero(X3) != X2
=> c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X2) ) ),
inference(rectify,[],[f968]) ).
fof(f968,axiom,
! [X10,X6,X26,X5] :
( class_Fields_Ofield(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X26
=> c_Groups_Oplus__class_Oplus(X5,c_Rings_Oinverse__class_Odivide(X5,X6,X26),X10) = c_Rings_Oinverse__class_Odivide(X5,c_Groups_Oplus__class_Oplus(X5,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X26),X10)),X26) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__add__eq__iff) ).
fof(f28912,plain,
spl47_1182,
inference(avatar_split_clause,[],[f5170,f28910]) ).
fof(f28910,plain,
( spl47_1182
<=> ! [X0,X3,X2,X1] :
( c_Groups_Oplus__class_Oplus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0),X2)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1182])]) ).
fof(f5170,plain,
! [X2,X3,X0,X1] :
( c_Groups_Oplus__class_Oplus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0),X2)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(cnf_transformation,[],[f3095]) ).
fof(f3095,plain,
! [X0,X1,X2,X3] :
( c_Groups_Oplus__class_Oplus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0),X2)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(flattening,[],[f3094]) ).
fof(f3094,plain,
! [X0,X1,X2,X3] :
( c_Groups_Oplus__class_Oplus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0),X2)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(ennf_transformation,[],[f2014]) ).
fof(f2014,plain,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( c_Groups_Ozero__class_Ozero(X3) != X2
=> c_Groups_Oplus__class_Oplus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0),X2) ) ),
inference(rectify,[],[f966]) ).
fof(f966,axiom,
! [X10,X6,X26,X5] :
( class_Fields_Ofield(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X26
=> c_Groups_Oplus__class_Oplus(X5,X6,c_Rings_Oinverse__class_Odivide(X5,X10,X26)) = c_Rings_Oinverse__class_Odivide(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X26),X6),X10),X26) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__eq__iff) ).
fof(f28908,plain,
spl47_1181,
inference(avatar_split_clause,[],[f5169,f28906]) ).
fof(f28906,plain,
( spl47_1181
<=> ! [X0,X3,X2,X1] :
( c_Groups_Ominus__class_Ominus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X2)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1181])]) ).
fof(f5169,plain,
! [X2,X3,X0,X1] :
( c_Groups_Ominus__class_Ominus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X2)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(cnf_transformation,[],[f3093]) ).
fof(f3093,plain,
! [X0,X1,X2,X3] :
( c_Groups_Ominus__class_Ominus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X2)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(flattening,[],[f3092]) ).
fof(f3092,plain,
! [X0,X1,X2,X3] :
( c_Groups_Ominus__class_Ominus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X2)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(ennf_transformation,[],[f2013]) ).
fof(f2013,plain,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( c_Groups_Ozero__class_Ozero(X3) != X2
=> c_Groups_Ominus__class_Ominus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X2) ) ),
inference(rectify,[],[f971]) ).
fof(f971,axiom,
! [X10,X6,X26,X5] :
( class_Fields_Ofield(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X26
=> c_Groups_Ominus__class_Ominus(X5,c_Rings_Oinverse__class_Odivide(X5,X6,X26),X10) = c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X26),X10)),X26) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__diff__eq__iff) ).
fof(f28904,plain,
spl47_1180,
inference(avatar_split_clause,[],[f5168,f28902]) ).
fof(f28902,plain,
( spl47_1180
<=> ! [X0,X3,X2,X1] :
( c_Groups_Ominus__class_Ominus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0),X2)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1180])]) ).
fof(f5168,plain,
! [X2,X3,X0,X1] :
( c_Groups_Ominus__class_Ominus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0),X2)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(cnf_transformation,[],[f3091]) ).
fof(f3091,plain,
! [X0,X1,X2,X3] :
( c_Groups_Ominus__class_Ominus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0),X2)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(flattening,[],[f3090]) ).
fof(f3090,plain,
! [X0,X1,X2,X3] :
( c_Groups_Ominus__class_Ominus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0),X2)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(ennf_transformation,[],[f2012]) ).
fof(f2012,plain,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( c_Groups_Ozero__class_Ozero(X3) != X2
=> c_Groups_Ominus__class_Ominus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0),X2) ) ),
inference(rectify,[],[f972]) ).
fof(f972,axiom,
! [X10,X6,X26,X5] :
( class_Fields_Ofield(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X26
=> c_Groups_Ominus__class_Ominus(X5,X6,c_Rings_Oinverse__class_Odivide(X5,X10,X26)) = c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X26),X6),X10),X26) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__divide__eq__iff) ).
fof(f28900,plain,
spl47_1179,
inference(avatar_split_clause,[],[f5164,f28898]) ).
fof(f28898,plain,
( spl47_1179
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Oplus__class_Oplus(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ class_RealVector_Oreal__normed__algebra(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1179])]) ).
fof(f5164,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Oplus__class_Oplus(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(cnf_transformation,[],[f3085]) ).
fof(f3085,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Oplus__class_Oplus(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(ennf_transformation,[],[f2008]) ).
fof(f2008,plain,
! [X0,X1,X2,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Oplus__class_Oplus(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
inference(rectify,[],[f745]) ).
fof(f745,axiom,
! [X75,X10,X6,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oplus__class_Oplus(X5,X6,X10)),X75) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X75),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X75)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).
fof(f28896,plain,
spl47_1178,
inference(avatar_split_clause,[],[f5162,f28894]) ).
fof(f28894,plain,
( spl47_1178
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Ominus__class_Ominus(X3,X2,X1)),X0) = c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ class_RealVector_Oreal__normed__algebra(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1178])]) ).
fof(f5162,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Ominus__class_Ominus(X3,X2,X1)),X0) = c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(cnf_transformation,[],[f3083]) ).
fof(f3083,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Ominus__class_Ominus(X3,X2,X1)),X0) = c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(ennf_transformation,[],[f2006]) ).
fof(f2006,plain,
! [X0,X1,X2,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Ominus__class_Ominus(X3,X2,X1)),X0) = c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
inference(rectify,[],[f847]) ).
fof(f847,axiom,
! [X75,X10,X6,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ominus__class_Ominus(X5,X6,X10)),X75) = c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X75),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X75)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Odiff) ).
fof(f28892,plain,
spl47_1177,
inference(avatar_split_clause,[],[f5160,f28890]) ).
fof(f28890,plain,
( spl47_1177
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_RealVector_Oreal__normed__algebra(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1177])]) ).
fof(f5160,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(cnf_transformation,[],[f3081]) ).
fof(f3081,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(ennf_transformation,[],[f2004]) ).
fof(f2004,plain,
! [X0,X1,X2,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(rectify,[],[f747]) ).
fof(f747,axiom,
! [X10,X6,X77,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X77),c_Groups_Oplus__class_Oplus(X5,X6,X10)) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X77),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X77),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).
fof(f28888,plain,
spl47_1176,
inference(avatar_split_clause,[],[f5158,f28886]) ).
fof(f28886,plain,
( spl47_1176
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Ominus__class_Ominus(X3,X1,X0)) = c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_RealVector_Oreal__normed__algebra(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1176])]) ).
fof(f5158,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Ominus__class_Ominus(X3,X1,X0)) = c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(cnf_transformation,[],[f3079]) ).
fof(f3079,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Ominus__class_Ominus(X3,X1,X0)) = c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(ennf_transformation,[],[f2002]) ).
fof(f2002,plain,
! [X0,X1,X2,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Ominus__class_Ominus(X3,X1,X0)) = c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(rectify,[],[f844]) ).
fof(f844,axiom,
! [X69,X17,X4,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ominus__class_Ominus(X5,X17,X69)) = c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X69)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__right) ).
fof(f28884,plain,
spl47_1175,
inference(avatar_split_clause,[],[f5130,f28882]) ).
fof(f28882,plain,
( spl47_1175
<=> ! [X0,X3,X2,X1] :
( c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2)),X2) = c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1175])]) ).
fof(f5130,plain,
! [X2,X3,X0,X1] :
( c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2)),X2) = c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(cnf_transformation,[],[f3065]) ).
fof(f3065,plain,
! [X0,X1,X2,X3] :
( c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2)),X2) = c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(flattening,[],[f3064]) ).
fof(f3064,plain,
! [X0,X1,X2,X3] :
( c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2)),X2) = c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(ennf_transformation,[],[f1992]) ).
fof(f1992,plain,
! [X0,X1,X2,X3] :
( class_Fields_Ofield__inverse__zero(X3)
=> ( c_Groups_Ozero__class_Ozero(X3) != X2
=> c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2)),X2) = c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X1,X2),X0) ) ),
inference(rectify,[],[f967]) ).
fof(f967,axiom,
! [X26,X6,X10,X5] :
( class_Fields_Ofield__inverse__zero(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X10
=> c_Rings_Oinverse__class_Odivide(X5,c_Groups_Oplus__class_Oplus(X5,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X26),X10)),X10) = c_Groups_Oplus__class_Oplus(X5,c_Rings_Oinverse__class_Odivide(X5,X6,X10),X26) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__num) ).
fof(f28880,plain,
spl47_1174,
inference(avatar_split_clause,[],[f5129,f28878]) ).
fof(f28878,plain,
( spl47_1174
<=> ! [X0,X3,X2,X1] :
( c_Groups_Oplus__class_Oplus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2)),X2)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1174])]) ).
fof(f5129,plain,
! [X2,X3,X0,X1] :
( c_Groups_Oplus__class_Oplus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2)),X2)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(cnf_transformation,[],[f3063]) ).
fof(f3063,plain,
! [X0,X1,X2,X3] :
( c_Groups_Oplus__class_Oplus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2)),X2)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(flattening,[],[f3062]) ).
fof(f3062,plain,
! [X0,X1,X2,X3] :
( c_Groups_Oplus__class_Oplus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2)),X2)
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(ennf_transformation,[],[f1991]) ).
fof(f1991,plain,
! [X0,X1,X2,X3] :
( class_Fields_Ofield__inverse__zero(X3)
=> ( c_Groups_Ozero__class_Ozero(X3) != X2
=> c_Groups_Oplus__class_Oplus(X3,X1,c_Rings_Oinverse__class_Odivide(X3,X0,X2)) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2)),X2) ) ),
inference(rectify,[],[f965]) ).
fof(f965,axiom,
! [X6,X26,X10,X5] :
( class_Fields_Ofield__inverse__zero(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X10
=> c_Groups_Oplus__class_Oplus(X5,X26,c_Rings_Oinverse__class_Odivide(X5,X6,X10)) = c_Rings_Oinverse__class_Odivide(X5,c_Groups_Oplus__class_Oplus(X5,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X26),X10)),X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__num__frac) ).
fof(f28876,plain,
spl47_1173,
inference(avatar_split_clause,[],[f5126,f28874]) ).
fof(f28874,plain,
( spl47_1173
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Rings_Oinverse__class_Odivide(X3,X2,X1)),X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))
| ~ class_Fields_Ofield__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1173])]) ).
fof(f5126,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Rings_Oinverse__class_Odivide(X3,X2,X1)),X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(cnf_transformation,[],[f3057]) ).
fof(f3057,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Rings_Oinverse__class_Odivide(X3,X2,X1)),X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(ennf_transformation,[],[f1988]) ).
fof(f1988,plain,
! [X0,X1,X2,X3] :
( class_Fields_Ofield__inverse__zero(X3)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Rings_Oinverse__class_Odivide(X3,X2,X1)),X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ),
inference(rectify,[],[f910]) ).
fof(f910,axiom,
! [X7,X17,X4,X5] :
( class_Fields_Ofield__inverse__zero(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Rings_Oinverse__class_Odivide(X5,X4,X17)),X7) = c_Rings_Oinverse__class_Odivide(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X17),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__divide) ).
fof(f28872,plain,
spl47_1172,
inference(avatar_split_clause,[],[f5038,f28870]) ).
fof(f28870,plain,
( spl47_1172
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1172])]) ).
fof(f5038,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X0))) ),
inference(cnf_transformation,[],[f3032]) ).
fof(f3032,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X0))) ),
inference(flattening,[],[f3031]) ).
fof(f3031,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X0))) ),
inference(ennf_transformation,[],[f1930]) ).
fof(f1930,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X0)))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(rectify,[],[f248]) ).
fof(f248,axiom,
! [X7,X21,X32] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X32),X21)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X32),X7)))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X32)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__dvd__imp__le) ).
fof(f28868,plain,
spl47_1171,
inference(avatar_split_clause,[],[f5008,f28866]) ).
fof(f28866,plain,
( spl47_1171
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)) != X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1171])]) ).
fof(f5008,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)) != X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(cnf_transformation,[],[f2994]) ).
fof(f2994,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)) != X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(flattening,[],[f2993]) ).
fof(f2993,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)) != X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(ennf_transformation,[],[f1907]) ).
fof(f1907,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
=> ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)) = X2
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
inference(rectify,[],[f711]) ).
fof(f711,axiom,
! [X13,X34,X4] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
=> ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X34,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X13)) = X4
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X34)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X13,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).
fof(f28864,plain,
spl47_1170,
inference(avatar_split_clause,[],[f4859,f28862]) ).
fof(f28862,plain,
( spl47_1170
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1170])]) ).
fof(f4859,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(cnf_transformation,[],[f2824]) ).
fof(f2824,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(flattening,[],[f2823]) ).
fof(f2823,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(ennf_transformation,[],[f1787]) ).
fof(f1787,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
=> c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))) ) ),
inference(rectify,[],[f623]) ).
fof(f623,axiom,
! [X7,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X4)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).
fof(f28860,plain,
spl47_1169,
inference(avatar_split_clause,[],[f4717,f28858]) ).
fof(f28858,plain,
( spl47_1169
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1169])]) ).
fof(f4717,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(cnf_transformation,[],[f2677]) ).
fof(f2677,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(flattening,[],[f2676]) ).
fof(f2676,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(ennf_transformation,[],[f1687]) ).
fof(f1687,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Oone__class_Oone(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1),X1) ) ) ) ),
inference(rectify,[],[f621]) ).
fof(f621,axiom,
! [X10,X6,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X6)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X10)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X10,c_Groups_Oone__class_Oone(X5))
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X6),X6) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
fof(f28856,plain,
spl47_1168,
inference(avatar_split_clause,[],[f4716,f28854]) ).
fof(f28854,plain,
( spl47_1168
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1168])]) ).
fof(f4716,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(cnf_transformation,[],[f2675]) ).
fof(f2675,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(flattening,[],[f2674]) ).
fof(f2674,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(ennf_transformation,[],[f1686]) ).
fof(f1686,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Oone__class_Oone(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1) ) ) ) ),
inference(rectify,[],[f622]) ).
fof(f622,axiom,
! [X10,X6,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X6)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X10)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X10,c_Groups_Oone__class_Oone(X5))
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X10),X6) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
fof(f28852,plain,
spl47_1167,
inference(avatar_split_clause,[],[f4642,f28850]) ).
fof(f28850,plain,
( spl47_1167
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1167])]) ).
fof(f4642,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X0)),
inference(cnf_transformation,[],[f1631]) ).
fof(f1631,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X0)),
inference(rectify,[],[f691]) ).
fof(f691,axiom,
! [X26,X10,X6] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X26)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),X10)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),X26)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).
fof(f28848,plain,
spl47_1166,
inference(avatar_split_clause,[],[f4260,f28846]) ).
fof(f28846,plain,
( spl47_1166
<=> ! [X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1166])]) ).
fof(f4260,plain,
! [X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
inference(cnf_transformation,[],[f2394]) ).
fof(f2394,plain,
! [X0,X1] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ),
inference(ennf_transformation,[],[f1374]) ).
fof(f1374,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) ) ),
inference(rectify,[],[f878]) ).
fof(f878,axiom,
! [X8,X21] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X21
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X8),X21) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X8),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X21
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X8),X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__if) ).
fof(f26659,plain,
spl47_1165,
inference(avatar_split_clause,[],[f5868,f26657]) ).
fof(f26657,plain,
( spl47_1165
<=> ! [X0,X3,X2,X1] :
( sP25(X0,X1,X2,X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X2),X0))
| ~ sP24(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1165])]) ).
fof(f5868,plain,
! [X2,X3,X0,X1] :
( sP25(X0,X1,X2,X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X2),X0))
| ~ sP24(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X2 ),
inference(equality_resolution,[],[f5407]) ).
fof(f5407,plain,
! [X2,X3,X0,X1,X4] :
( sP25(X0,X1,X2,X3,X4)
| ~ sP24(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X2
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X2),X0) != X4 ),
inference(cnf_transformation,[],[f3884]) ).
fof(f3884,plain,
! [X0,X1,X2,X3,X4] :
( ( sP25(X0,X1,X2,X3,X4)
| ~ sP24(X2,X1,X0)
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X3
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X2 )
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X2),X0) != X4 )
& ( ( sP24(X2,X1,X0)
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X3
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X2 )
& c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X2),X0) = X4 )
| ~ sP25(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f3883]) ).
fof(f3883,plain,
! [X0,X4,X2,X1,X3] :
( ( sP25(X0,X4,X2,X1,X3)
| ~ sP24(X2,X4,X0)
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X1
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2 )
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X1),X2),X0) != X3 )
& ( ( sP24(X2,X4,X0)
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2 )
& c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X1),X2),X0) = X3 )
| ~ sP25(X0,X4,X2,X1,X3) ) ),
inference(flattening,[],[f3882]) ).
fof(f3882,plain,
! [X0,X4,X2,X1,X3] :
( ( sP25(X0,X4,X2,X1,X3)
| ~ sP24(X2,X4,X0)
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X1
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2 )
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X1),X2),X0) != X3 )
& ( ( sP24(X2,X4,X0)
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2 )
& c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X1),X2),X0) = X3 )
| ~ sP25(X0,X4,X2,X1,X3) ) ),
inference(nnf_transformation,[],[f3515]) ).
fof(f3515,plain,
! [X0,X4,X2,X1,X3] :
( sP25(X0,X4,X2,X1,X3)
<=> ( sP24(X2,X4,X0)
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2 )
& c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X1),X2),X0) = X3 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP25])]) ).
fof(f26655,plain,
spl47_1164,
inference(avatar_split_clause,[],[f5650,f26653]) ).
fof(f26653,plain,
( spl47_1164
<=> ! [X4,X0,X3,X2,X1] : hAPP(hAPP(X2,X1),hAPP(hAPP(c_Power_Opower_Opower(X4,X3,X2),X1),X0)) = hAPP(hAPP(c_Power_Opower_Opower(X4,X3,X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1164])]) ).
fof(f5650,plain,
! [X2,X3,X0,X1,X4] : hAPP(hAPP(X2,X1),hAPP(hAPP(c_Power_Opower_Opower(X4,X3,X2),X1),X0)) = hAPP(hAPP(c_Power_Opower_Opower(X4,X3,X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(definition_unfolding,[],[f5395,f4118]) ).
fof(f5395,plain,
! [X2,X3,X0,X1,X4] : hAPP(hAPP(c_Power_Opower_Opower(X4,X3,X2),X1),c_Nat_OSuc(X0)) = hAPP(hAPP(X2,X1),hAPP(hAPP(c_Power_Opower_Opower(X4,X3,X2),X1),X0)),
inference(cnf_transformation,[],[f2187]) ).
fof(f2187,plain,
! [X0,X1,X2,X3,X4] : hAPP(hAPP(c_Power_Opower_Opower(X4,X3,X2),X1),c_Nat_OSuc(X0)) = hAPP(hAPP(X2,X1),hAPP(hAPP(c_Power_Opower_Opower(X4,X3,X2),X1),X0)),
inference(rectify,[],[f695]) ).
fof(f695,axiom,
! [X11,X12,X65,X66,X5] : hAPP(hAPP(c_Power_Opower_Opower(X5,X66,X65),X12),c_Nat_OSuc(X11)) = hAPP(hAPP(X65,X12),hAPP(hAPP(c_Power_Opower_Opower(X5,X66,X65),X12),X11)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).
fof(f26651,plain,
spl47_1163,
inference(avatar_split_clause,[],[f5625,f26649]) ).
fof(f26649,plain,
( spl47_1163
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1163])]) ).
fof(f5625,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(definition_unfolding,[],[f4856,f4118]) ).
fof(f4856,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(cnf_transformation,[],[f2818]) ).
fof(f2818,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(flattening,[],[f2817]) ).
fof(f2817,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(ennf_transformation,[],[f1784]) ).
fof(f1784,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Oone__class_Oone(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)),X1) ) ) ),
inference(rectify,[],[f300]) ).
fof(f300,axiom,
! [X7,X34,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X34)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X34,c_Groups_Oone__class_Oone(X5))
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X34),c_Nat_OSuc(X7)),X34) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__Suc__le__self) ).
fof(f26647,plain,
spl47_1162,
inference(avatar_split_clause,[],[f5439,f26645]) ).
fof(f26645,plain,
( spl47_1162
<=> ! [X4,X0,X3,X2,X1] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),c_Polynomial_OpCons(X4,X3,X2),c_Polynomial_OpCons(X4,X1,X0)) = c_Polynomial_OpCons(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),X2,X0))
| ~ class_Groups_Ocomm__monoid__add(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1162])]) ).
fof(f5439,plain,
! [X2,X3,X0,X1,X4] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),c_Polynomial_OpCons(X4,X3,X2),c_Polynomial_OpCons(X4,X1,X0)) = c_Polynomial_OpCons(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),X2,X0))
| ~ class_Groups_Ocomm__monoid__add(X4) ),
inference(cnf_transformation,[],[f3410]) ).
fof(f3410,plain,
! [X0,X1,X2,X3,X4] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),c_Polynomial_OpCons(X4,X3,X2),c_Polynomial_OpCons(X4,X1,X0)) = c_Polynomial_OpCons(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),X2,X0))
| ~ class_Groups_Ocomm__monoid__add(X4) ),
inference(ennf_transformation,[],[f2215]) ).
fof(f2215,plain,
! [X0,X1,X2,X3,X4] :
( class_Groups_Ocomm__monoid__add(X4)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),c_Polynomial_OpCons(X4,X3,X2),c_Polynomial_OpCons(X4,X1,X0)) = c_Polynomial_OpCons(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),X2,X0)) ),
inference(rectify,[],[f177]) ).
fof(f177,axiom,
! [X13,X17,X8,X4,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),c_Polynomial_OpCons(X5,X4,X8),c_Polynomial_OpCons(X5,X17,X13)) = c_Polynomial_OpCons(X5,c_Groups_Oplus__class_Oplus(X5,X4,X17),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),X8,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pCons) ).
fof(f26643,plain,
spl47_1161,
inference(avatar_split_clause,[],[f5429,f26641]) ).
fof(f26641,plain,
( spl47_1161
<=> ! [X4,X0,X3,X2,X1] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4),c_Polynomial_OpCons(X4,X3,X2),c_Polynomial_OpCons(X4,X1,X0)) = c_Polynomial_OpCons(X4,c_Groups_Ominus__class_Ominus(X4,X3,X1),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4),X2,X0))
| ~ class_Groups_Oab__group__add(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1161])]) ).
fof(f5429,plain,
! [X2,X3,X0,X1,X4] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4),c_Polynomial_OpCons(X4,X3,X2),c_Polynomial_OpCons(X4,X1,X0)) = c_Polynomial_OpCons(X4,c_Groups_Ominus__class_Ominus(X4,X3,X1),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4),X2,X0))
| ~ class_Groups_Oab__group__add(X4) ),
inference(cnf_transformation,[],[f3404]) ).
fof(f3404,plain,
! [X0,X1,X2,X3,X4] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4),c_Polynomial_OpCons(X4,X3,X2),c_Polynomial_OpCons(X4,X1,X0)) = c_Polynomial_OpCons(X4,c_Groups_Ominus__class_Ominus(X4,X3,X1),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4),X2,X0))
| ~ class_Groups_Oab__group__add(X4) ),
inference(ennf_transformation,[],[f2210]) ).
fof(f2210,plain,
! [X0,X1,X2,X3,X4] :
( class_Groups_Oab__group__add(X4)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4),c_Polynomial_OpCons(X4,X3,X2),c_Polynomial_OpCons(X4,X1,X0)) = c_Polynomial_OpCons(X4,c_Groups_Ominus__class_Ominus(X4,X3,X1),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4),X2,X0)) ),
inference(rectify,[],[f774]) ).
fof(f774,axiom,
! [X13,X17,X8,X4,X5] :
( class_Groups_Oab__group__add(X5)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5),c_Polynomial_OpCons(X5,X4,X8),c_Polynomial_OpCons(X5,X17,X13)) = c_Polynomial_OpCons(X5,c_Groups_Ominus__class_Ominus(X5,X4,X17),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5),X8,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__pCons) ).
fof(f26639,plain,
spl47_1160,
inference(avatar_split_clause,[],[f5348,f26637]) ).
fof(f26637,plain,
( spl47_1160
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1160])]) ).
fof(f5348,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3294]) ).
fof(f3294,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2144]) ).
fof(f2144,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X1) ),
inference(rectify,[],[f506]) ).
fof(f506,axiom,
! [X54,X55,X56,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X56),X55)),X54) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X56),X54)),X55) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(f26635,plain,
spl47_1159,
inference(avatar_split_clause,[],[f5346,f26633]) ).
fof(f26633,plain,
( spl47_1159
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),X0)
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1159])]) ).
fof(f5346,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),X0)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3292]) ).
fof(f3292,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),X0)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2142]) ).
fof(f2142,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),X0) ),
inference(rectify,[],[f649]) ).
fof(f649,axiom,
! [X13,X8,X6,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X8)),X13) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(f26631,plain,
spl47_1158,
inference(avatar_split_clause,[],[f5345,f26629]) ).
fof(f26629,plain,
( spl47_1158
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1158])]) ).
fof(f5345,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3291]) ).
fof(f3291,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2141]) ).
fof(f2141,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
inference(rectify,[],[f508]) ).
fof(f508,axiom,
! [X53,X54,X56,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X54),X53)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X56),X54)),X53) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(f26622,plain,
spl47_1157,
inference(avatar_split_clause,[],[f5344,f26620]) ).
fof(f26620,plain,
( spl47_1157
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1157])]) ).
fof(f5344,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3290]) ).
fof(f3290,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2140]) ).
fof(f2140,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(rectify,[],[f509]) ).
fof(f509,axiom,
! [X53,X54,X56,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X54),X53)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X54),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X56),X53)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(f26618,plain,
spl47_1156,
inference(avatar_split_clause,[],[f5303,f26616]) ).
fof(f26616,plain,
( spl47_1156
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),X0)
| ~ class_Groups_Omonoid__mult(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1156])]) ).
fof(f5303,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),X0)
| ~ class_Groups_Omonoid__mult(X3) ),
inference(cnf_transformation,[],[f3245]) ).
fof(f3245,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),X0)
| ~ class_Groups_Omonoid__mult(X3) ),
inference(ennf_transformation,[],[f2101]) ).
fof(f2101,plain,
! [X0,X1,X2,X3] :
( class_Groups_Omonoid__mult(X3)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)),X0) ),
inference(rectify,[],[f655]) ).
fof(f655,axiom,
! [X7,X21,X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X7)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X21)),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult) ).
fof(f26614,plain,
spl47_1155,
inference(avatar_split_clause,[],[f5292,f26612]) ).
fof(f26612,plain,
( spl47_1155
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ class_Groups_Oab__semigroup__mult(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1155])]) ).
fof(f5292,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ class_Groups_Oab__semigroup__mult(X3) ),
inference(cnf_transformation,[],[f3232]) ).
fof(f3232,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ class_Groups_Oab__semigroup__mult(X3) ),
inference(ennf_transformation,[],[f2092]) ).
fof(f2092,plain,
! [X0,X1,X2,X3] :
( class_Groups_Oab__semigroup__mult(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
inference(rectify,[],[f540]) ).
fof(f540,axiom,
! [X16,X17,X4,X5] :
( class_Groups_Oab__semigroup__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17)),X16) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
fof(f26610,plain,
spl47_1154,
inference(avatar_split_clause,[],[f5288,f26608]) ).
fof(f26608,plain,
( spl47_1154
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
| ~ class_Rings_Olinordered__semidom(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1154])]) ).
fof(f5288,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(cnf_transformation,[],[f3226]) ).
fof(f3226,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(flattening,[],[f3225]) ).
fof(f3225,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(ennf_transformation,[],[f2088]) ).
fof(f2088,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ) ),
inference(rectify,[],[f279]) ).
fof(f279,axiom,
! [X17,X7,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X17),X7))
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X17)
=> c_Orderings_Oord__class_Oless(X5,X4,X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).
fof(f26606,plain,
spl47_1153,
inference(avatar_split_clause,[],[f5283,f26604]) ).
fof(f26604,plain,
( spl47_1153
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ~ class_Rings_Olinordered__semidom(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1153])]) ).
fof(f5283,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(cnf_transformation,[],[f3866]) ).
fof(f3866,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0)) ) )
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(nnf_transformation,[],[f3218]) ).
fof(f3218,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(flattening,[],[f3217]) ).
fof(f3217,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(ennf_transformation,[],[f2084]) ).
fof(f2084,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ) ),
inference(rectify,[],[f246]) ).
fof(f246,axiom,
! [X25,X15,X29,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X29)
=> ( c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X29),X15),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X29),X25))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X25) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing__iff) ).
fof(f26602,plain,
spl47_1152,
inference(avatar_split_clause,[],[f5279,f26600]) ).
fof(f26600,plain,
( spl47_1152
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ~ class_Rings_Olinordered__semidom(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1152])]) ).
fof(f5279,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(cnf_transformation,[],[f3214]) ).
fof(f3214,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(flattening,[],[f3213]) ).
fof(f3213,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(ennf_transformation,[],[f2082]) ).
fof(f2082,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
=> ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ) ),
inference(rectify,[],[f138]) ).
fof(f138,axiom,
! [X7,X21,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X4)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X21),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).
fof(f26598,plain,
spl47_1151,
inference(avatar_split_clause,[],[f5278,f26596]) ).
fof(f26596,plain,
( spl47_1151
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ~ class_Rings_Olinordered__semidom(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1151])]) ).
fof(f5278,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(cnf_transformation,[],[f3212]) ).
fof(f3212,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(flattening,[],[f3211]) ).
fof(f3211,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(ennf_transformation,[],[f2081]) ).
fof(f2081,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ) ),
inference(rectify,[],[f245]) ).
fof(f245,axiom,
! [X7,X21,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X21),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).
fof(f26594,plain,
spl47_1150,
inference(avatar_split_clause,[],[f5276,f26592]) ).
fof(f26592,plain,
( spl47_1150
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ class_Rings_Olinordered__semidom(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1150])]) ).
fof(f5276,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(cnf_transformation,[],[f3208]) ).
fof(f3208,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(flattening,[],[f3207]) ).
fof(f3207,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(ennf_transformation,[],[f2079]) ).
fof(f2079,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X0)
=> c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)) ) ) ),
inference(rectify,[],[f139]) ).
fof(f139,axiom,
! [X4,X36,X7,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X36)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X4)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X36)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing) ).
fof(f26590,plain,
spl47_1149,
inference(avatar_split_clause,[],[f5273,f26588]) ).
fof(f26588,plain,
( spl47_1149
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ class_Rings_Olinordered__semidom(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1149])]) ).
fof(f5273,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(cnf_transformation,[],[f3202]) ).
fof(f3202,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(flattening,[],[f3201]) ).
fof(f3201,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(ennf_transformation,[],[f2076]) ).
fof(f2076,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),X0)
=> c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)) ) ) ),
inference(rectify,[],[f281]) ).
fof(f281,axiom,
! [X4,X36,X7,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X36)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5),X4)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X36)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing) ).
fof(f26586,plain,
spl47_1148,
inference(avatar_split_clause,[],[f5272,f26584]) ).
fof(f26584,plain,
( spl47_1148
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Rings_Olinordered__semidom(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1148])]) ).
fof(f5272,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(cnf_transformation,[],[f3200]) ).
fof(f3200,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(flattening,[],[f3199]) ).
fof(f3199,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(ennf_transformation,[],[f2075]) ).
fof(f2075,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ) ) ),
inference(rectify,[],[f107]) ).
fof(f107,axiom,
! [X7,X17,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X17)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X17),X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mono) ).
fof(f26579,plain,
spl47_1147,
inference(avatar_split_clause,[],[f5261,f26577]) ).
fof(f26577,plain,
( spl47_1147
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_Rings_Olinordered__semiring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1147])]) ).
fof(f5261,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_Rings_Olinordered__semiring__strict(X3) ),
inference(cnf_transformation,[],[f3190]) ).
fof(f3190,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_Rings_Olinordered__semiring__strict(X3) ),
inference(flattening,[],[f3189]) ).
fof(f3189,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_Rings_Olinordered__semiring__strict(X3) ),
inference(ennf_transformation,[],[f2068]) ).
fof(f2068,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> c_Orderings_Oord__class_Oless(X3,X1,X0) ) ) ),
inference(rectify,[],[f607]) ).
fof(f607,axiom,
! [X17,X4,X16,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X16),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X16),X17))
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X16)
=> c_Orderings_Oord__class_Oless(X5,X4,X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).
fof(f26575,plain,
spl47_1146,
inference(avatar_split_clause,[],[f5260,f26573]) ).
fof(f26573,plain,
( spl47_1146
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ class_Rings_Olinordered__semiring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1146])]) ).
fof(f5260,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ class_Rings_Olinordered__semiring__strict(X3) ),
inference(cnf_transformation,[],[f3188]) ).
fof(f3188,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ class_Rings_Olinordered__semiring__strict(X3) ),
inference(flattening,[],[f3187]) ).
fof(f3187,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ class_Rings_Olinordered__semiring__strict(X3) ),
inference(ennf_transformation,[],[f2067]) ).
fof(f2067,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ) ),
inference(rectify,[],[f609]) ).
fof(f609,axiom,
! [X17,X16,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X16))
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X16)
=> c_Orderings_Oord__class_Oless(X5,X4,X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).
fof(f26571,plain,
spl47_1145,
inference(avatar_split_clause,[],[f5259,f26569]) ).
fof(f26569,plain,
( spl47_1145
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ class_Rings_Olinordered__semiring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1145])]) ).
fof(f5259,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ class_Rings_Olinordered__semiring__strict(X3) ),
inference(cnf_transformation,[],[f3186]) ).
fof(f3186,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ class_Rings_Olinordered__semiring__strict(X3) ),
inference(flattening,[],[f3185]) ).
fof(f3185,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ class_Rings_Olinordered__semiring__strict(X3) ),
inference(ennf_transformation,[],[f2066]) ).
fof(f2066,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1)
=> c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ) ) ),
inference(rectify,[],[f606]) ).
fof(f606,axiom,
! [X17,X16,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X16))
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X16)
=> c_Orderings_Oord__class_Oless__eq(X5,X4,X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).
fof(f26567,plain,
spl47_1144,
inference(avatar_split_clause,[],[f5258,f26565]) ).
fof(f26565,plain,
( spl47_1144
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_Rings_Olinordered__semiring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1144])]) ).
fof(f5258,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_Rings_Olinordered__semiring__strict(X3) ),
inference(cnf_transformation,[],[f3184]) ).
fof(f3184,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_Rings_Olinordered__semiring__strict(X3) ),
inference(flattening,[],[f3183]) ).
fof(f3183,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_Rings_Olinordered__semiring__strict(X3) ),
inference(ennf_transformation,[],[f2065]) ).
fof(f2065,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> c_Orderings_Oord__class_Oless__eq(X3,X1,X0) ) ) ),
inference(rectify,[],[f605]) ).
fof(f605,axiom,
! [X17,X4,X16,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X16),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X16),X17))
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X16)
=> c_Orderings_Oord__class_Oless__eq(X5,X4,X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).
fof(f26563,plain,
spl47_1143,
inference(avatar_split_clause,[],[f5257,f26561]) ).
fof(f26561,plain,
( spl47_1143
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Rings_Olinordered__semiring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1143])]) ).
fof(f5257,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Rings_Olinordered__semiring__strict(X3) ),
inference(cnf_transformation,[],[f3182]) ).
fof(f3182,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Rings_Olinordered__semiring__strict(X3) ),
inference(flattening,[],[f3181]) ).
fof(f3181,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Rings_Olinordered__semiring__strict(X3) ),
inference(ennf_transformation,[],[f2064]) ).
fof(f2064,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ) ) ),
inference(rectify,[],[f567]) ).
fof(f567,axiom,
! [X16,X17,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X17)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X16)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X16),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X16),X17)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).
fof(f26559,plain,
spl47_1142,
inference(avatar_split_clause,[],[f5256,f26557]) ).
fof(f26557,plain,
( spl47_1142
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Rings_Olinordered__semiring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1142])]) ).
fof(f5256,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Rings_Olinordered__semiring__strict(X3) ),
inference(cnf_transformation,[],[f3180]) ).
fof(f3180,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Rings_Olinordered__semiring__strict(X3) ),
inference(flattening,[],[f3179]) ).
fof(f3179,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Rings_Olinordered__semiring__strict(X3) ),
inference(ennf_transformation,[],[f2063]) ).
fof(f2063,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ) ) ),
inference(rectify,[],[f568]) ).
fof(f568,axiom,
! [X16,X17,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X17)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X16)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X16)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).
fof(f26555,plain,
spl47_1141,
inference(avatar_split_clause,[],[f5231,f26553]) ).
fof(f26553,plain,
( spl47_1141
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Rings_Oordered__semiring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1141])]) ).
fof(f5231,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Rings_Oordered__semiring(X3) ),
inference(cnf_transformation,[],[f3146]) ).
fof(f3146,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Rings_Oordered__semiring(X3) ),
inference(flattening,[],[f3145]) ).
fof(f3145,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Rings_Oordered__semiring(X3) ),
inference(ennf_transformation,[],[f2042]) ).
fof(f2042,plain,
! [X0,X1,X2,X3] :
( class_Rings_Oordered__semiring(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ) ) ),
inference(rectify,[],[f556]) ).
fof(f556,axiom,
! [X16,X17,X4,X5] :
( class_Rings_Oordered__semiring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X17)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X16)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X16),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X16),X17)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono) ).
fof(f26551,plain,
spl47_1140,
inference(avatar_split_clause,[],[f5230,f26549]) ).
fof(f26549,plain,
( spl47_1140
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Rings_Oordered__semiring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1140])]) ).
fof(f5230,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Rings_Oordered__semiring(X3) ),
inference(cnf_transformation,[],[f3144]) ).
fof(f3144,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Rings_Oordered__semiring(X3) ),
inference(flattening,[],[f3143]) ).
fof(f3143,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Rings_Oordered__semiring(X3) ),
inference(ennf_transformation,[],[f2041]) ).
fof(f2041,plain,
! [X0,X1,X2,X3] :
( class_Rings_Oordered__semiring(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ) ) ),
inference(rectify,[],[f555]) ).
fof(f555,axiom,
! [X16,X17,X4,X5] :
( class_Rings_Oordered__semiring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X17)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X16)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X16)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono) ).
fof(f26547,plain,
spl47_1139,
inference(avatar_split_clause,[],[f5227,f26545]) ).
fof(f26545,plain,
( spl47_1139
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_Rings_Olinordered__semiring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1139])]) ).
fof(f5227,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_Rings_Olinordered__semiring(X3) ),
inference(cnf_transformation,[],[f3138]) ).
fof(f3138,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_Rings_Olinordered__semiring(X3) ),
inference(flattening,[],[f3137]) ).
fof(f3137,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_Rings_Olinordered__semiring(X3) ),
inference(ennf_transformation,[],[f2038]) ).
fof(f2038,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semiring(X3)
=> ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> c_Orderings_Oord__class_Oless(X3,X1,X0) ) ) ),
inference(rectify,[],[f608]) ).
fof(f608,axiom,
! [X17,X4,X16,X5] :
( class_Rings_Olinordered__semiring(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X16),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X16),X17))
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X16)
=> c_Orderings_Oord__class_Oless(X5,X4,X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).
fof(f26543,plain,
spl47_1138,
inference(avatar_split_clause,[],[f5226,f26541]) ).
fof(f26541,plain,
( spl47_1138
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ class_Rings_Olinordered__semiring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1138])]) ).
fof(f5226,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ class_Rings_Olinordered__semiring(X3) ),
inference(cnf_transformation,[],[f3136]) ).
fof(f3136,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ class_Rings_Olinordered__semiring(X3) ),
inference(flattening,[],[f3135]) ).
fof(f3135,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ class_Rings_Olinordered__semiring(X3) ),
inference(ennf_transformation,[],[f2037]) ).
fof(f2037,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semiring(X3)
=> ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ) ),
inference(rectify,[],[f610]) ).
fof(f610,axiom,
! [X17,X16,X4,X5] :
( class_Rings_Olinordered__semiring(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X16))
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X16)
=> c_Orderings_Oord__class_Oless(X5,X4,X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).
fof(f26507,plain,
spl47_1137,
inference(avatar_split_clause,[],[f5225,f26505]) ).
fof(f26505,plain,
( spl47_1137
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Rings_Olinordered__comm__semiring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1137])]) ).
fof(f5225,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Rings_Olinordered__comm__semiring__strict(X3) ),
inference(cnf_transformation,[],[f3134]) ).
fof(f3134,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Rings_Olinordered__comm__semiring__strict(X3) ),
inference(flattening,[],[f3133]) ).
fof(f3133,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Rings_Olinordered__comm__semiring__strict(X3) ),
inference(ennf_transformation,[],[f2036]) ).
fof(f2036,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__comm__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ) ) ),
inference(rectify,[],[f566]) ).
fof(f566,axiom,
! [X16,X17,X4,X5] :
( class_Rings_Olinordered__comm__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X17)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X16)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X16),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X16),X17)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
fof(f26503,plain,
spl47_1136,
inference(avatar_split_clause,[],[f5224,f26501]) ).
fof(f26501,plain,
( spl47_1136
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Rings_Oordered__comm__semiring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1136])]) ).
fof(f5224,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Rings_Oordered__comm__semiring(X3) ),
inference(cnf_transformation,[],[f3132]) ).
fof(f3132,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Rings_Oordered__comm__semiring(X3) ),
inference(flattening,[],[f3131]) ).
fof(f3131,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Rings_Oordered__comm__semiring(X3) ),
inference(ennf_transformation,[],[f2035]) ).
fof(f2035,plain,
! [X0,X1,X2,X3] :
( class_Rings_Oordered__comm__semiring(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ) ) ),
inference(rectify,[],[f557]) ).
fof(f557,axiom,
! [X16,X17,X4,X5] :
( class_Rings_Oordered__comm__semiring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X17)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X16)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X16),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X16),X17)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).
fof(f26499,plain,
spl47_1135,
inference(avatar_split_clause,[],[f5205,f26497]) ).
fof(f26497,plain,
( spl47_1135
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1135])]) ).
fof(f5205,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f3846]) ).
fof(f3846,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0) )
& ( c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ) )
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(nnf_transformation,[],[f3128]) ).
fof(f3128,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless(X3,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(flattening,[],[f3127]) ).
fof(f3127,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless(X3,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(ennf_transformation,[],[f2032]) ).
fof(f2032,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless(X3,X1,X0) ) ) ),
inference(rectify,[],[f577]) ).
fof(f577,axiom,
! [X29,X12,X24,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X24)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X29))
<=> c_Orderings_Oord__class_Oless(X5,X12,X29) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).
fof(f26495,plain,
spl47_1134,
inference(avatar_split_clause,[],[f5204,f26493]) ).
fof(f26493,plain,
( spl47_1134
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1134])]) ).
fof(f5204,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f3846]) ).
fof(f26491,plain,
spl47_1133,
inference(avatar_split_clause,[],[f5203,f26489]) ).
fof(f26489,plain,
( spl47_1133
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1133])]) ).
fof(f5203,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f3845]) ).
fof(f3845,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ) )
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(nnf_transformation,[],[f3126]) ).
fof(f3126,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(X3,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(flattening,[],[f3125]) ).
fof(f3125,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(X3,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(ennf_transformation,[],[f2031]) ).
fof(f2031,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(X3,X1,X0) ) ) ),
inference(rectify,[],[f616]) ).
fof(f616,axiom,
! [X29,X12,X24,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X24)
=> ( c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X29))
<=> c_Orderings_Oord__class_Oless__eq(X5,X12,X29) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).
fof(f26487,plain,
spl47_1132,
inference(avatar_split_clause,[],[f5202,f26485]) ).
fof(f26485,plain,
( spl47_1132
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1132])]) ).
fof(f5202,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f3845]) ).
fof(f26483,plain,
spl47_1131,
inference(avatar_split_clause,[],[f5200,f26481]) ).
fof(f26481,plain,
( spl47_1131
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1131])]) ).
fof(f5200,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f3844]) ).
fof(f3844,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,X0,X1) )
& ( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ) )
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(nnf_transformation,[],[f3124]) ).
fof(f3124,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless(X3,X0,X1) )
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(flattening,[],[f3123]) ).
fof(f3123,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless(X3,X0,X1) )
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(ennf_transformation,[],[f2030]) ).
fof(f2030,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
=> ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless(X3,X0,X1) ) ) ),
inference(rectify,[],[f571]) ).
fof(f571,axiom,
! [X29,X12,X24,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X24,c_Groups_Ozero__class_Ozero(X5))
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X29))
<=> c_Orderings_Oord__class_Oless(X5,X29,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).
fof(f26479,plain,
spl47_1130,
inference(avatar_split_clause,[],[f5199,f26477]) ).
fof(f26477,plain,
( spl47_1130
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1130])]) ).
fof(f5199,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f3843]) ).
fof(f3843,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X1) )
& ( c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ) )
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(nnf_transformation,[],[f3122]) ).
fof(f3122,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(X3,X0,X1) )
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(flattening,[],[f3121]) ).
fof(f3121,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(X3,X0,X1) )
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(ennf_transformation,[],[f2029]) ).
fof(f2029,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
=> ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(X3,X0,X1) ) ) ),
inference(rectify,[],[f615]) ).
fof(f615,axiom,
! [X29,X12,X24,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X24,c_Groups_Ozero__class_Ozero(X5))
=> ( c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X29))
<=> c_Orderings_Oord__class_Oless__eq(X5,X29,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).
fof(f26475,plain,
spl47_1129,
inference(avatar_split_clause,[],[f5198,f26473]) ).
fof(f26473,plain,
( spl47_1129
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1129])]) ).
fof(f5198,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f3843]) ).
fof(f26471,plain,
spl47_1128,
inference(avatar_split_clause,[],[f5197,f26469]) ).
fof(f26469,plain,
( spl47_1128
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1128])]) ).
fof(f5197,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f3120]) ).
fof(f3120,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(flattening,[],[f3119]) ).
fof(f3119,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(ennf_transformation,[],[f2028]) ).
fof(f2028,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ) ) ),
inference(rectify,[],[f565]) ).
fof(f565,axiom,
! [X16,X4,X17,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X17,X4)
=> ( c_Orderings_Oord__class_Oless(X5,X16,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X16)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).
fof(f26467,plain,
( spl47_1127
| ~ spl47_156
| ~ spl47_844 ),
inference(avatar_split_clause,[],[f17563,f17325,f6803,f26465]) ).
fof(f26465,plain,
( spl47_1127
<=> ! [X0,X1] :
( sP7(tc_Nat_Onat,X0,X1)
| ~ sP8(X1,X0,tc_Nat_Onat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1127])]) ).
fof(f6803,plain,
( spl47_156
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_156])]) ).
fof(f17325,plain,
( spl47_844
<=> ! [X2,X0,X1] :
( sP7(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1))
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_844])]) ).
fof(f17563,plain,
( ! [X0,X1] :
( sP7(tc_Nat_Onat,X0,X1)
| ~ sP8(X1,X0,tc_Nat_Onat) )
| ~ spl47_156
| ~ spl47_844 ),
inference(resolution,[],[f17326,f6804]) ).
fof(f6804,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ spl47_156 ),
inference(avatar_component_clause,[],[f6803]) ).
fof(f17326,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1))
| sP7(X2,X1,X0)
| ~ sP8(X0,X1,X2) )
| ~ spl47_844 ),
inference(avatar_component_clause,[],[f17325]) ).
fof(f26463,plain,
spl47_1126,
inference(avatar_split_clause,[],[f5196,f26461]) ).
fof(f26461,plain,
( spl47_1126
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2))
| ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1126])]) ).
fof(f5196,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2))
| ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f3118]) ).
fof(f3118,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2))
| ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(flattening,[],[f3117]) ).
fof(f3117,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2))
| ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(ennf_transformation,[],[f2027]) ).
fof(f2027,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2)) ) ) ),
inference(rectify,[],[f564]) ).
fof(f564,axiom,
! [X16,X4,X17,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X17,X4)
=> ( c_Orderings_Oord__class_Oless(X5,X16,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X16),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X16),X17)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).
fof(f26459,plain,
spl47_1125,
inference(avatar_split_clause,[],[f5195,f26457]) ).
fof(f26457,plain,
( spl47_1125
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Ozero__class_Ozero(X3))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Rings_Oordered__ring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1125])]) ).
fof(f5195,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Ozero__class_Ozero(X3))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Rings_Oordered__ring(X3) ),
inference(cnf_transformation,[],[f3116]) ).
fof(f3116,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Ozero__class_Ozero(X3))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Rings_Oordered__ring(X3) ),
inference(flattening,[],[f3115]) ).
fof(f3115,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Ozero__class_Ozero(X3))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Rings_Oordered__ring(X3) ),
inference(ennf_transformation,[],[f2026]) ).
fof(f2026,plain,
! [X0,X1,X2,X3] :
( class_Rings_Oordered__ring(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2)) ) ) ),
inference(rectify,[],[f559]) ).
fof(f559,axiom,
! [X16,X4,X17,X5] :
( class_Rings_Oordered__ring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X17,X4)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X16,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X16),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X16),X17)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).
fof(f26455,plain,
spl47_1124,
inference(avatar_split_clause,[],[f5194,f26453]) ).
fof(f26453,plain,
( spl47_1124
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Ozero__class_Ozero(X3))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Rings_Oordered__ring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1124])]) ).
fof(f5194,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Ozero__class_Ozero(X3))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Rings_Oordered__ring(X3) ),
inference(cnf_transformation,[],[f3114]) ).
fof(f3114,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Ozero__class_Ozero(X3))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Rings_Oordered__ring(X3) ),
inference(flattening,[],[f3113]) ).
fof(f3113,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Ozero__class_Ozero(X3))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Rings_Oordered__ring(X3) ),
inference(ennf_transformation,[],[f2025]) ).
fof(f2025,plain,
! [X0,X1,X2,X3] :
( class_Rings_Oordered__ring(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X0,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ) ) ),
inference(rectify,[],[f558]) ).
fof(f558,axiom,
! [X16,X4,X17,X5] :
( class_Rings_Oordered__ring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X17,X4)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X16,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X16)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).
fof(f26451,plain,
spl47_1123,
inference(avatar_split_clause,[],[f5177,f26449]) ).
fof(f26449,plain,
( spl47_1123
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X0,X2)),X1))
| c_Groups_Ozero__class_Ozero(X3) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),X1))
| ~ class_Fields_Ofield(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1123])]) ).
fof(f5177,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X0,X2)),X1))
| c_Groups_Ozero__class_Ozero(X3) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),X1))
| ~ class_Fields_Ofield(X3) ),
inference(cnf_transformation,[],[f3107]) ).
fof(f3107,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X0,X2)),X1))
| c_Groups_Ozero__class_Ozero(X3) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),X1))
| ~ class_Fields_Ofield(X3) ),
inference(flattening,[],[f3106]) ).
fof(f3106,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X0,X2)),X1))
| c_Groups_Ozero__class_Ozero(X3) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),X1))
| ~ class_Fields_Ofield(X3) ),
inference(ennf_transformation,[],[f2020]) ).
fof(f2020,plain,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),X1))
=> ( c_Groups_Ozero__class_Ozero(X3) != X0
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X0,X2)),X1)) ) ) ),
inference(rectify,[],[f115]) ).
fof(f115,axiom,
! [X4,X13,X8,X5] :
( class_Fields_Ofield(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),X8),X13))
=> ( c_Groups_Ozero__class_Ozero(X5) != X4
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),c_Polynomial_Osmult(X5,X4,X8)),X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd) ).
fof(f26447,plain,
spl47_1122,
inference(avatar_split_clause,[],[f5175,f26445]) ).
fof(f26445,plain,
( spl47_1122
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),c_Polynomial_Osmult(X3,X2,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1122])]) ).
fof(f5175,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),c_Polynomial_Osmult(X3,X2,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(cnf_transformation,[],[f3833]) ).
fof(f3833,plain,
! [X0,X1,X2,X3] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),c_Polynomial_Osmult(X3,X2,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),c_Polynomial_Osmult(X3,X2,X0))) ) )
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(nnf_transformation,[],[f3103]) ).
fof(f3103,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),c_Polynomial_Osmult(X3,X2,X0)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0)) )
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(flattening,[],[f3102]) ).
fof(f3102,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),c_Polynomial_Osmult(X3,X2,X0)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0)) )
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(ennf_transformation,[],[f2018]) ).
fof(f2018,plain,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( c_Groups_Ozero__class_Ozero(X3) != X2
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),c_Polynomial_Osmult(X3,X2,X0)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0)) ) ) ),
inference(rectify,[],[f116]) ).
fof(f116,axiom,
! [X18,X9,X12,X5] :
( class_Fields_Ofield(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X12
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),X9),c_Polynomial_Osmult(X5,X12,X18)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),X9),X18)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult__iff) ).
fof(f26443,plain,
spl47_1121,
inference(avatar_split_clause,[],[f5174,f26441]) ).
fof(f26441,plain,
( spl47_1121
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),c_Polynomial_Osmult(X3,X2,X0)))
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1121])]) ).
fof(f5174,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),c_Polynomial_Osmult(X3,X2,X0)))
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(cnf_transformation,[],[f3833]) ).
fof(f26439,plain,
spl47_1120,
inference(avatar_split_clause,[],[f5128,f26437]) ).
fof(f26437,plain,
( spl47_1120
<=> ! [X0,X3,X2,X1] :
( c_Rings_Oinverse__class_Odivide(X3,X1,X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2))
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1120])]) ).
fof(f5128,plain,
! [X2,X3,X0,X1] :
( c_Rings_Oinverse__class_Odivide(X3,X1,X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2))
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(cnf_transformation,[],[f3061]) ).
fof(f3061,plain,
! [X0,X1,X2,X3] :
( c_Rings_Oinverse__class_Odivide(X3,X1,X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2))
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(flattening,[],[f3060]) ).
fof(f3060,plain,
! [X0,X1,X2,X3] :
( c_Rings_Oinverse__class_Odivide(X3,X1,X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2))
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(ennf_transformation,[],[f1990]) ).
fof(f1990,plain,
! [X0,X1,X2,X3] :
( class_Fields_Ofield__inverse__zero(X3)
=> ( c_Groups_Ozero__class_Ozero(X3) != X2
=> c_Rings_Oinverse__class_Odivide(X3,X1,X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X2)) ) ),
inference(rectify,[],[f945]) ).
fof(f945,axiom,
! [X17,X4,X16,X5] :
( class_Fields_Ofield__inverse__zero(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X16
=> c_Rings_Oinverse__class_Odivide(X5,X4,X17) = c_Rings_Oinverse__class_Odivide(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__right) ).
fof(f26435,plain,
spl47_1119,
inference(avatar_split_clause,[],[f5127,f26433]) ).
fof(f26433,plain,
( spl47_1119
<=> ! [X0,X3,X2,X1] :
( c_Rings_Oinverse__class_Odivide(X3,X1,X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1119])]) ).
fof(f5127,plain,
! [X2,X3,X0,X1] :
( c_Rings_Oinverse__class_Odivide(X3,X1,X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(cnf_transformation,[],[f3059]) ).
fof(f3059,plain,
! [X0,X1,X2,X3] :
( c_Rings_Oinverse__class_Odivide(X3,X1,X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(flattening,[],[f3058]) ).
fof(f3058,plain,
! [X0,X1,X2,X3] :
( c_Rings_Oinverse__class_Odivide(X3,X1,X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(ennf_transformation,[],[f1989]) ).
fof(f1989,plain,
! [X0,X1,X2,X3] :
( class_Fields_Ofield__inverse__zero(X3)
=> ( c_Groups_Ozero__class_Ozero(X3) != X2
=> c_Rings_Oinverse__class_Odivide(X3,X1,X0) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ) ),
inference(rectify,[],[f944]) ).
fof(f944,axiom,
! [X17,X4,X16,X5] :
( class_Fields_Ofield__inverse__zero(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X16
=> c_Rings_Oinverse__class_Odivide(X5,X4,X17) = c_Rings_Oinverse__class_Odivide(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X16),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X16),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__left) ).
fof(f26431,plain,
spl47_1118,
inference(avatar_split_clause,[],[f5007,f26429]) ).
fof(f26429,plain,
( spl47_1118
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)) != X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1118])]) ).
fof(f5007,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)) != X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(cnf_transformation,[],[f2992]) ).
fof(f2992,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)) != X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(flattening,[],[f2991]) ).
fof(f2991,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)) != X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(ennf_transformation,[],[f1906]) ).
fof(f1906,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
=> ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)) = X2
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ) ) ),
inference(rectify,[],[f712]) ).
fof(f712,axiom,
! [X13,X34,X4] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
=> ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X34,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X13)) = X4
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X34,X4)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X13) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).
fof(f26427,plain,
spl47_1117,
inference(avatar_split_clause,[],[f4920,f26425]) ).
fof(f26425,plain,
( spl47_1117
<=> ! [X2,X0,X1] :
( c_Groups_Oone__class_Oone(X2) = hAPP(c_Polynomial_Ocoeff(X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0)),X0)
| ~ class_Rings_Ocomm__semiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1117])]) ).
fof(f4920,plain,
! [X2,X0,X1] :
( c_Groups_Oone__class_Oone(X2) = hAPP(c_Polynomial_Ocoeff(X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0)),X0)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(cnf_transformation,[],[f2890]) ).
fof(f2890,plain,
! [X0,X1,X2] :
( c_Groups_Oone__class_Oone(X2) = hAPP(c_Polynomial_Ocoeff(X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0)),X0)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f1838]) ).
fof(f1838,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oone__class_Oone(X2) = hAPP(c_Polynomial_Ocoeff(X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0)),X0) ),
inference(rectify,[],[f882]) ).
fof(f882,axiom,
! [X7,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oone__class_Oone(X5) = hAPP(c_Polynomial_Ocoeff(X5,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X5)),c_Polynomial_OpCons(X5,X4,c_Polynomial_OpCons(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))))),X7)),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__linear__power) ).
fof(f26391,plain,
spl47_1116,
inference(avatar_split_clause,[],[f4903,f26389]) ).
fof(f26389,plain,
( spl47_1116
<=> ! [X2,X0,X1] :
( c_Polynomial_OpCons(X2,hAPP(c_Polynomial_Opoly(X2,X1),X0),c_Polynomial_Osynthetic__div(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,c_Polynomial_Osmult(X2,X0,c_Polynomial_Osynthetic__div(X2,X1,X0)))
| ~ class_Rings_Ocomm__semiring__0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1116])]) ).
fof(f4903,plain,
! [X2,X0,X1] :
( c_Polynomial_OpCons(X2,hAPP(c_Polynomial_Opoly(X2,X1),X0),c_Polynomial_Osynthetic__div(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,c_Polynomial_Osmult(X2,X0,c_Polynomial_Osynthetic__div(X2,X1,X0)))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(cnf_transformation,[],[f2875]) ).
fof(f2875,plain,
! [X0,X1,X2] :
( c_Polynomial_OpCons(X2,hAPP(c_Polynomial_Opoly(X2,X1),X0),c_Polynomial_Osynthetic__div(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,c_Polynomial_Osmult(X2,X0,c_Polynomial_Osynthetic__div(X2,X1,X0)))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(ennf_transformation,[],[f1823]) ).
fof(f1823,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__0(X2)
=> c_Polynomial_OpCons(X2,hAPP(c_Polynomial_Opoly(X2,X1),X0),c_Polynomial_Osynthetic__div(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,c_Polynomial_Osmult(X2,X0,c_Polynomial_Osynthetic__div(X2,X1,X0))) ),
inference(rectify,[],[f126]) ).
fof(f126,axiom,
! [X16,X8,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Polynomial_OpCons(X5,hAPP(c_Polynomial_Opoly(X5,X8),X16),c_Polynomial_Osynthetic__div(X5,X8,X16)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),X8,c_Polynomial_Osmult(X5,X16,c_Polynomial_Osynthetic__div(X5,X8,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__correct) ).
fof(f26387,plain,
spl47_1115,
inference(avatar_split_clause,[],[f4873,f26385]) ).
fof(f26385,plain,
( spl47_1115
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1)
| ~ class_Groups_Omonoid__mult(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1115])]) ).
fof(f4873,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1)
| ~ class_Groups_Omonoid__mult(X2) ),
inference(cnf_transformation,[],[f2843]) ).
fof(f2843,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1)
| ~ class_Groups_Omonoid__mult(X2) ),
inference(ennf_transformation,[],[f1799]) ).
fof(f1799,plain,
! [X0,X1,X2] :
( class_Groups_Omonoid__mult(X2)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1) ),
inference(rectify,[],[f533]) ).
fof(f533,axiom,
! [X7,X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__commutes) ).
fof(f24351,plain,
spl47_1114,
inference(avatar_split_clause,[],[f5867,f24349]) ).
fof(f24349,plain,
( spl47_1114
<=> ! [X2,X0,X1] :
( sP25(X0,X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2),X0))
| ~ sP24(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1114])]) ).
fof(f5867,plain,
! [X2,X0,X1] :
( sP25(X0,X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2),X0))
| ~ sP24(X2,X1,X0) ),
inference(equality_resolution,[],[f5866]) ).
fof(f5866,plain,
! [X2,X0,X1,X4] :
( sP25(X0,X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X4)
| ~ sP24(X2,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2),X0) != X4 ),
inference(equality_resolution,[],[f5408]) ).
fof(f5408,plain,
! [X2,X3,X0,X1,X4] :
( sP25(X0,X1,X2,X3,X4)
| ~ sP24(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X3
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X2),X0) != X4 ),
inference(cnf_transformation,[],[f3884]) ).
fof(f24347,plain,
spl47_1113,
inference(avatar_split_clause,[],[f5743,f24345]) ).
fof(f24345,plain,
( spl47_1113
<=> ! [X2] :
( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),c_Groups_Ozero__class_Ozero(X2))))
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1113])]) ).
fof(f5743,plain,
! [X2] :
( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),c_Groups_Ozero__class_Ozero(X2))))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(equality_resolution,[],[f5742]) ).
fof(f5742,plain,
! [X2,X1] :
( c_Groups_Ozero__class_Ozero(X2) != X1
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),c_Groups_Ozero__class_Ozero(X2))))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(equality_resolution,[],[f4693]) ).
fof(f4693,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f3689]) ).
fof(f3689,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)))
| ( c_Groups_Ozero__class_Ozero(X2) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 ) )
& ( c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0))) ) )
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(flattening,[],[f3688]) ).
fof(f3688,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)))
| ( c_Groups_Ozero__class_Ozero(X2) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 ) )
& ( c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0))) ) )
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(nnf_transformation,[],[f2657]) ).
fof(f2657,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)))
<=> ( c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1 ) )
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(ennf_transformation,[],[f1673]) ).
fof(f1673,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)))
<=> ( c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1 ) ) ),
inference(rectify,[],[f620]) ).
fof(f620,axiom,
! [X25,X15,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),X25)))
<=> ( c_Groups_Ozero__class_Ozero(X5) != X25
| c_Groups_Ozero__class_Ozero(X5) != X15 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
fof(f24343,plain,
spl47_1112,
inference(avatar_split_clause,[],[f5741,f24341]) ).
fof(f24341,plain,
( spl47_1112
<=> ! [X2] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),c_Groups_Ozero__class_Ozero(X2))),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1112])]) ).
fof(f5741,plain,
! [X2] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),c_Groups_Ozero__class_Ozero(X2))),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(equality_resolution,[],[f5740]) ).
fof(f5740,plain,
! [X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),c_Groups_Ozero__class_Ozero(X2))),c_Groups_Ozero__class_Ozero(X2))
| c_Groups_Ozero__class_Ozero(X2) != X1
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(equality_resolution,[],[f4692]) ).
fof(f4692,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)),c_Groups_Ozero__class_Ozero(X2))
| c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f3687]) ).
fof(f3687,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)),c_Groups_Ozero__class_Ozero(X2))
| c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(X2) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 )
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)),c_Groups_Ozero__class_Ozero(X2)) ) )
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(flattening,[],[f3686]) ).
fof(f3686,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)),c_Groups_Ozero__class_Ozero(X2))
| c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(X2) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 )
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)),c_Groups_Ozero__class_Ozero(X2)) ) )
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(nnf_transformation,[],[f2656]) ).
fof(f2656,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)),c_Groups_Ozero__class_Ozero(X2))
<=> ( c_Groups_Ozero__class_Ozero(X2) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 ) )
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(ennf_transformation,[],[f1672]) ).
fof(f1672,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)),c_Groups_Ozero__class_Ozero(X2))
<=> ( c_Groups_Ozero__class_Ozero(X2) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 ) ) ),
inference(rectify,[],[f618]) ).
fof(f618,axiom,
! [X25,X15,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),X25)),c_Groups_Ozero__class_Ozero(X5))
<=> ( c_Groups_Ozero__class_Ozero(X5) = X25
& c_Groups_Ozero__class_Ozero(X5) = X15 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).
fof(f24339,plain,
spl47_1111,
inference(avatar_split_clause,[],[f5641,f24337]) ).
fof(f24337,plain,
( spl47_1111
<=> ! [X2,X0,X1] :
( X0 = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1111])]) ).
fof(f5641,plain,
! [X2,X0,X1] :
( X0 = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0) ),
inference(definition_unfolding,[],[f5111,f4118,f4118]) ).
fof(f5111,plain,
! [X2,X0,X1] :
( X0 = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X0) ),
inference(cnf_transformation,[],[f3815]) ).
fof(f3815,plain,
! [X0,X1,X2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X0)
| X0 != X1 )
& ( X0 = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X0) ) ),
inference(nnf_transformation,[],[f1955]) ).
fof(f1955,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X2)),X0)
<=> X0 = X1 ),
inference(rectify,[],[f656]) ).
fof(f656,axiom,
! [X11,X14,X44] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X44)),X14) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X44)),X11)
<=> X11 = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
fof(f24335,plain,
spl47_1110,
inference(avatar_split_clause,[],[f5636,f24333]) ).
fof(f24333,plain,
( spl47_1110
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Ocomm__semiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1110])]) ).
fof(f5636,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(definition_unfolding,[],[f4915,f4118]) ).
fof(f4915,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(cnf_transformation,[],[f2885]) ).
fof(f2885,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f1833]) ).
fof(f1833,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1) ),
inference(rectify,[],[f598]) ).
fof(f598,axiom,
! [X13,X6,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),c_Nat_OSuc(X13)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X13)),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
fof(f24331,plain,
spl47_1109,
inference(avatar_split_clause,[],[f5634,f24329]) ).
fof(f24329,plain,
( spl47_1109
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Ocomm__semiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1109])]) ).
fof(f5634,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(definition_unfolding,[],[f4913,f4118]) ).
fof(f4913,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(cnf_transformation,[],[f2883]) ).
fof(f2883,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f1831]) ).
fof(f1831,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(rectify,[],[f597]) ).
fof(f597,axiom,
! [X13,X6,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),c_Nat_OSuc(X13)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
fof(f24327,plain,
spl47_1108,
inference(avatar_split_clause,[],[f5629,f24325]) ).
fof(f24325,plain,
( spl47_1108
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Groups_Omonoid__mult(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1108])]) ).
fof(f5629,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Groups_Omonoid__mult(X2) ),
inference(definition_unfolding,[],[f4872,f4118]) ).
fof(f4872,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1)
| ~ class_Groups_Omonoid__mult(X2) ),
inference(cnf_transformation,[],[f2842]) ).
fof(f2842,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1)
| ~ class_Groups_Omonoid__mult(X2) ),
inference(ennf_transformation,[],[f1798]) ).
fof(f1798,plain,
! [X0,X1,X2] :
( class_Groups_Omonoid__mult(X2)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)),X1) ),
inference(rectify,[],[f595]) ).
fof(f595,axiom,
! [X7,X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Nat_OSuc(X7)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7)),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc2) ).
fof(f24323,plain,
spl47_1107,
inference(avatar_split_clause,[],[f5628,f24321]) ).
fof(f24321,plain,
( spl47_1107
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Power_Opower(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1107])]) ).
fof(f5628,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Power_Opower(X2) ),
inference(definition_unfolding,[],[f4869,f4118]) ).
fof(f4869,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ class_Power_Opower(X2) ),
inference(cnf_transformation,[],[f2840]) ).
fof(f2840,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ class_Power_Opower(X2) ),
inference(ennf_transformation,[],[f1796]) ).
fof(f1796,plain,
! [X0,X1,X2] :
( class_Power_Opower(X2)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ),
inference(rectify,[],[f594]) ).
fof(f594,axiom,
! [X7,X4,X5] :
( class_Power_Opower(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Nat_OSuc(X7)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc) ).
fof(f24319,plain,
spl47_1106,
inference(avatar_split_clause,[],[f5343,f24317]) ).
fof(f24317,plain,
( spl47_1106
<=> ! [X0,X3,X2,X1] :
( hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X3)),X2),X1)),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(c_Polynomial_Opoly(X3,X2),X0)),X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1106])]) ).
fof(f5343,plain,
! [X2,X3,X0,X1] :
( hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X3)),X2),X1)),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(c_Polynomial_Opoly(X3,X2),X0)),X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3289]) ).
fof(f3289,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X3)),X2),X1)),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(c_Polynomial_Opoly(X3,X2),X0)),X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2139]) ).
fof(f2139,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(c_Polynomial_Opoly(X3,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X3)),X2),X1)),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),hAPP(c_Polynomial_Opoly(X3,X2),X0)),X1) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X6,X7,X8,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(c_Polynomial_Opoly(X5,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X5)),X8),X7)),X6) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Polynomial_Opoly(X5,X8),X6)),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__power) ).
fof(f24310,plain,
spl47_1105,
inference(avatar_split_clause,[],[f5329,f24308]) ).
fof(f24308,plain,
( spl47_1105
<=> ! [X0,X3,X2,X1] :
( hAPP(c_Polynomial_Opoly(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(c_Polynomial_Opoly(X3,X2),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1105])]) ).
fof(f5329,plain,
! [X2,X3,X0,X1] :
( hAPP(c_Polynomial_Opoly(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(c_Polynomial_Opoly(X3,X2),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f3273]) ).
fof(f3273,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Opoly(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(c_Polynomial_Opoly(X3,X2),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f2125]) ).
fof(f2125,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(c_Polynomial_Opoly(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(c_Polynomial_Opoly(X3,X2),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
inference(rectify,[],[f181]) ).
fof(f181,axiom,
! [X6,X13,X8,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> hAPP(c_Polynomial_Opoly(X5,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),X8,X13)),X6) = c_Groups_Oplus__class_Oplus(X5,hAPP(c_Polynomial_Opoly(X5,X8),X6),hAPP(c_Polynomial_Opoly(X5,X13),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__add) ).
fof(f24306,plain,
spl47_1104,
inference(avatar_split_clause,[],[f5328,f24304]) ).
fof(f24304,plain,
( spl47_1104
<=> ! [X0,X3,X2,X1] :
( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0)))
| ~ class_Rings_Ocomm__semiring__0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1104])]) ).
fof(f5328,plain,
! [X2,X3,X0,X1] :
( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0)))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f3272]) ).
fof(f3272,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0)))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f2124]) ).
fof(f2124,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(c_Polynomial_Opoly(X3,c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0))) ),
inference(rectify,[],[f628]) ).
fof(f628,axiom,
! [X6,X8,X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> hAPP(c_Polynomial_Opoly(X5,c_Polynomial_OpCons(X5,X4,X8)),X6) = c_Groups_Oplus__class_Oplus(X5,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Polynomial_Opoly(X5,X8),X6))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pCons) ).
fof(f24302,plain,
spl47_1103,
inference(avatar_split_clause,[],[f5313,f24300]) ).
fof(f24300,plain,
( spl47_1103
<=> ! [X0,X3,X2,X1] :
( c_Polynomial_Opoly__rec(X0,X3,X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))) = X1
| hAPP(hAPP(hAPP(X2,c_Groups_Ozero__class_Ozero(X3)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),X1) != X1
| ~ class_Groups_Ozero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1103])]) ).
fof(f5313,plain,
! [X2,X3,X0,X1] :
( c_Polynomial_Opoly__rec(X0,X3,X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))) = X1
| hAPP(hAPP(hAPP(X2,c_Groups_Ozero__class_Ozero(X3)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),X1) != X1
| ~ class_Groups_Ozero(X3) ),
inference(cnf_transformation,[],[f3258]) ).
fof(f3258,plain,
! [X0,X1,X2,X3] :
( c_Polynomial_Opoly__rec(X0,X3,X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))) = X1
| hAPP(hAPP(hAPP(X2,c_Groups_Ozero__class_Ozero(X3)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),X1) != X1
| ~ class_Groups_Ozero(X3) ),
inference(flattening,[],[f3257]) ).
fof(f3257,plain,
! [X0,X1,X2,X3] :
( c_Polynomial_Opoly__rec(X0,X3,X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))) = X1
| hAPP(hAPP(hAPP(X2,c_Groups_Ozero__class_Ozero(X3)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),X1) != X1
| ~ class_Groups_Ozero(X3) ),
inference(ennf_transformation,[],[f2110]) ).
fof(f2110,plain,
! [X0,X1,X2,X3] :
( class_Groups_Ozero(X3)
=> ( hAPP(hAPP(hAPP(X2,c_Groups_Ozero__class_Ozero(X3)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),X1) = X1
=> c_Polynomial_Opoly__rec(X0,X3,X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))) = X1 ) ),
inference(rectify,[],[f73]) ).
fof(f73,axiom,
! [X5,X30,X1,X31] :
( class_Groups_Ozero(X31)
=> ( hAPP(hAPP(hAPP(X1,c_Groups_Ozero__class_Ozero(X31)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X31))),X30) = X30
=> c_Polynomial_Opoly__rec(X5,X31,X30,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X31))) = X30 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__rec__0) ).
fof(f24298,plain,
spl47_1102,
inference(avatar_split_clause,[],[f5309,f24296]) ).
fof(f24296,plain,
( spl47_1102
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X0)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ class_Groups_Ocomm__monoid__add(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1102])]) ).
fof(f5309,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X0)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ class_Groups_Ocomm__monoid__add(X3) ),
inference(cnf_transformation,[],[f3254]) ).
fof(f3254,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X0)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ class_Groups_Ocomm__monoid__add(X3) ),
inference(flattening,[],[f3253]) ).
fof(f3253,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X0)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ class_Groups_Ocomm__monoid__add(X3) ),
inference(ennf_transformation,[],[f2107]) ).
fof(f2107,plain,
! [X0,X1,X2,X3] :
( class_Groups_Ocomm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X0)),X1) ) ) ),
inference(rectify,[],[f180]) ).
fof(f180,axiom,
! [X13,X7,X8,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5,X8),X7)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5,X13),X7)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),X8,X13)),X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__add__less) ).
fof(f24294,plain,
spl47_1101,
inference(avatar_split_clause,[],[f5308,f24292]) ).
fof(f24292,plain,
( spl47_1101
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X0)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ class_Groups_Ocomm__monoid__add(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1101])]) ).
fof(f5308,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X0)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ class_Groups_Ocomm__monoid__add(X3) ),
inference(cnf_transformation,[],[f3252]) ).
fof(f3252,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X0)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ class_Groups_Ocomm__monoid__add(X3) ),
inference(flattening,[],[f3251]) ).
fof(f3251,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X0)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ class_Groups_Ocomm__monoid__add(X3) ),
inference(ennf_transformation,[],[f2106]) ).
fof(f2106,plain,
! [X0,X1,X2,X3] :
( class_Groups_Ocomm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X0)),X1) ) ) ),
inference(rectify,[],[f267]) ).
fof(f267,axiom,
! [X13,X7,X8,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X5,X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X5,X13),X7)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X5,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),X8,X13)),X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__add__le) ).
fof(f24290,plain,
spl47_1100,
inference(avatar_split_clause,[],[f5307,f24288]) ).
fof(f24288,plain,
( spl47_1100
<=> ! [X0,X3,X2,X1] :
( hAPP(c_Polynomial_Ocoeff(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(c_Polynomial_Ocoeff(X3,X2),X0),hAPP(c_Polynomial_Ocoeff(X3,X1),X0))
| ~ class_Groups_Ocomm__monoid__add(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1100])]) ).
fof(f5307,plain,
! [X2,X3,X0,X1] :
( hAPP(c_Polynomial_Ocoeff(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(c_Polynomial_Ocoeff(X3,X2),X0),hAPP(c_Polynomial_Ocoeff(X3,X1),X0))
| ~ class_Groups_Ocomm__monoid__add(X3) ),
inference(cnf_transformation,[],[f3250]) ).
fof(f3250,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Ocoeff(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(c_Polynomial_Ocoeff(X3,X2),X0),hAPP(c_Polynomial_Ocoeff(X3,X1),X0))
| ~ class_Groups_Ocomm__monoid__add(X3) ),
inference(ennf_transformation,[],[f2105]) ).
fof(f2105,plain,
! [X0,X1,X2,X3] :
( class_Groups_Ocomm__monoid__add(X3)
=> hAPP(c_Polynomial_Ocoeff(X3,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,hAPP(c_Polynomial_Ocoeff(X3,X2),X0),hAPP(c_Polynomial_Ocoeff(X3,X1),X0)) ),
inference(rectify,[],[f758]) ).
fof(f758,axiom,
! [X7,X13,X8,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> hAPP(c_Polynomial_Ocoeff(X5,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),X8,X13)),X7) = c_Groups_Oplus__class_Oplus(X5,hAPP(c_Polynomial_Ocoeff(X5,X8),X7),hAPP(c_Polynomial_Ocoeff(X5,X13),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__add) ).
fof(f24286,plain,
spl47_1099,
inference(avatar_split_clause,[],[f5271,f24284]) ).
fof(f24284,plain,
( spl47_1099
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X0)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ class_Groups_Oab__group__add(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1099])]) ).
fof(f5271,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X0)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ class_Groups_Oab__group__add(X3) ),
inference(cnf_transformation,[],[f3198]) ).
fof(f3198,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X0)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ class_Groups_Oab__group__add(X3) ),
inference(flattening,[],[f3197]) ).
fof(f3197,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X0)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ class_Groups_Oab__group__add(X3) ),
inference(ennf_transformation,[],[f2074]) ).
fof(f2074,plain,
! [X0,X1,X2,X3] :
( class_Groups_Oab__group__add(X3)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X0)),X1) ) ) ),
inference(rectify,[],[f894]) ).
fof(f894,axiom,
! [X13,X7,X8,X5] :
( class_Groups_Oab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5,X8),X7)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5,X13),X7)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5),X8,X13)),X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__diff__less) ).
fof(f24282,plain,
spl47_1098,
inference(avatar_split_clause,[],[f5270,f24280]) ).
fof(f24280,plain,
( spl47_1098
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X0)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ class_Groups_Oab__group__add(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1098])]) ).
fof(f5270,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X0)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ class_Groups_Oab__group__add(X3) ),
inference(cnf_transformation,[],[f3196]) ).
fof(f3196,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X0)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ class_Groups_Oab__group__add(X3) ),
inference(flattening,[],[f3195]) ).
fof(f3195,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X0)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
| ~ class_Groups_Oab__group__add(X3) ),
inference(ennf_transformation,[],[f2073]) ).
fof(f2073,plain,
! [X0,X1,X2,X3] :
( class_Groups_Oab__group__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X2),X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,X0),X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X0)),X1) ) ) ),
inference(rectify,[],[f893]) ).
fof(f893,axiom,
! [X13,X7,X8,X5] :
( class_Groups_Oab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X5,X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X5,X13),X7)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X5,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5),X8,X13)),X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__diff__le) ).
fof(f24278,plain,
spl47_1097,
inference(avatar_split_clause,[],[f5269,f24276]) ).
fof(f24276,plain,
( spl47_1097
<=> ! [X0,X3,X2,X1] :
( hAPP(c_Polynomial_Ocoeff(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Ominus__class_Ominus(X3,hAPP(c_Polynomial_Ocoeff(X3,X2),X0),hAPP(c_Polynomial_Ocoeff(X3,X1),X0))
| ~ class_Groups_Oab__group__add(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1097])]) ).
fof(f5269,plain,
! [X2,X3,X0,X1] :
( hAPP(c_Polynomial_Ocoeff(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Ominus__class_Ominus(X3,hAPP(c_Polynomial_Ocoeff(X3,X2),X0),hAPP(c_Polynomial_Ocoeff(X3,X1),X0))
| ~ class_Groups_Oab__group__add(X3) ),
inference(cnf_transformation,[],[f3194]) ).
fof(f3194,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Ocoeff(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Ominus__class_Ominus(X3,hAPP(c_Polynomial_Ocoeff(X3,X2),X0),hAPP(c_Polynomial_Ocoeff(X3,X1),X0))
| ~ class_Groups_Oab__group__add(X3) ),
inference(ennf_transformation,[],[f2072]) ).
fof(f2072,plain,
! [X0,X1,X2,X3] :
( class_Groups_Oab__group__add(X3)
=> hAPP(c_Polynomial_Ocoeff(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Ominus__class_Ominus(X3,hAPP(c_Polynomial_Ocoeff(X3,X2),X0),hAPP(c_Polynomial_Ocoeff(X3,X1),X0)) ),
inference(rectify,[],[f778]) ).
fof(f778,axiom,
! [X7,X13,X8,X5] :
( class_Groups_Oab__group__add(X5)
=> hAPP(c_Polynomial_Ocoeff(X5,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5),X8,X13)),X7) = c_Groups_Ominus__class_Ominus(X5,hAPP(c_Polynomial_Ocoeff(X5,X8),X7),hAPP(c_Polynomial_Ocoeff(X5,X13),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__diff) ).
fof(f24274,plain,
spl47_1096,
inference(avatar_split_clause,[],[f5249,f24272]) ).
fof(f24272,plain,
( spl47_1096
<=> ! [X0,X3,X2,X1] :
( hAPP(c_Polynomial_Opoly(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Ominus__class_Ominus(X3,hAPP(c_Polynomial_Opoly(X3,X2),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0))
| ~ class_Rings_Ocomm__ring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1096])]) ).
fof(f5249,plain,
! [X2,X3,X0,X1] :
( hAPP(c_Polynomial_Opoly(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Ominus__class_Ominus(X3,hAPP(c_Polynomial_Opoly(X3,X2),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0))
| ~ class_Rings_Ocomm__ring(X3) ),
inference(cnf_transformation,[],[f3167]) ).
fof(f3167,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Opoly(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Ominus__class_Ominus(X3,hAPP(c_Polynomial_Opoly(X3,X2),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0))
| ~ class_Rings_Ocomm__ring(X3) ),
inference(ennf_transformation,[],[f2056]) ).
fof(f2056,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__ring(X3)
=> hAPP(c_Polynomial_Opoly(X3,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X2,X1)),X0) = c_Groups_Ominus__class_Ominus(X3,hAPP(c_Polynomial_Opoly(X3,X2),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
inference(rectify,[],[f775]) ).
fof(f775,axiom,
! [X6,X13,X8,X5] :
( class_Rings_Ocomm__ring(X5)
=> hAPP(c_Polynomial_Opoly(X5,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5),X8,X13)),X6) = c_Groups_Ominus__class_Ominus(X5,hAPP(c_Polynomial_Opoly(X5,X8),X6),hAPP(c_Polynomial_Opoly(X5,X13),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__diff) ).
fof(f24248,plain,
spl47_1095,
inference(avatar_split_clause,[],[f5216,f24246]) ).
fof(f24246,plain,
( spl47_1095
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X0))
| ~ sP22(X3,X2,X1,X0)
| ~ sP23(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1095])]) ).
fof(f5216,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X0))
| ~ sP22(X3,X2,X1,X0)
| ~ sP23(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3853]) ).
fof(f3853,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X0))
| ~ sP22(X3,X2,X1,X0) )
& ( sP22(X3,X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X0)) ) )
| ~ sP23(X0,X1,X2,X3) ),
inference(rectify,[],[f3852]) ).
fof(f3852,plain,
! [X1,X3,X0,X2] :
( ( ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ sP22(X2,X0,X3,X1) )
& ( sP22(X2,X0,X3,X1)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ) )
| ~ sP23(X1,X3,X0,X2) ),
inference(nnf_transformation,[],[f3512]) ).
fof(f3512,plain,
! [X1,X3,X0,X2] :
( ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
<=> sP22(X2,X0,X3,X1) )
| ~ sP23(X1,X3,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP23])]) ).
fof(f24244,plain,
spl47_1094,
inference(avatar_split_clause,[],[f5215,f24242]) ).
fof(f24242,plain,
( spl47_1094
<=> ! [X0,X3,X2,X1] :
( sP22(X3,X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X0))
| ~ sP23(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1094])]) ).
fof(f5215,plain,
! [X2,X3,X0,X1] :
( sP22(X3,X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X0))
| ~ sP23(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3853]) ).
fof(f24240,plain,
spl47_1093,
inference(avatar_split_clause,[],[f5207,f24238]) ).
fof(f24238,plain,
( spl47_1093
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2))
| ~ sP20(X3,X2,X1,X0)
| ~ sP21(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1093])]) ).
fof(f5207,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2))
| ~ sP20(X3,X2,X1,X0)
| ~ sP21(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3848]) ).
fof(f3848,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2))
| ~ sP20(X3,X2,X1,X0) )
& ( sP20(X3,X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2)) ) )
| ~ sP21(X0,X1,X2,X3) ),
inference(rectify,[],[f3847]) ).
fof(f3847,plain,
! [X2,X3,X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ sP20(X1,X0,X3,X2) )
& ( sP20(X1,X0,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ) )
| ~ sP21(X2,X3,X0,X1) ),
inference(nnf_transformation,[],[f3509]) ).
fof(f3509,plain,
! [X2,X3,X0,X1] :
( ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> sP20(X1,X0,X3,X2) )
| ~ sP21(X2,X3,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP21])]) ).
fof(f24236,plain,
spl47_1092,
inference(avatar_split_clause,[],[f5206,f24234]) ).
fof(f24234,plain,
( spl47_1092
<=> ! [X0,X3,X2,X1] :
( sP20(X3,X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2))
| ~ sP21(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1092])]) ).
fof(f5206,plain,
! [X2,X3,X0,X1] :
( sP20(X3,X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2))
| ~ sP21(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3848]) ).
fof(f24232,plain,
spl47_1091,
inference(avatar_split_clause,[],[f5121,f24230]) ).
fof(f24230,plain,
( spl47_1091
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1091])]) ).
fof(f5121,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f3820]) ).
fof(f24228,plain,
spl47_1090,
inference(avatar_split_clause,[],[f5030,f24226]) ).
fof(f24226,plain,
( spl47_1090
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1090])]) ).
fof(f5030,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0))) ),
inference(cnf_transformation,[],[f3016]) ).
fof(f3016,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0))) ),
inference(flattening,[],[f3015]) ).
fof(f3015,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0))) ),
inference(ennf_transformation,[],[f1922]) ).
fof(f1922,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X0))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1)) ) ),
inference(rectify,[],[f889]) ).
fof(f889,axiom,
! [X7,X21,X20] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X20),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X21,X7)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X20),X7))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X20),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__zdiffD) ).
fof(f24224,plain,
spl47_1089,
inference(avatar_split_clause,[],[f5022,f24222]) ).
fof(f24222,plain,
( spl47_1089
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1089])]) ).
fof(f5022,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(cnf_transformation,[],[f3008]) ).
fof(f3008,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(flattening,[],[f3007]) ).
fof(f3007,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(ennf_transformation,[],[f1916]) ).
fof(f1916,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
inference(rectify,[],[f772]) ).
fof(f772,axiom,
! [X7,X21,X20] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X20),X21))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X20),X7))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X20),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X7))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diff__nat) ).
fof(f24220,plain,
spl47_1088,
inference(avatar_split_clause,[],[f4695,f24218]) ).
fof(f24218,plain,
( spl47_1088
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)))
| c_Groups_Ozero__class_Ozero(X2) = X0
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1088])]) ).
fof(f4695,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)))
| c_Groups_Ozero__class_Ozero(X2) = X0
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f3689]) ).
fof(f24216,plain,
spl47_1087,
inference(avatar_split_clause,[],[f4694,f24214]) ).
fof(f24214,plain,
( spl47_1087
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)))
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1087])]) ).
fof(f4694,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)))
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f3689]) ).
fof(f24212,plain,
spl47_1086,
inference(avatar_split_clause,[],[f4691,f24210]) ).
fof(f24210,plain,
( spl47_1086
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1086])]) ).
fof(f4691,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f3687]) ).
fof(f24168,plain,
spl47_1085,
inference(avatar_split_clause,[],[f4690,f24166]) ).
fof(f24166,plain,
( spl47_1085
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1085])]) ).
fof(f4690,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f3687]) ).
fof(f24164,plain,
spl47_1084,
inference(avatar_split_clause,[],[f4641,f24162]) ).
fof(f24162,plain,
( spl47_1084
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1084])]) ).
fof(f4641,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
inference(cnf_transformation,[],[f1630]) ).
fof(f1630,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
inference(rectify,[],[f658]) ).
fof(f658,axiom,
! [X20,X7,X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X7)),X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
fof(f24160,plain,
spl47_1083,
inference(avatar_split_clause,[],[f4640,f24158]) ).
fof(f24158,plain,
( spl47_1083
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1083])]) ).
fof(f4640,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
inference(cnf_transformation,[],[f1629]) ).
fof(f1629,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
inference(rectify,[],[f841]) ).
fof(f841,axiom,
! [X20,X7,X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X7)),X20) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
fof(f24156,plain,
spl47_1082,
inference(avatar_split_clause,[],[f4639,f24154]) ).
fof(f24154,plain,
( spl47_1082
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1082])]) ).
fof(f4639,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)),
inference(cnf_transformation,[],[f1628]) ).
fof(f1628,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)),
inference(rectify,[],[f642]) ).
fof(f642,axiom,
! [X48,X61,X62] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X62,X61)),X48) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X62),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X48)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
fof(f24152,plain,
spl47_1081,
inference(avatar_split_clause,[],[f4638,f24150]) ).
fof(f24150,plain,
( spl47_1081
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X1)),X0) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1081])]) ).
fof(f4638,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X1)),X0) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)),
inference(cnf_transformation,[],[f1627]) ).
fof(f1627,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X1)),X0) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)),
inference(rectify,[],[f897]) ).
fof(f897,axiom,
! [X48,X61,X62] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X62,X61)),X48) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X62),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X48)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).
fof(f24148,plain,
spl47_1080,
inference(avatar_split_clause,[],[f4637,f24146]) ).
fof(f24146,plain,
( spl47_1080
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1080])]) ).
fof(f4637,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)),
inference(cnf_transformation,[],[f1626]) ).
fof(f1626,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)),
inference(rectify,[],[f659]) ).
fof(f659,axiom,
! [X7,X21,X20] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X7)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
fof(f24144,plain,
spl47_1079,
inference(avatar_split_clause,[],[f4636,f24142]) ).
fof(f24142,plain,
( spl47_1079
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1079])]) ).
fof(f4636,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)),
inference(cnf_transformation,[],[f1625]) ).
fof(f1625,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)),
inference(rectify,[],[f840]) ).
fof(f840,axiom,
! [X7,X21,X20] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X7)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).
fof(f24140,plain,
spl47_1078,
inference(avatar_split_clause,[],[f4635,f24138]) ).
fof(f24138,plain,
( spl47_1078
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1078])]) ).
fof(f4635,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)),
inference(cnf_transformation,[],[f1624]) ).
fof(f1624,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)),
inference(rectify,[],[f643]) ).
fof(f643,axiom,
! [X61,X62,X48] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X62,X61)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X62),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X61)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
fof(f24136,plain,
spl47_1077,
inference(avatar_split_clause,[],[f4634,f24134]) ).
fof(f24134,plain,
( spl47_1077
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1077])]) ).
fof(f4634,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)),
inference(cnf_transformation,[],[f1623]) ).
fof(f1623,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)),
inference(rectify,[],[f896]) ).
fof(f896,axiom,
! [X61,X62,X48] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X62,X61)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X62),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X61)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).
fof(f24132,plain,
spl47_1076,
inference(avatar_split_clause,[],[f4262,f24130]) ).
fof(f24130,plain,
( spl47_1076
<=> ! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1076])]) ).
fof(f4262,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
inference(cnf_transformation,[],[f2395]) ).
fof(f2395,plain,
! [X0,X1] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ),
inference(ennf_transformation,[],[f1375]) ).
fof(f1375,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ) ),
inference(rectify,[],[f877]) ).
fof(f877,axiom,
! [X7,X21] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X21
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X7) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X7)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X21
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__if) ).
fof(f23805,plain,
( ~ spl47_1075
| ~ spl47_286
| spl47_219
| spl47_153 ),
inference(avatar_split_clause,[],[f4070,f6789,f7059,f7367,f23802]) ).
fof(f23802,plain,
( spl47_1075
<=> sP2 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1075])]) ).
fof(f6789,plain,
( spl47_153
<=> v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_153])]) ).
fof(f4070,plain,
( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ~ sP1
| ~ sP2 ),
inference(cnf_transformation,[],[f3525]) ).
fof(f3525,plain,
( ( ( sP1
| ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
| v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) )
& ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ~ sP1 ) )
| ~ sP2 ),
inference(flattening,[],[f3524]) ).
fof(f3524,plain,
( ( ( sP1
| ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
| v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) )
& ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ~ sP1 ) )
| ~ sP2 ),
inference(nnf_transformation,[],[f3478]) ).
fof(f3478,plain,
( ( sP1
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) )
| ~ sP2 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f23800,plain,
( spl47_287
| ~ spl47_285
| ~ spl47_786 ),
inference(avatar_split_clause,[],[f16410,f16396,f7363,f7372]) ).
fof(f7372,plain,
( spl47_287
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_287])]) ).
fof(f7363,plain,
( spl47_285
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_285])]) ).
fof(f16410,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK28)
| ~ spl47_285
| ~ spl47_786 ),
inference(trivial_inequality_removal,[],[f16407]) ).
fof(f16407,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK28)
| ~ spl47_285
| ~ spl47_786 ),
inference(superposition,[],[f16397,f7365]) ).
fof(f7365,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK28)
| ~ spl47_285 ),
inference(avatar_component_clause,[],[f7363]) ).
fof(f23694,plain,
( ~ spl47_1074
| ~ spl47_289
| spl47_219
| spl47_153 ),
inference(avatar_split_clause,[],[f4078,f6789,f7059,f7381,f23691]) ).
fof(f23691,plain,
( spl47_1074
<=> sP4 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1074])]) ).
fof(f4078,plain,
( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ~ sP3
| ~ sP4 ),
inference(cnf_transformation,[],[f3531]) ).
fof(f3531,plain,
( ( ( sP3
| ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
| v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) )
& ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ~ sP3 ) )
| ~ sP4 ),
inference(flattening,[],[f3530]) ).
fof(f3530,plain,
( ( ( sP3
| ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
| v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) )
& ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ~ sP3 ) )
| ~ sP4 ),
inference(nnf_transformation,[],[f3481]) ).
fof(f3481,plain,
( ( sP3
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) )
| ~ sP4 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f23689,plain,
( spl47_290
| ~ spl47_288
| ~ spl47_786 ),
inference(avatar_split_clause,[],[f16409,f16396,f7377,f7388]) ).
fof(f23378,plain,
( spl47_1073
| ~ spl47_414
| ~ spl47_498 ),
inference(avatar_split_clause,[],[f9696,f9165,f8250,f23376]) ).
fof(f23376,plain,
( spl47_1073
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1073])]) ).
fof(f8250,plain,
( spl47_414
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_414])]) ).
fof(f9165,plain,
( spl47_498
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_498])]) ).
fof(f9696,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| ~ spl47_414
| ~ spl47_498 ),
inference(resolution,[],[f9166,f8251]) ).
fof(f8251,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
| ~ spl47_414 ),
inference(avatar_component_clause,[],[f8250]) ).
fof(f9166,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| ~ spl47_498 ),
inference(avatar_component_clause,[],[f9165]) ).
fof(f23082,plain,
spl47_1072,
inference(avatar_split_clause,[],[f6024,f23080]) ).
fof(f23080,plain,
( spl47_1072
<=> ! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1072])]) ).
fof(f6024,plain,
! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(forward_demodulation,[],[f4983,f4623]) ).
fof(f4623,plain,
! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
inference(cnf_transformation,[],[f1612]) ).
fof(f1612,plain,
! [X0,X1,X2] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
inference(rectify,[],[f764]) ).
fof(f764,axiom,
! [X20,X33,X32] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,X33),X20) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__left) ).
fof(f4983,plain,
! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2963]) ).
fof(f2963,plain,
! [X0,X1,X2] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(flattening,[],[f2962]) ).
fof(f2962,plain,
! [X0,X1,X2] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1887]) ).
fof(f1887,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) ) ),
inference(rectify,[],[f784]) ).
fof(f784,axiom,
! [X7,X21,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X21)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X7)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X7) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X20),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
fof(f23078,plain,
spl47_1071,
inference(avatar_split_clause,[],[f6007,f23076]) ).
fof(f23076,plain,
( spl47_1071
<=> ! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1071])]) ).
fof(f6007,plain,
! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(forward_demodulation,[],[f5618,f4623]) ).
fof(f5618,plain,
! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(definition_unfolding,[],[f4630,f4118,f4118]) ).
fof(f4630,plain,
! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X2),X1),c_Nat_OSuc(X0)),
inference(cnf_transformation,[],[f1619]) ).
fof(f1619,plain,
! [X0,X1,X2] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X2),X1),c_Nat_OSuc(X0)),
inference(rectify,[],[f770]) ).
fof(f770,axiom,
! [X20,X7,X21] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X21),X7),c_Nat_OSuc(X20)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X7),X20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).
fof(f23074,plain,
spl47_1070,
inference(avatar_split_clause,[],[f5739,f23072]) ).
fof(f23072,plain,
( spl47_1070
<=> ! [X2] :
( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),c_Groups_Ozero__class_Ozero(X2)))
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1070])]) ).
fof(f5739,plain,
! [X2] :
( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),c_Groups_Ozero__class_Ozero(X2)))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(equality_resolution,[],[f5738]) ).
fof(f5738,plain,
! [X2,X1] :
( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),c_Groups_Ozero__class_Ozero(X2)))
| c_Groups_Ozero__class_Ozero(X2) != X1
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(equality_resolution,[],[f4689]) ).
fof(f4689,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0))
| c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f3685]) ).
fof(f3685,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0))
| c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(X2) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 )
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)) ) )
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(flattening,[],[f3684]) ).
fof(f3684,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0))
| c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(X2) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 )
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)) ) )
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(nnf_transformation,[],[f2655]) ).
fof(f2655,plain,
! [X0,X1,X2] :
( ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0))
<=> ( c_Groups_Ozero__class_Ozero(X2) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 ) )
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(ennf_transformation,[],[f1671]) ).
fof(f1671,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0))
<=> ( c_Groups_Ozero__class_Ozero(X2) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 ) ) ),
inference(rectify,[],[f581]) ).
fof(f581,axiom,
! [X25,X15,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),X25))
<=> ( c_Groups_Ozero__class_Ozero(X5) = X25
& c_Groups_Ozero__class_Ozero(X5) = X15 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
fof(f23070,plain,
spl47_1069,
inference(avatar_split_clause,[],[f5475,f23068]) ).
fof(f23068,plain,
( spl47_1069
<=> ! [X3,X4,X0,X5,X2,X1] :
( c_Polynomial_Opdivmod__rel(X5,c_Polynomial_Osmult(X5,X0,X4),X3,c_Polynomial_Osmult(X5,X0,X2),c_Polynomial_Osmult(X5,X0,X1))
| ~ c_Polynomial_Opdivmod__rel(X5,X4,X3,X2,X1)
| ~ class_Fields_Ofield(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1069])]) ).
fof(f5475,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Polynomial_Opdivmod__rel(X5,c_Polynomial_Osmult(X5,X0,X4),X3,c_Polynomial_Osmult(X5,X0,X2),c_Polynomial_Osmult(X5,X0,X1))
| ~ c_Polynomial_Opdivmod__rel(X5,X4,X3,X2,X1)
| ~ class_Fields_Ofield(X5) ),
inference(cnf_transformation,[],[f3445]) ).
fof(f3445,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Polynomial_Opdivmod__rel(X5,c_Polynomial_Osmult(X5,X0,X4),X3,c_Polynomial_Osmult(X5,X0,X2),c_Polynomial_Osmult(X5,X0,X1))
| ~ c_Polynomial_Opdivmod__rel(X5,X4,X3,X2,X1)
| ~ class_Fields_Ofield(X5) ),
inference(flattening,[],[f3444]) ).
fof(f3444,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Polynomial_Opdivmod__rel(X5,c_Polynomial_Osmult(X5,X0,X4),X3,c_Polynomial_Osmult(X5,X0,X2),c_Polynomial_Osmult(X5,X0,X1))
| ~ c_Polynomial_Opdivmod__rel(X5,X4,X3,X2,X1)
| ~ class_Fields_Ofield(X5) ),
inference(ennf_transformation,[],[f2241]) ).
fof(f2241,plain,
! [X0,X1,X2,X3,X4,X5] :
( class_Fields_Ofield(X5)
=> ( c_Polynomial_Opdivmod__rel(X5,X4,X3,X2,X1)
=> c_Polynomial_Opdivmod__rel(X5,c_Polynomial_Osmult(X5,X0,X4),X3,c_Polynomial_Osmult(X5,X0,X2),c_Polynomial_Osmult(X5,X0,X1)) ) ),
inference(rectify,[],[f736]) ).
fof(f736,axiom,
! [X4,X34,X13,X10,X6,X5] :
( class_Fields_Ofield(X5)
=> ( c_Polynomial_Opdivmod__rel(X5,X6,X10,X13,X34)
=> c_Polynomial_Opdivmod__rel(X5,c_Polynomial_Osmult(X5,X4,X6),X10,c_Polynomial_Osmult(X5,X4,X13),c_Polynomial_Osmult(X5,X4,X34)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__smult__left) ).
fof(f23066,plain,
spl47_1068,
inference(avatar_split_clause,[],[f5446,f23064]) ).
fof(f23064,plain,
( spl47_1068
<=> ! [X4,X0,X3,X2,X1] :
( c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,X3,X2),c_Groups_Oplus__class_Oplus(X4,X1,X0)) = c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
| ~ class_Rings_Ocomm__semiring__1(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1068])]) ).
fof(f5446,plain,
! [X2,X3,X0,X1,X4] :
( c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,X3,X2),c_Groups_Oplus__class_Oplus(X4,X1,X0)) = c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
| ~ class_Rings_Ocomm__semiring__1(X4) ),
inference(cnf_transformation,[],[f3415]) ).
fof(f3415,plain,
! [X0,X1,X2,X3,X4] :
( c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,X3,X2),c_Groups_Oplus__class_Oplus(X4,X1,X0)) = c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
| ~ class_Rings_Ocomm__semiring__1(X4) ),
inference(ennf_transformation,[],[f2219]) ).
fof(f2219,plain,
! [X0,X1,X2,X3,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,X3,X2),c_Groups_Oplus__class_Oplus(X4,X1,X0)) = c_Groups_Oplus__class_Oplus(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ),
inference(rectify,[],[f442]) ).
fof(f442,axiom,
! [X46,X16,X17,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Oplus__class_Oplus(X5,X4,X17),c_Groups_Oplus__class_Oplus(X5,X16,X46)) = c_Groups_Oplus__class_Oplus(X5,c_Groups_Oplus__class_Oplus(X5,X4,X16),c_Groups_Oplus__class_Oplus(X5,X17,X46)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(f23062,plain,
spl47_1067,
inference(avatar_split_clause,[],[f5358,f23060]) ).
fof(f5358,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3309]) ).
fof(f3309,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(flattening,[],[f3308]) ).
fof(f3308,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2154]) ).
fof(f2154,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0)) ) ) ),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
! [X16,X17,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X4),X17))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X17),X16))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X4),X16)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__trans) ).
fof(f23058,plain,
( spl47_1066
| ~ spl47_495
| ~ spl47_497 ),
inference(avatar_split_clause,[],[f9678,f9161,f9153,f23056]) ).
fof(f23056,plain,
( spl47_1066
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1066])]) ).
fof(f9153,plain,
( spl47_495
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_495])]) ).
fof(f9161,plain,
( spl47_497
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_497])]) ).
fof(f9678,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| ~ spl47_495
| ~ spl47_497 ),
inference(resolution,[],[f9162,f9154]) ).
fof(f9154,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| ~ spl47_495 ),
inference(avatar_component_clause,[],[f9153]) ).
fof(f9162,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| ~ spl47_497 ),
inference(avatar_component_clause,[],[f9161]) ).
fof(f23054,plain,
spl47_1065,
inference(avatar_split_clause,[],[f5354,f23052]) ).
fof(f23052,plain,
( spl47_1065
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1065])]) ).
fof(f5354,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3301]) ).
fof(f3301,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(flattening,[],[f3300]) ).
fof(f3300,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2150]) ).
fof(f2150,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))) ) ),
inference(rectify,[],[f113]) ).
fof(f113,axiom,
! [X4,X7,X21,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X7)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X21)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__power__dvd) ).
fof(f23050,plain,
spl47_1064,
inference(avatar_split_clause,[],[f5327,f23048]) ).
fof(f23048,plain,
( spl47_1064
<=> ! [X0,X3,X2,X1] :
( c_Polynomial_Osmult(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X3,X1,X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1064])]) ).
fof(f5327,plain,
! [X2,X3,X0,X1] :
( c_Polynomial_Osmult(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X3,X1,X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f3271]) ).
fof(f3271,plain,
! [X0,X1,X2,X3] :
( c_Polynomial_Osmult(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X3,X1,X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f2123]) ).
fof(f2123,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Polynomial_Osmult(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X3,X1,X0)) ),
inference(rectify,[],[f545]) ).
fof(f545,axiom,
! [X13,X4,X8,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Polynomial_Osmult(X5,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X8),X13)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X8),c_Polynomial_Osmult(X5,X4,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__smult__right) ).
fof(f23046,plain,
spl47_1063,
inference(avatar_split_clause,[],[f5326,f23044]) ).
fof(f23044,plain,
( spl47_1063
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0) = c_Polynomial_Osmult(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1063])]) ).
fof(f5326,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0) = c_Polynomial_Osmult(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f3270]) ).
fof(f3270,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0) = c_Polynomial_Osmult(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f2122]) ).
fof(f2122,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0) = c_Polynomial_Osmult(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X1),X0)) ),
inference(rectify,[],[f544]) ).
fof(f544,axiom,
! [X13,X8,X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),c_Polynomial_Osmult(X5,X4,X8)),X13) = c_Polynomial_Osmult(X5,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X8),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__smult__left) ).
fof(f23042,plain,
spl47_1062,
inference(avatar_split_clause,[],[f5280,f23040]) ).
fof(f23040,plain,
( spl47_1062
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ~ class_Rings_Olinordered__semidom(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1062])]) ).
fof(f5280,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(cnf_transformation,[],[f3865]) ).
fof(f3865,plain,
! [X0,X1,X2,X3] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)
| X0 != X1 )
& ( X0 = X1
| hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1) ) )
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(nnf_transformation,[],[f3216]) ).
fof(f3216,plain,
! [X0,X1,X2,X3] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)
<=> X0 = X1 )
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(flattening,[],[f3215]) ).
fof(f3215,plain,
! [X0,X1,X2,X3] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)
<=> X0 = X1 )
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(ennf_transformation,[],[f2083]) ).
fof(f2083,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X1)
<=> X0 = X1 ) ) ),
inference(rectify,[],[f143]) ).
fof(f143,axiom,
! [X11,X14,X12,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X12)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),X11) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),X14)
<=> X11 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__exp) ).
fof(f23038,plain,
spl47_1061,
inference(avatar_split_clause,[],[f5099,f23036]) ).
fof(f23036,plain,
( spl47_1061
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1061])]) ).
fof(f5099,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
inference(cnf_transformation,[],[f3808]) ).
fof(f3808,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
inference(flattening,[],[f3807]) ).
fof(f3807,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
inference(nnf_transformation,[],[f3053]) ).
fof(f3053,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
inference(ennf_transformation,[],[f1951]) ).
fof(f1951,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ) ),
inference(rectify,[],[f701]) ).
fof(f701,axiom,
! [X11,X44,X14] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X44),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X44))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X44)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
fof(f23034,plain,
spl47_1060,
inference(avatar_split_clause,[],[f5014,f23032]) ).
fof(f23032,plain,
( spl47_1060
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1060])]) ).
fof(f5014,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(cnf_transformation,[],[f3768]) ).
fof(f3768,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(nnf_transformation,[],[f3000]) ).
fof(f3000,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(ennf_transformation,[],[f1911]) ).
fof(f1911,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(rectify,[],[f723]) ).
fof(f723,axiom,
! [X11,X14,X44] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X44)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X11))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
fof(f23030,plain,
spl47_1059,
inference(avatar_split_clause,[],[f5011,f23028]) ).
fof(f23028,plain,
( spl47_1059
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1059])]) ).
fof(f5011,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(cnf_transformation,[],[f2998]) ).
fof(f2998,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(flattening,[],[f2997]) ).
fof(f2997,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(ennf_transformation,[],[f1909]) ).
fof(f1909,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X0))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(rectify,[],[f270]) ).
fof(f270,axiom,
! [X7,X21,X32] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X32)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X32),X21),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X32),X7))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).
fof(f23026,plain,
spl47_1058,
inference(avatar_split_clause,[],[f5006,f23024]) ).
fof(f23024,plain,
( spl47_1058
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1058])]) ).
fof(f5006,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2990]) ).
fof(f2990,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(flattening,[],[f2989]) ).
fof(f2989,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1905]) ).
fof(f1905,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ) ),
inference(rectify,[],[f679]) ).
fof(f679,axiom,
! [X20,X33,X32] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32,X33)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
fof(f23022,plain,
spl47_1057,
inference(avatar_split_clause,[],[f5005,f23020]) ).
fof(f23020,plain,
( spl47_1057
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1057])]) ).
fof(f5005,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2988]) ).
fof(f2988,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(flattening,[],[f2987]) ).
fof(f2987,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1904]) ).
fof(f1904,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
inference(rectify,[],[f678]) ).
fof(f678,axiom,
! [X20,X33,X32] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32,X33)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X32),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X33)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
fof(f23018,plain,
spl47_1056,
inference(avatar_split_clause,[],[f4995,f23016]) ).
fof(f23016,plain,
( spl47_1056
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1056])]) ).
fof(f4995,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
inference(cnf_transformation,[],[f2974]) ).
fof(f2974,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
inference(flattening,[],[f2973]) ).
fof(f2973,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
inference(ennf_transformation,[],[f1894]) ).
fof(f1894,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1)) ) ),
inference(rectify,[],[f686]) ).
fof(f686,axiom,
! [X20,X33,X32] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X32,X33)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X32),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X33)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
fof(f23014,plain,
( spl47_1055
| ~ spl47_494
| ~ spl47_496 ),
inference(avatar_split_clause,[],[f9655,f9157,f9149,f23012]) ).
fof(f23012,plain,
( spl47_1055
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1055])]) ).
fof(f9149,plain,
( spl47_494
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_494])]) ).
fof(f9157,plain,
( spl47_496
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_496])]) ).
fof(f9655,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| ~ spl47_494
| ~ spl47_496 ),
inference(resolution,[],[f9158,f9150]) ).
fof(f9150,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| ~ spl47_494 ),
inference(avatar_component_clause,[],[f9149]) ).
fof(f9158,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| ~ spl47_496 ),
inference(avatar_component_clause,[],[f9157]) ).
fof(f23010,plain,
spl47_1054,
inference(avatar_split_clause,[],[f4836,f23008]) ).
fof(f23008,plain,
( spl47_1054
<=> ! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| X0 = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)
| ~ class_Rings_Oidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1054])]) ).
fof(f4836,plain,
! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| X0 = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f3731]) ).
fof(f3731,plain,
! [X0,X1,X2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)
| ( c_Groups_Ouminus__class_Ouminus(X2,X0) != X1
& X0 != X1 ) )
& ( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| X0 = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0) ) )
| ~ class_Rings_Oidom(X2) ),
inference(flattening,[],[f3730]) ).
fof(f3730,plain,
! [X0,X1,X2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)
| ( c_Groups_Ouminus__class_Ouminus(X2,X0) != X1
& X0 != X1 ) )
& ( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| X0 = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0) ) )
| ~ class_Rings_Oidom(X2) ),
inference(nnf_transformation,[],[f2801]) ).
fof(f2801,plain,
! [X0,X1,X2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)
<=> ( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| X0 = X1 ) )
| ~ class_Rings_Oidom(X2) ),
inference(ennf_transformation,[],[f1770]) ).
fof(f1770,plain,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)
<=> ( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| X0 = X1 ) ) ),
inference(rectify,[],[f502]) ).
fof(f502,axiom,
! [X29,X12,X5] :
( class_Rings_Oidom(X5)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X12) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X29),X29)
<=> ( c_Groups_Ouminus__class_Ouminus(X5,X29) = X12
| X12 = X29 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__iff) ).
fof(f23006,plain,
spl47_1053,
inference(avatar_split_clause,[],[f4814,f23004]) ).
fof(f4814,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f2789]) ).
fof(f2789,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
| ~ class_Rings_Oidom(X2) ),
inference(flattening,[],[f2788]) ).
fof(f2788,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
| ~ class_Rings_Oidom(X2) ),
inference(ennf_transformation,[],[f1759]) ).
fof(f1759,plain,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0)) ) ) ),
inference(rectify,[],[f76]) ).
fof(f76,axiom,
! [X13,X8,X5] :
( class_Rings_Oidom(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),X8),X13))
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) != X13
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X5,X8),c_Polynomial_Odegree(X5,X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__degree__le) ).
fof(f23002,plain,
spl47_1052,
inference(avatar_split_clause,[],[f4760,f23000]) ).
fof(f23000,plain,
( spl47_1052
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X0
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Groups_Oordered__comm__monoid__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1052])]) ).
fof(f4760,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X0
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(cnf_transformation,[],[f3709]) ).
fof(f3709,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(X2) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 )
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0) ) )
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(flattening,[],[f3708]) ).
fof(f3708,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(X2) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 )
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0) ) )
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(nnf_transformation,[],[f2718]) ).
fof(f2718,plain,
! [X0,X1,X2] :
( ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0)
<=> ( c_Groups_Ozero__class_Ozero(X2) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 ) )
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(flattening,[],[f2717]) ).
fof(f2717,plain,
! [X0,X1,X2] :
( ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0)
<=> ( c_Groups_Ozero__class_Ozero(X2) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 ) )
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(ennf_transformation,[],[f1717]) ).
fof(f1717,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__comm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
=> ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0)
<=> ( c_Groups_Ozero__class_Ozero(X2) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 ) ) ) ) ),
inference(rectify,[],[f376]) ).
fof(f376,axiom,
! [X25,X15,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X15)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X25)
=> ( c_Groups_Ozero__class_Ozero(X5) = c_Groups_Oplus__class_Oplus(X5,X15,X25)
<=> ( c_Groups_Ozero__class_Ozero(X5) = X25
& c_Groups_Ozero__class_Ozero(X5) = X15 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
fof(f22998,plain,
spl47_1051,
inference(avatar_split_clause,[],[f4759,f22996]) ).
fof(f22996,plain,
( spl47_1051
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X1
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Groups_Oordered__comm__monoid__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1051])]) ).
fof(f4759,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X1
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(cnf_transformation,[],[f3709]) ).
fof(f22994,plain,
spl47_1050,
inference(avatar_split_clause,[],[f4688,f22992]) ).
fof(f22992,plain,
( spl47_1050
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X0
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0))
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1050])]) ).
fof(f4688,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X0
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f3685]) ).
fof(f22990,plain,
spl47_1049,
inference(avatar_split_clause,[],[f4687,f22988]) ).
fof(f22988,plain,
( spl47_1049
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X1
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0))
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1049])]) ).
fof(f4687,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X1
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f3685]) ).
fof(f22986,plain,
spl47_1048,
inference(avatar_split_clause,[],[f4646,f22984]) ).
fof(f22984,plain,
( spl47_1048
<=> ! [X2,X0,X1] :
( c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oone__class_Oone(X2),X1)),X0)
| ~ class_Fields_Ofield__inverse__zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1048])]) ).
fof(f4646,plain,
! [X2,X0,X1] :
( c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oone__class_Oone(X2),X1)),X0)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(cnf_transformation,[],[f2627]) ).
fof(f2627,plain,
! [X0,X1,X2] :
( c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oone__class_Oone(X2),X1)),X0)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(ennf_transformation,[],[f1650]) ).
fof(f1650,plain,
! [X0,X1,X2] :
( class_Fields_Ofield__inverse__zero(X2)
=> c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oone__class_Oone(X2),X1)),X0) ),
inference(rectify,[],[f913]) ).
fof(f913,axiom,
! [X7,X4,X5] :
( class_Fields_Ofield__inverse__zero(X5)
=> c_Rings_Oinverse__class_Odivide(X5,c_Groups_Oone__class_Oone(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Rings_Oinverse__class_Odivide(X5,c_Groups_Oone__class_Oone(X5),X4)),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__over) ).
fof(f22982,plain,
spl47_1047,
inference(avatar_split_clause,[],[f4633,f22980]) ).
fof(f22980,plain,
( spl47_1047
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1047])]) ).
fof(f4633,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
inference(cnf_transformation,[],[f1622]) ).
fof(f1622,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
inference(rectify,[],[f716]) ).
fof(f716,axiom,
! [X20,X7,X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X7)),X20) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
fof(f22978,plain,
spl47_1046,
inference(avatar_split_clause,[],[f4632,f22976]) ).
fof(f22976,plain,
( spl47_1046
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1046])]) ).
fof(f4632,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)),
inference(cnf_transformation,[],[f1621]) ).
fof(f1621,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)),
inference(rectify,[],[f714]) ).
fof(f714,axiom,
! [X64,X61,X62] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X62),X61)),X64) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X62),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X64)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__assoc) ).
fof(f22974,plain,
spl47_1045,
inference(avatar_split_clause,[],[f4631,f22972]) ).
fof(f22972,plain,
( spl47_1045
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1)),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1045])]) ).
fof(f4631,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1)),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
inference(cnf_transformation,[],[f1620]) ).
fof(f1620,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1)),X0) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
inference(rectify,[],[f671]) ).
fof(f671,axiom,
! [X26,X10,X6] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),X10)),X26) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10),X26)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zpower) ).
fof(f22970,plain,
( spl47_1044
| ~ spl47_152
| ~ spl47_478 ),
inference(avatar_split_clause,[],[f9436,f9073,f6785,f22968]) ).
fof(f22968,plain,
( spl47_1044
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1044])]) ).
fof(f6785,plain,
( spl47_152
<=> ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_152])]) ).
fof(f9073,plain,
( spl47_478
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_478])]) ).
fof(f9436,plain,
( ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
| ~ spl47_152
| ~ spl47_478 ),
inference(resolution,[],[f9074,f6786]) ).
fof(f6786,plain,
( ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1)
| ~ spl47_152 ),
inference(avatar_component_clause,[],[f6785]) ).
fof(f9074,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) )
| ~ spl47_478 ),
inference(avatar_component_clause,[],[f9073]) ).
fof(f22852,plain,
( spl47_1043
| ~ spl47_152
| ~ spl47_477 ),
inference(avatar_split_clause,[],[f9418,f9069,f6785,f22850]) ).
fof(f22850,plain,
( spl47_1043
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1043])]) ).
fof(f9069,plain,
( spl47_477
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_477])]) ).
fof(f9418,plain,
( ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
| ~ spl47_152
| ~ spl47_477 ),
inference(resolution,[],[f9070,f6786]) ).
fof(f9070,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
| ~ spl47_477 ),
inference(avatar_component_clause,[],[f9069]) ).
fof(f22653,plain,
( spl47_1042
| ~ spl47_149
| ~ spl47_473 ),
inference(avatar_split_clause,[],[f9374,f9053,f6773,f22651]) ).
fof(f22651,plain,
( spl47_1042
<=> ! [X0] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1042])]) ).
fof(f9053,plain,
( spl47_473
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_473])]) ).
fof(f9374,plain,
( ! [X0] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
| ~ spl47_149
| ~ spl47_473 ),
inference(resolution,[],[f9054,f6774]) ).
fof(f9054,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) )
| ~ spl47_473 ),
inference(avatar_component_clause,[],[f9053]) ).
fof(f22289,plain,
( spl47_1041
| ~ spl47_150
| ~ spl47_470 ),
inference(avatar_split_clause,[],[f9342,f9038,f6777,f22287]) ).
fof(f22287,plain,
( spl47_1041
<=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK36(X0,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1041])]) ).
fof(f9038,plain,
( spl47_470
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK36(X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_470])]) ).
fof(f9342,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK36(X0,X0)) = X0
| ~ spl47_150
| ~ spl47_470 ),
inference(resolution,[],[f9039,f6778]) ).
fof(f9039,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK36(X0,X1)) = X0 )
| ~ spl47_470 ),
inference(avatar_component_clause,[],[f9038]) ).
fof(f22158,plain,
spl47_1040,
inference(avatar_split_clause,[],[f5801,f22156]) ).
fof(f22156,plain,
( spl47_1040
<=> ! [X2,X0] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ozero__class_Ozero(X2)),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1040])]) ).
fof(f5801,plain,
! [X2,X0] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ozero__class_Ozero(X2)),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2) ),
inference(equality_resolution,[],[f5047]) ).
fof(f5047,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(X2) != X1
| ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2) ),
inference(cnf_transformation,[],[f3778]) ).
fof(f3778,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(X2) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& c_Groups_Ozero__class_Ozero(X2) = X1 )
| c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) ) )
| ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2) ),
inference(flattening,[],[f3777]) ).
fof(f3777,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(X2) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& c_Groups_Ozero__class_Ozero(X2) = X1 )
| c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) ) )
| ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2) ),
inference(nnf_transformation,[],[f3040]) ).
fof(f3040,plain,
! [X0,X1,X2] :
( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& c_Groups_Ozero__class_Ozero(X2) = X1 ) )
| ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2) ),
inference(flattening,[],[f3039]) ).
fof(f3039,plain,
! [X0,X1,X2] :
( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& c_Groups_Ozero__class_Ozero(X2) = X1 ) )
| ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2) ),
inference(ennf_transformation,[],[f1934]) ).
fof(f1934,plain,
! [X0,X1,X2] :
( ( class_Rings_Ozero__neq__one(X2)
& class_Rings_Ono__zero__divisors(X2)
& class_Rings_Omult__zero(X2)
& class_Power_Opower(X2) )
=> ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& c_Groups_Ozero__class_Ozero(X2) = X1 ) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X11,X12,X5] :
( ( class_Rings_Ozero__neq__one(X5)
& class_Rings_Ono__zero__divisors(X5)
& class_Rings_Omult__zero(X5)
& class_Power_Opower(X5) )
=> ( c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),X11)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X11
& c_Groups_Ozero__class_Ozero(X5) = X12 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).
fof(f22154,plain,
spl47_1039,
inference(avatar_split_clause,[],[f5444,f22152]) ).
fof(f22152,plain,
( spl47_1039
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(c_Polynomial_Opoly(X4,X3),X2) = X0
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),X3,c_Polynomial_Osmult(X4,X2,X1)) != c_Polynomial_OpCons(X4,X0,X1)
| ~ class_Rings_Ocomm__semiring__0(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1039])]) ).
fof(f5444,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(c_Polynomial_Opoly(X4,X3),X2) = X0
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),X3,c_Polynomial_Osmult(X4,X2,X1)) != c_Polynomial_OpCons(X4,X0,X1)
| ~ class_Rings_Ocomm__semiring__0(X4) ),
inference(cnf_transformation,[],[f3414]) ).
fof(f3414,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Polynomial_Osynthetic__div(X4,X3,X2) = X1
& hAPP(c_Polynomial_Opoly(X4,X3),X2) = X0 )
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),X3,c_Polynomial_Osmult(X4,X2,X1)) != c_Polynomial_OpCons(X4,X0,X1)
| ~ class_Rings_Ocomm__semiring__0(X4) ),
inference(flattening,[],[f3413]) ).
fof(f3413,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Polynomial_Osynthetic__div(X4,X3,X2) = X1
& hAPP(c_Polynomial_Opoly(X4,X3),X2) = X0 )
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),X3,c_Polynomial_Osmult(X4,X2,X1)) != c_Polynomial_OpCons(X4,X0,X1)
| ~ class_Rings_Ocomm__semiring__0(X4) ),
inference(ennf_transformation,[],[f2218]) ).
fof(f2218,plain,
! [X0,X1,X2,X3,X4] :
( class_Rings_Ocomm__semiring__0(X4)
=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),X3,c_Polynomial_Osmult(X4,X2,X1)) = c_Polynomial_OpCons(X4,X0,X1)
=> ( c_Polynomial_Osynthetic__div(X4,X3,X2) = X1
& hAPP(c_Polynomial_Opoly(X4,X3),X2) = X0 ) ) ),
inference(rectify,[],[f125]) ).
fof(f125,axiom,
! [X34,X13,X16,X8,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),X8,c_Polynomial_Osmult(X5,X16,X13)) = c_Polynomial_OpCons(X5,X34,X13)
=> ( c_Polynomial_Osynthetic__div(X5,X8,X16) = X13
& hAPP(c_Polynomial_Opoly(X5,X8),X16) = X34 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__unique) ).
fof(f22150,plain,
spl47_1038,
inference(avatar_split_clause,[],[f5409,f22148]) ).
fof(f22148,plain,
( spl47_1038
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X1,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X2
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
| ~ sP24(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1038])]) ).
fof(f5409,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X1,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X2
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
| ~ sP24(X0,X1,X2) ),
inference(cnf_transformation,[],[f3887]) ).
fof(f3887,plain,
! [X0,X1,X2] :
( ( sP24(X0,X1,X2)
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X1,X0))
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X2
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X0 ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X1,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X2
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
| ~ sP24(X0,X1,X2) ) ),
inference(rectify,[],[f3886]) ).
fof(f3886,plain,
! [X2,X4,X0] :
( ( sP24(X2,X4,X0)
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X0),c_Polynomial_Odegree(X4,X2))
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X0
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2 ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X0),c_Polynomial_Odegree(X4,X2))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X0
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2
| ~ sP24(X2,X4,X0) ) ),
inference(flattening,[],[f3885]) ).
fof(f3885,plain,
! [X2,X4,X0] :
( ( sP24(X2,X4,X0)
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X0),c_Polynomial_Odegree(X4,X2))
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X0
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2 ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X0),c_Polynomial_Odegree(X4,X2))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X0
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2
| ~ sP24(X2,X4,X0) ) ),
inference(nnf_transformation,[],[f3514]) ).
fof(f3514,plain,
! [X2,X4,X0] :
( sP24(X2,X4,X0)
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X0),c_Polynomial_Odegree(X4,X2))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X0
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP24])]) ).
fof(f22146,plain,
spl47_1037,
inference(avatar_split_clause,[],[f5387,f22144]) ).
fof(f22144,plain,
( spl47_1037
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1037])]) ).
fof(f5387,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(cnf_transformation,[],[f3358]) ).
fof(f3358,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(flattening,[],[f3357]) ).
fof(f3357,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(ennf_transformation,[],[f2181]) ).
fof(f2181,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ) ),
inference(rectify,[],[f660]) ).
fof(f660,axiom,
! [X43,X20,X33,X32] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32,X33)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X43)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X43)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono) ).
fof(f22142,plain,
spl47_1036,
inference(avatar_split_clause,[],[f5370,f22140]) ).
fof(f5370,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,sK46(X0,X1,X3)),hAPP(X0,sK46(X0,X1,X3)))
| ~ class_Orderings_Oord(X3) ),
inference(cnf_transformation,[],[f3874]) ).
fof(f3874,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,sK46(X0,X1,X3)),hAPP(X0,sK46(X0,X1,X3))) )
& ( ! [X5] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X5),hAPP(X0,X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) ) )
| ~ class_Orderings_Oord(X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK46])],[f3872,f3873]) ).
fof(f3873,plain,
! [X0,X1,X3] :
( ? [X4] : ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X0,X4))
=> ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,sK46(X0,X1,X3)),hAPP(X0,sK46(X0,X1,X3))) ),
introduced(choice_axiom,[]) ).
fof(f3872,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ? [X4] : ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X0,X4)) )
& ( ! [X5] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X5),hAPP(X0,X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) ) )
| ~ class_Orderings_Oord(X3) ),
inference(rectify,[],[f3871]) ).
fof(f3871,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ? [X4] : ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X0,X4)) )
& ( ! [X4] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X0,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) ) )
| ~ class_Orderings_Oord(X3) ),
inference(nnf_transformation,[],[f3329]) ).
fof(f3329,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
<=> ! [X4] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X0,X4)) )
| ~ class_Orderings_Oord(X3) ),
inference(ennf_transformation,[],[f2165]) ).
fof(f2165,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Oord(X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
<=> ! [X4] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X0,X4)) ) ),
inference(rectify,[],[f298]) ).
fof(f298,axiom,
! [X0,X1,X5,X31] :
( class_Orderings_Oord(X31)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X31),X1,X0)
<=> ! [X2] : c_Orderings_Oord__class_Oless__eq(X31,hAPP(X1,X2),hAPP(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).
fof(f22138,plain,
spl47_1035,
inference(avatar_split_clause,[],[f5342,f22136]) ).
fof(f22136,plain,
( spl47_1035
<=> ! [X0,X3,X2,X1] :
( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Omonom(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1035])]) ).
fof(f5342,plain,
! [X2,X3,X0,X1] :
( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Omonom(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3288]) ).
fof(f3288,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Omonom(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2138]) ).
fof(f2138,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Omonom(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)) ),
inference(rectify,[],[f632]) ).
fof(f632,axiom,
! [X6,X7,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(c_Polynomial_Opoly(X5,c_Polynomial_Omonom(X5,X4,X7)),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__monom) ).
fof(f22134,plain,
spl47_1034,
inference(avatar_split_clause,[],[f5337,f22132]) ).
fof(f22132,plain,
( spl47_1034
<=> ! [X0,X3,X2,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1))
| ~ class_Rings_Ocomm__semiring__0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1034])]) ).
fof(f5337,plain,
! [X2,X3,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f3283]) ).
fof(f3283,plain,
! [X0,X1,X2,X3] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(flattening,[],[f3282]) ).
fof(f3282,plain,
! [X0,X1,X2,X3] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f2133]) ).
fof(f2133,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1))
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 ) ),
inference(rectify,[],[f299]) ).
fof(f299,axiom,
! [X4,X8,X16,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),c_Polynomial_Osmult(X5,X16,X8),c_Polynomial_OpCons(X5,X4,X8))
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__eq__0__lemma) ).
fof(f22130,plain,
( spl47_1033
| ~ spl47_150
| ~ spl47_469 ),
inference(avatar_split_clause,[],[f9322,f9034,f6777,f22128]) ).
fof(f9034,plain,
( spl47_469
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK35(X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_469])]) ).
fof(f9322,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK35(X0,X0)) = X0
| ~ spl47_150
| ~ spl47_469 ),
inference(resolution,[],[f9035,f6778]) ).
fof(f9035,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK35(X0,X1)) = X0 )
| ~ spl47_469 ),
inference(avatar_component_clause,[],[f9034]) ).
fof(f22126,plain,
spl47_1032,
inference(avatar_split_clause,[],[f5325,f22124]) ).
fof(f22124,plain,
( spl47_1032
<=> ! [X0,X3,X2,X1] :
( c_Polynomial_Osmult(X3,X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_Osmult(X3,X2,X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1032])]) ).
fof(f5325,plain,
! [X2,X3,X0,X1] :
( c_Polynomial_Osmult(X3,X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_Osmult(X3,X2,X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f3269]) ).
fof(f3269,plain,
! [X0,X1,X2,X3] :
( c_Polynomial_Osmult(X3,X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_Osmult(X3,X2,X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f2121]) ).
fof(f2121,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Polynomial_Osmult(X3,X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_Osmult(X3,X2,X0)) ),
inference(rectify,[],[f241]) ).
fof(f241,axiom,
! [X13,X8,X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Polynomial_Osmult(X5,X4,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),X8,X13)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),c_Polynomial_Osmult(X5,X4,X8),c_Polynomial_Osmult(X5,X4,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__add__right) ).
fof(f22122,plain,
spl47_1031,
inference(avatar_split_clause,[],[f5324,f22120]) ).
fof(f22120,plain,
( spl47_1031
<=> ! [X0,X3,X2,X1] :
( c_Polynomial_Osmult(X3,X2,c_Polynomial_OpCons(X3,X1,X0)) = c_Polynomial_OpCons(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),c_Polynomial_Osmult(X3,X2,X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1031])]) ).
fof(f5324,plain,
! [X2,X3,X0,X1] :
( c_Polynomial_Osmult(X3,X2,c_Polynomial_OpCons(X3,X1,X0)) = c_Polynomial_OpCons(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),c_Polynomial_Osmult(X3,X2,X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f3268]) ).
fof(f3268,plain,
! [X0,X1,X2,X3] :
( c_Polynomial_Osmult(X3,X2,c_Polynomial_OpCons(X3,X1,X0)) = c_Polynomial_OpCons(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),c_Polynomial_Osmult(X3,X2,X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f2120]) ).
fof(f2120,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Polynomial_Osmult(X3,X2,c_Polynomial_OpCons(X3,X1,X0)) = c_Polynomial_OpCons(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),c_Polynomial_Osmult(X3,X2,X0)) ),
inference(rectify,[],[f602]) ).
fof(f602,axiom,
! [X8,X17,X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Polynomial_Osmult(X5,X4,c_Polynomial_OpCons(X5,X17,X8)) = c_Polynomial_OpCons(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17),c_Polynomial_Osmult(X5,X4,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__pCons) ).
fof(f22118,plain,
spl47_1030,
inference(avatar_split_clause,[],[f5248,f22116]) ).
fof(f22116,plain,
( spl47_1030
<=> ! [X0,X3,X2,X1] :
( c_Polynomial_Osmult(X3,X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_Osmult(X3,X2,X0))
| ~ class_Rings_Ocomm__ring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1030])]) ).
fof(f5248,plain,
! [X2,X3,X0,X1] :
( c_Polynomial_Osmult(X3,X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_Osmult(X3,X2,X0))
| ~ class_Rings_Ocomm__ring(X3) ),
inference(cnf_transformation,[],[f3166]) ).
fof(f3166,plain,
! [X0,X1,X2,X3] :
( c_Polynomial_Osmult(X3,X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_Osmult(X3,X2,X0))
| ~ class_Rings_Ocomm__ring(X3) ),
inference(ennf_transformation,[],[f2055]) ).
fof(f2055,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__ring(X3)
=> c_Polynomial_Osmult(X3,X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_Osmult(X3,X2,X0)) ),
inference(rectify,[],[f888]) ).
fof(f888,axiom,
! [X13,X8,X4,X5] :
( class_Rings_Ocomm__ring(X5)
=> c_Polynomial_Osmult(X5,X4,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5),X8,X13)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5),c_Polynomial_Osmult(X5,X4,X8),c_Polynomial_Osmult(X5,X4,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__diff__right) ).
fof(f22114,plain,
spl47_1029,
inference(avatar_split_clause,[],[f5114,f22112]) ).
fof(f22112,plain,
( spl47_1029
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1029])]) ).
fof(f5114,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1)) ),
inference(cnf_transformation,[],[f3816]) ).
fof(f3816,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)))) ) ),
inference(nnf_transformation,[],[f1956]) ).
fof(f1956,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0))))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1)) ),
inference(rectify,[],[f670]) ).
fof(f670,axiom,
! [X14,X11,X44] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X44),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X44),X14))))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X44),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__reduce) ).
fof(f22110,plain,
spl47_1028,
inference(avatar_split_clause,[],[f5113,f22108]) ).
fof(f22108,plain,
( spl47_1028
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1028])]) ).
fof(f5113,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X0)))) ),
inference(cnf_transformation,[],[f3816]) ).
fof(f22106,plain,
spl47_1027,
inference(avatar_split_clause,[],[f4988,f22104]) ).
fof(f22104,plain,
( spl47_1027
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1027])]) ).
fof(f4988,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f3761]) ).
fof(f3761,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(nnf_transformation,[],[f2969]) ).
fof(f2969,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(flattening,[],[f2968]) ).
fof(f2968,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1890]) ).
fof(f1890,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ) ),
inference(rectify,[],[f820]) ).
fof(f820,axiom,
! [X11,X14,X44] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X14)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X11)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X14,X44),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X44))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X11) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__iff) ).
fof(f22102,plain,
spl47_1026,
inference(avatar_split_clause,[],[f4986,f22100]) ).
fof(f22100,plain,
( spl47_1026
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1026])]) ).
fof(f4986,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f3760]) ).
fof(f3760,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(nnf_transformation,[],[f2967]) ).
fof(f2967,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(flattening,[],[f2966]) ).
fof(f2966,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1889]) ).
fof(f1889,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ) ),
inference(rectify,[],[f783]) ).
fof(f783,axiom,
! [X11,X14,X44] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X14)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X11)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X14,X44),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X44))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X11) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__iff) ).
fof(f22098,plain,
spl47_1025,
inference(avatar_split_clause,[],[f4919,f22096]) ).
fof(f22096,plain,
( spl47_1025
<=> ! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0)) = X0
| ~ class_Rings_Ocomm__semiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1025])]) ).
fof(f4919,plain,
! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0)) = X0
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(cnf_transformation,[],[f2889]) ).
fof(f2889,plain,
! [X0,X1,X2] :
( c_Polynomial_Odegree(X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0)) = X0
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f1837]) ).
fof(f1837,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Polynomial_Odegree(X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),c_Polynomial_OpCons(X2,X1,c_Polynomial_OpCons(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))),X0)) = X0 ),
inference(rectify,[],[f127]) ).
fof(f127,axiom,
! [X7,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Polynomial_Odegree(X5,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X5)),c_Polynomial_OpCons(X5,X4,c_Polynomial_OpCons(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))))),X7)) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__linear__power) ).
fof(f22094,plain,
spl47_1024,
inference(avatar_split_clause,[],[f4918,f22092]) ).
fof(f22092,plain,
( spl47_1024
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oone__class_Oone(X2))),X0) = c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X0)
| ~ class_Rings_Ocomm__semiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1024])]) ).
fof(f4918,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oone__class_Oone(X2))),X0) = c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X0)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(cnf_transformation,[],[f2888]) ).
fof(f2888,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oone__class_Oone(X2))),X0) = c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X0)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f1836]) ).
fof(f1836,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oone__class_Oone(X2))),X0) = c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X0) ),
inference(rectify,[],[f588]) ).
fof(f588,axiom,
! [X21,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Oone__class_Oone(X5))),X21) = c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X21),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(f22090,plain,
spl47_1023,
inference(avatar_split_clause,[],[f4917,f22088]) ).
fof(f22088,plain,
( spl47_1023
<=> ! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(X2,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Oplus__class_Oplus(X2,X0,c_Groups_Oone__class_Oone(X2))),X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1023])]) ).
fof(f4917,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(X2,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Oplus__class_Oplus(X2,X0,c_Groups_Oone__class_Oone(X2))),X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(cnf_transformation,[],[f2887]) ).
fof(f2887,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(X2,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Oplus__class_Oplus(X2,X0,c_Groups_Oone__class_Oone(X2))),X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f1835]) ).
fof(f1835,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Oplus__class_Oplus(X2,X0,c_Groups_Oone__class_Oone(X2))),X1) ),
inference(rectify,[],[f587]) ).
fof(f587,axiom,
! [X4,X21,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,X21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X21)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Oone__class_Oone(X5))),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(f22086,plain,
( spl47_1022
| ~ spl47_420
| ~ spl47_424 ),
inference(avatar_split_clause,[],[f8818,f8291,f8274,f22084]) ).
fof(f22084,plain,
( spl47_1022
<=> ! [X2,X0,X1] :
( ~ sP13(X0,X1,X2)
| sP12(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1022])]) ).
fof(f8274,plain,
( spl47_420
<=> ! [X2,X0,X1] :
( sP12(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_420])]) ).
fof(f8291,plain,
( spl47_424
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP13(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_424])]) ).
fof(f8818,plain,
( ! [X2,X0,X1] :
( ~ sP13(X0,X1,X2)
| sP12(X0,X1,X2) )
| ~ spl47_420
| ~ spl47_424 ),
inference(resolution,[],[f8292,f8275]) ).
fof(f8275,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| sP12(X2,X1,X0) )
| ~ spl47_420 ),
inference(avatar_component_clause,[],[f8274]) ).
fof(f8292,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP13(X2,X1,X0) )
| ~ spl47_424 ),
inference(avatar_component_clause,[],[f8291]) ).
fof(f22082,plain,
spl47_1021,
inference(avatar_split_clause,[],[f4889,f22080]) ).
fof(f22080,plain,
( spl47_1021
<=> ! [X2,X0,X1] :
( X0 = X1
| hAPP(c_Polynomial_Ocoeff(X2,X1),sK39(X0,X1,X2)) != hAPP(c_Polynomial_Ocoeff(X2,X0),sK39(X0,X1,X2))
| ~ class_Groups_Ozero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1021])]) ).
fof(f4889,plain,
! [X2,X0,X1] :
( X0 = X1
| hAPP(c_Polynomial_Ocoeff(X2,X1),sK39(X0,X1,X2)) != hAPP(c_Polynomial_Ocoeff(X2,X0),sK39(X0,X1,X2))
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f3740]) ).
fof(f3740,plain,
! [X0,X1,X2] :
( ( ( X0 = X1
| hAPP(c_Polynomial_Ocoeff(X2,X1),sK39(X0,X1,X2)) != hAPP(c_Polynomial_Ocoeff(X2,X0),sK39(X0,X1,X2)) )
& ( ! [X4] : hAPP(c_Polynomial_Ocoeff(X2,X1),X4) = hAPP(c_Polynomial_Ocoeff(X2,X0),X4)
| X0 != X1 ) )
| ~ class_Groups_Ozero(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39])],[f3738,f3739]) ).
fof(f3739,plain,
! [X0,X1,X2] :
( ? [X3] : hAPP(c_Polynomial_Ocoeff(X2,X1),X3) != hAPP(c_Polynomial_Ocoeff(X2,X0),X3)
=> hAPP(c_Polynomial_Ocoeff(X2,X1),sK39(X0,X1,X2)) != hAPP(c_Polynomial_Ocoeff(X2,X0),sK39(X0,X1,X2)) ),
introduced(choice_axiom,[]) ).
fof(f3738,plain,
! [X0,X1,X2] :
( ( ( X0 = X1
| ? [X3] : hAPP(c_Polynomial_Ocoeff(X2,X1),X3) != hAPP(c_Polynomial_Ocoeff(X2,X0),X3) )
& ( ! [X4] : hAPP(c_Polynomial_Ocoeff(X2,X1),X4) = hAPP(c_Polynomial_Ocoeff(X2,X0),X4)
| X0 != X1 ) )
| ~ class_Groups_Ozero(X2) ),
inference(rectify,[],[f3737]) ).
fof(f3737,plain,
! [X0,X1,X2] :
( ( ( X0 = X1
| ? [X3] : hAPP(c_Polynomial_Ocoeff(X2,X1),X3) != hAPP(c_Polynomial_Ocoeff(X2,X0),X3) )
& ( ! [X3] : hAPP(c_Polynomial_Ocoeff(X2,X1),X3) = hAPP(c_Polynomial_Ocoeff(X2,X0),X3)
| X0 != X1 ) )
| ~ class_Groups_Ozero(X2) ),
inference(nnf_transformation,[],[f2865]) ).
fof(f2865,plain,
! [X0,X1,X2] :
( ( X0 = X1
<=> ! [X3] : hAPP(c_Polynomial_Ocoeff(X2,X1),X3) = hAPP(c_Polynomial_Ocoeff(X2,X0),X3) )
| ~ class_Groups_Ozero(X2) ),
inference(ennf_transformation,[],[f1813]) ).
fof(f1813,plain,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( X0 = X1
<=> ! [X3] : hAPP(c_Polynomial_Ocoeff(X2,X1),X3) = hAPP(c_Polynomial_Ocoeff(X2,X0),X3) ) ),
inference(rectify,[],[f780]) ).
fof(f780,axiom,
! [X18,X9,X5] :
( class_Groups_Ozero(X5)
=> ( X9 = X18
<=> ! [X19] : hAPP(c_Polynomial_Ocoeff(X5,X9),X19) = hAPP(c_Polynomial_Ocoeff(X5,X18),X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_expand__poly__eq) ).
fof(f22078,plain,
spl47_1020,
inference(avatar_split_clause,[],[f4861,f22076]) ).
fof(f22076,plain,
( spl47_1020
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1020])]) ).
fof(f4861,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(cnf_transformation,[],[f2828]) ).
fof(f2828,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(flattening,[],[f2827]) ).
fof(f2827,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(ennf_transformation,[],[f1789]) ).
fof(f1789,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ) ) ),
inference(rectify,[],[f206]) ).
fof(f206,axiom,
! [X7,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X4)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__power) ).
fof(f22074,plain,
spl47_1019,
inference(avatar_split_clause,[],[f4860,f22072]) ).
fof(f22072,plain,
( spl47_1019
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1019])]) ).
fof(f4860,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(cnf_transformation,[],[f2826]) ).
fof(f2826,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(flattening,[],[f2825]) ).
fof(f2825,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(ennf_transformation,[],[f1788]) ).
fof(f1788,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X0)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ) ) ),
inference(rectify,[],[f583]) ).
fof(f583,axiom,
! [X7,X21,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X21)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X7)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X21),X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__1__mult) ).
fof(f22070,plain,
spl47_1018,
inference(avatar_split_clause,[],[f4858,f22068]) ).
fof(f22068,plain,
( spl47_1018
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1018])]) ).
fof(f4858,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(cnf_transformation,[],[f2822]) ).
fof(f2822,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(flattening,[],[f2821]) ).
fof(f2821,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(ennf_transformation,[],[f1786]) ).
fof(f1786,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))) ) ),
inference(rectify,[],[f624]) ).
fof(f624,axiom,
! [X7,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X4)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).
fof(f22066,plain,
spl47_1017,
inference(avatar_split_clause,[],[f4830,f22064]) ).
fof(f22064,plain,
( spl47_1017
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X2,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X1),X0)
| ~ class_Rings_Oidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1017])]) ).
fof(f4830,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X2,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X1),X0)
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f3727]) ).
fof(f3727,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Oorder(X2,X0,X1)
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X2,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X1),X0) ) )
| ~ class_Rings_Oidom(X2) ),
inference(flattening,[],[f3726]) ).
fof(f3726,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Oorder(X2,X0,X1)
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X2,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X1),X0) ) )
| ~ class_Rings_Oidom(X2) ),
inference(nnf_transformation,[],[f2799]) ).
fof(f2799,plain,
! [X0,X1,X2] :
( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X2,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1 ) )
| ~ class_Rings_Oidom(X2) ),
inference(ennf_transformation,[],[f1768]) ).
fof(f1768,plain,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X2,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1 ) ) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X12,X9,X5] :
( class_Rings_Oidom(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Polynomial_Opoly(X5,X9),X12)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X5,X12,X9)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X9 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__root) ).
fof(f22062,plain,
spl47_1016,
inference(avatar_split_clause,[],[f4787,f22060]) ).
fof(f22060,plain,
( spl47_1016
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ class_Rings_Olinordered__semiring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1016])]) ).
fof(f4787,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ class_Rings_Olinordered__semiring__strict(X2) ),
inference(cnf_transformation,[],[f2764]) ).
fof(f2764,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ class_Rings_Olinordered__semiring__strict(X2) ),
inference(flattening,[],[f2763]) ).
fof(f2763,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ class_Rings_Olinordered__semiring__strict(X2) ),
inference(ennf_transformation,[],[f1740]) ).
fof(f1740,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) ),
inference(rectify,[],[f572]) ).
fof(f572,axiom,
! [X4,X17,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X4))
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).
fof(f22058,plain,
spl47_1015,
inference(avatar_split_clause,[],[f4786,f22056]) ).
fof(f22056,plain,
( spl47_1015
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ class_Rings_Olinordered__semiring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1015])]) ).
fof(f4786,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ class_Rings_Olinordered__semiring__strict(X2) ),
inference(cnf_transformation,[],[f2762]) ).
fof(f2762,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ class_Rings_Olinordered__semiring__strict(X2) ),
inference(flattening,[],[f2761]) ).
fof(f2761,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ class_Rings_Olinordered__semiring__strict(X2) ),
inference(ennf_transformation,[],[f1739]) ).
fof(f1739,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0) ) ) ),
inference(rectify,[],[f573]) ).
fof(f573,axiom,
! [X17,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17))
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).
fof(f22054,plain,
spl47_1014,
inference(avatar_split_clause,[],[f4785,f22052]) ).
fof(f22052,plain,
( spl47_1014
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semiring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1014])]) ).
fof(f4785,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semiring__strict(X2) ),
inference(cnf_transformation,[],[f2760]) ).
fof(f2760,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semiring__strict(X2) ),
inference(flattening,[],[f2759]) ).
fof(f2759,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semiring__strict(X2) ),
inference(ennf_transformation,[],[f1738]) ).
fof(f1738,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ) ) ),
inference(rectify,[],[f576]) ).
fof(f576,axiom,
! [X17,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X17)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
fof(f22050,plain,
spl47_1013,
inference(avatar_split_clause,[],[f4783,f22048]) ).
fof(f22048,plain,
( spl47_1013
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semiring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1013])]) ).
fof(f4783,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semiring__strict(X2) ),
inference(cnf_transformation,[],[f2756]) ).
fof(f2756,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semiring__strict(X2) ),
inference(flattening,[],[f2755]) ).
fof(f2755,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semiring__strict(X2) ),
inference(ennf_transformation,[],[f1736]) ).
fof(f1736,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
inference(rectify,[],[f575]) ).
fof(f575,axiom,
! [X17,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> ( c_Orderings_Oord__class_Oless(X5,X17,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17),c_Groups_Ozero__class_Ozero(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg) ).
fof(f22046,plain,
spl47_1012,
inference(avatar_split_clause,[],[f4782,f22044]) ).
fof(f22044,plain,
( spl47_1012
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__semiring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1012])]) ).
fof(f4782,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__semiring__strict(X2) ),
inference(cnf_transformation,[],[f2754]) ).
fof(f2754,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__semiring__strict(X2) ),
inference(flattening,[],[f2753]) ).
fof(f2753,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__semiring__strict(X2) ),
inference(ennf_transformation,[],[f1735]) ).
fof(f1735,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
=> c_Orderings_Oord__class_Oless(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
inference(rectify,[],[f570]) ).
fof(f570,axiom,
! [X17,X4,X5] :
( class_Rings_Olinordered__semiring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,c_Groups_Ozero__class_Ozero(X5))
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X17)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17),c_Groups_Ozero__class_Ozero(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__pos) ).
fof(f22042,plain,
( spl47_1011
| ~ spl47_421
| ~ spl47_423 ),
inference(avatar_split_clause,[],[f8805,f8287,f8278,f22040]) ).
fof(f22040,plain,
( spl47_1011
<=> ! [X2,X0,X1] :
( sP13(X0,X1,X2)
| ~ sP12(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1011])]) ).
fof(f8278,plain,
( spl47_421
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP12(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_421])]) ).
fof(f8287,plain,
( spl47_423
<=> ! [X2,X0,X1] :
( sP13(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_423])]) ).
fof(f8805,plain,
( ! [X2,X0,X1] :
( sP13(X0,X1,X2)
| ~ sP12(X0,X1,X2) )
| ~ spl47_421
| ~ spl47_423 ),
inference(resolution,[],[f8288,f8279]) ).
fof(f8279,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP12(X2,X1,X0) )
| ~ spl47_421 ),
inference(avatar_component_clause,[],[f8278]) ).
fof(f8288,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| sP13(X2,X1,X0) )
| ~ spl47_423 ),
inference(avatar_component_clause,[],[f8287]) ).
fof(f22038,plain,
spl47_1010,
inference(avatar_split_clause,[],[f4735,f22036]) ).
fof(f22036,plain,
( spl47_1010
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Oordered__cancel__semiring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1010])]) ).
fof(f4735,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Oordered__cancel__semiring(X2) ),
inference(cnf_transformation,[],[f2692]) ).
fof(f2692,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Oordered__cancel__semiring(X2) ),
inference(flattening,[],[f2691]) ).
fof(f2691,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Oordered__cancel__semiring(X2) ),
inference(ennf_transformation,[],[f1697]) ).
fof(f1697,plain,
! [X0,X1,X2] :
( class_Rings_Oordered__cancel__semiring(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ) ) ),
inference(rectify,[],[f550]) ).
fof(f550,axiom,
! [X17,X4,X5] :
( class_Rings_Oordered__cancel__semiring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X17)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).
fof(f22034,plain,
spl47_1009,
inference(avatar_split_clause,[],[f4733,f22032]) ).
fof(f22032,plain,
( spl47_1009
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Oordered__cancel__semiring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1009])]) ).
fof(f4733,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Oordered__cancel__semiring(X2) ),
inference(cnf_transformation,[],[f2688]) ).
fof(f2688,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Oordered__cancel__semiring(X2) ),
inference(flattening,[],[f2687]) ).
fof(f2687,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Oordered__cancel__semiring(X2) ),
inference(ennf_transformation,[],[f1695]) ).
fof(f1695,plain,
! [X0,X1,X2] :
( class_Rings_Oordered__cancel__semiring(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
inference(rectify,[],[f551]) ).
fof(f551,axiom,
! [X17,X4,X5] :
( class_Rings_Oordered__cancel__semiring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X17,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17),c_Groups_Ozero__class_Ozero(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).
fof(f22030,plain,
spl47_1008,
inference(avatar_split_clause,[],[f4732,f22028]) ).
fof(f22028,plain,
( spl47_1008
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Oordered__cancel__semiring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1008])]) ).
fof(f4732,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Oordered__cancel__semiring(X2) ),
inference(cnf_transformation,[],[f2686]) ).
fof(f2686,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Oordered__cancel__semiring(X2) ),
inference(flattening,[],[f2685]) ).
fof(f2685,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Oordered__cancel__semiring(X2) ),
inference(ennf_transformation,[],[f1694]) ).
fof(f1694,plain,
! [X0,X1,X2] :
( class_Rings_Oordered__cancel__semiring(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
=> c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
inference(rectify,[],[f553]) ).
fof(f553,axiom,
! [X17,X4,X5] :
( class_Rings_Oordered__cancel__semiring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,c_Groups_Ozero__class_Ozero(X5))
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X17)
=> c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17),c_Groups_Ozero__class_Ozero(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).
fof(f22026,plain,
spl47_1007,
inference(avatar_split_clause,[],[f4668,f22024]) ).
fof(f22024,plain,
( spl47_1007
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1007])]) ).
fof(f4668,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f2652]) ).
fof(f2652,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(flattening,[],[f2651]) ).
fof(f2651,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(ennf_transformation,[],[f1668]) ).
fof(f1668,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ) ) ),
inference(rectify,[],[f569]) ).
fof(f569,axiom,
! [X17,X4,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,c_Groups_Ozero__class_Ozero(X5))
=> ( c_Orderings_Oord__class_Oless(X5,X17,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
fof(f22022,plain,
spl47_1006,
inference(avatar_split_clause,[],[f4666,f22020]) ).
fof(f22020,plain,
( spl47_1006
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Oordered__ring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1006])]) ).
fof(f4666,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Oordered__ring(X2) ),
inference(cnf_transformation,[],[f2650]) ).
fof(f2650,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) )
| ~ class_Rings_Oordered__ring(X2) ),
inference(flattening,[],[f2649]) ).
fof(f2649,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) )
| ~ class_Rings_Oordered__ring(X2) ),
inference(ennf_transformation,[],[f1667]) ).
fof(f1667,plain,
! [X0,X1,X2] :
( class_Rings_Oordered__ring(X2)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) )
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ) ),
inference(rectify,[],[f562]) ).
fof(f562,axiom,
! [X17,X4,X5] :
( class_Rings_Oordered__ring(X5)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X5,X17,c_Groups_Ozero__class_Ozero(X5))
& c_Orderings_Oord__class_Oless__eq(X5,X4,c_Groups_Ozero__class_Ozero(X5)) )
| ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X17)
& c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X4) ) )
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).
fof(f22018,plain,
spl47_1005,
inference(avatar_split_clause,[],[f4665,f22016]) ).
fof(f22016,plain,
( spl47_1005
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Oordered__ring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1005])]) ).
fof(f4665,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Oordered__ring(X2) ),
inference(cnf_transformation,[],[f2648]) ).
fof(f2648,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Oordered__ring(X2) ),
inference(flattening,[],[f2647]) ).
fof(f2647,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Oordered__ring(X2) ),
inference(ennf_transformation,[],[f1666]) ).
fof(f1666,plain,
! [X0,X1,X2] :
( class_Rings_Oordered__ring(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ) ) ),
inference(rectify,[],[f554]) ).
fof(f554,axiom,
! [X17,X4,X5] :
( class_Rings_Oordered__ring(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,c_Groups_Ozero__class_Ozero(X5))
=> ( c_Orderings_Oord__class_Oless__eq(X5,X17,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).
fof(f21826,plain,
( spl47_1004
| ~ spl47_268
| ~ spl47_423 ),
inference(avatar_split_clause,[],[f8802,f8287,f7275,f21824]) ).
fof(f21824,plain,
( spl47_1004
<=> ! [X0,X1] : sP13(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1004])]) ).
fof(f7275,plain,
( spl47_268
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_268])]) ).
fof(f8802,plain,
( ! [X0,X1] : sP13(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0,X1)
| ~ spl47_268
| ~ spl47_423 ),
inference(resolution,[],[f8288,f7276]) ).
fof(f7276,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0))
| ~ spl47_268 ),
inference(avatar_component_clause,[],[f7275]) ).
fof(f21438,plain,
( spl47_1003
| ~ spl47_268
| ~ spl47_420 ),
inference(avatar_split_clause,[],[f8776,f8274,f7275,f21436]) ).
fof(f21436,plain,
( spl47_1003
<=> ! [X0,X1] : sP12(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1003])]) ).
fof(f8776,plain,
( ! [X0,X1] : sP12(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0,X1)
| ~ spl47_268
| ~ spl47_420 ),
inference(resolution,[],[f8275,f7276]) ).
fof(f21376,plain,
( spl47_1002
| ~ spl47_246
| ~ spl47_366 ),
inference(avatar_split_clause,[],[f8071,f7862,f7173,f21374]) ).
fof(f21374,plain,
( spl47_1002
<=> ! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
| sP6(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1002])]) ).
fof(f7173,plain,
( spl47_246
<=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_246])]) ).
fof(f7862,plain,
( spl47_366
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_366])]) ).
fof(f8071,plain,
( ! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
| sP6(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl47_246
| ~ spl47_366 ),
inference(superposition,[],[f7863,f7174]) ).
fof(f7174,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0
| ~ spl47_246 ),
inference(avatar_component_clause,[],[f7173]) ).
fof(f7863,plain,
( ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| sP6(X0,X1) )
| ~ spl47_366 ),
inference(avatar_component_clause,[],[f7862]) ).
fof(f21237,plain,
spl47_1001,
inference(avatar_split_clause,[],[f6020,f21235]) ).
fof(f21235,plain,
( spl47_1001
<=> ! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Groups_Ozero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1001])]) ).
fof(f6020,plain,
! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Groups_Ozero(X2) ),
inference(forward_demodulation,[],[f5632,f4240]) ).
fof(f5632,plain,
! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Groups_Ozero(X2) ),
inference(definition_unfolding,[],[f4882,f4118]) ).
fof(f4882,plain,
! [X2,X0,X1] :
( c_Nat_OSuc(c_Polynomial_Odegree(X2,X1)) = c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f2854]) ).
fof(f2854,plain,
! [X0,X1,X2] :
( ( ( c_Nat_OSuc(c_Polynomial_Odegree(X2,X1)) = c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1 ) )
| ~ class_Groups_Ozero(X2) ),
inference(ennf_transformation,[],[f1807]) ).
fof(f1807,plain,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1
=> c_Nat_OSuc(c_Polynomial_Odegree(X2,X1)) = c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1)) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X0,X1)) ) ) ),
inference(rectify,[],[f74]) ).
fof(f74,axiom,
! [X4,X8,X5] :
( class_Groups_Ozero(X5)
=> ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) != X8
=> c_Nat_OSuc(c_Polynomial_Odegree(X5,X8)) = c_Polynomial_Odegree(X5,c_Polynomial_OpCons(X5,X4,X8)) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X8
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X5,c_Polynomial_OpCons(X5,X4,X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__pCons__eq__if) ).
fof(f21233,plain,
( spl47_1000
| ~ spl47_245
| ~ spl47_366 ),
inference(avatar_split_clause,[],[f8068,f7862,f7169,f21231]) ).
fof(f21231,plain,
( spl47_1000
<=> ! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
| sP6(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1000])]) ).
fof(f7169,plain,
( spl47_245
<=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_245])]) ).
fof(f8068,plain,
( ! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
| sP6(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) )
| ~ spl47_245
| ~ spl47_366 ),
inference(superposition,[],[f7863,f7170]) ).
fof(f7170,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| ~ spl47_245 ),
inference(avatar_component_clause,[],[f7169]) ).
fof(f21229,plain,
spl47_999,
inference(avatar_split_clause,[],[f5940,f21227]) ).
fof(f21227,plain,
( spl47_999
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK38(X0,X1)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_999])]) ).
fof(f5940,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK38(X0,X1)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(forward_demodulation,[],[f5587,f4240]) ).
fof(f5587,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK38(X0,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(definition_unfolding,[],[f4535,f4118,f4118]) ).
fof(f4535,plain,
! [X0,X1] :
( c_Nat_OSuc(sK38(X0,X1)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
inference(cnf_transformation,[],[f3624]) ).
fof(f3624,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ( ! [X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Nat_OSuc(X2) != X1 )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK38(X0,X1),X0)
& c_Nat_OSuc(sK38(X0,X1)) = X1 )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK38])],[f3622,f3623]) ).
fof(f3623,plain,
! [X0,X1] :
( ? [X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X0)
& c_Nat_OSuc(X3) = X1 )
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK38(X0,X1),X0)
& c_Nat_OSuc(sK38(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f3622,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ( ! [X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Nat_OSuc(X2) != X1 )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) )
& ( ? [X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X0)
& c_Nat_OSuc(X3) = X1 )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
inference(rectify,[],[f3621]) ).
fof(f3621,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ( ! [X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Nat_OSuc(X2) != X1 )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) )
& ( ? [X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
& c_Nat_OSuc(X2) = X1 )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
inference(flattening,[],[f3620]) ).
fof(f3620,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ( ! [X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Nat_OSuc(X2) != X1 )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) )
& ( ? [X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
& c_Nat_OSuc(X2) = X1 )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
inference(nnf_transformation,[],[f1583]) ).
fof(f1583,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
<=> ( ? [X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
& c_Nat_OSuc(X2) = X1 )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) ),
inference(rectify,[],[f255]) ).
fof(f255,axiom,
! [X11,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,c_Nat_OSuc(X11))
<=> ( ? [X40] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X40,X11)
& c_Nat_OSuc(X40) = X14 )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
fof(f21225,plain,
spl47_998,
inference(avatar_split_clause,[],[f5851,f21223]) ).
fof(f21223,plain,
( spl47_998
<=> ! [X0,X1,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Ozero__class_Ozero(X3)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Ozero__class_Ozero(X3)),X0)))
| ~ class_Rings_Oidom(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_998])]) ).
fof(f5851,plain,
! [X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Ozero__class_Ozero(X3)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Ozero__class_Ozero(X3)),X0)))
| ~ class_Rings_Oidom(X3) ),
inference(equality_resolution,[],[f5266]) ).
fof(f5266,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)))
| c_Groups_Ozero__class_Ozero(X3) != X2
| ~ class_Rings_Oidom(X3) ),
inference(cnf_transformation,[],[f3864]) ).
fof(f21221,plain,
spl47_997,
inference(avatar_split_clause,[],[f5850,f21219]) ).
fof(f21219,plain,
( spl47_997
<=> ! [X2,X0,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Ozero__class_Ozero(X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),c_Groups_Ozero__class_Ozero(X3))))
| ~ class_Rings_Oidom(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_997])]) ).
fof(f5850,plain,
! [X2,X3,X0] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Ozero__class_Ozero(X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),c_Groups_Ozero__class_Ozero(X3))))
| ~ class_Rings_Oidom(X3) ),
inference(equality_resolution,[],[f5263]) ).
fof(f5263,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
| c_Groups_Ozero__class_Ozero(X3) != X1
| ~ class_Rings_Oidom(X3) ),
inference(cnf_transformation,[],[f3862]) ).
fof(f21217,plain,
spl47_996,
inference(avatar_split_clause,[],[f5626,f21215]) ).
fof(f21215,plain,
( spl47_996
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_996])]) ).
fof(f5626,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(definition_unfolding,[],[f4857,f4118]) ).
fof(f4857,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(cnf_transformation,[],[f2820]) ).
fof(f2820,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(flattening,[],[f2819]) ).
fof(f2819,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0)))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(ennf_transformation,[],[f1785]) ).
fof(f1785,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Nat_OSuc(X0))) ) ),
inference(rectify,[],[f208]) ).
fof(f208,axiom,
! [X7,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X4)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Nat_OSuc(X7))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1) ).
fof(f21213,plain,
spl47_995,
inference(avatar_split_clause,[],[f5540,f21211]) ).
fof(f21211,plain,
( spl47_995
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_995])]) ).
fof(f5540,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
inference(definition_unfolding,[],[f4258,f4118]) ).
fof(f4258,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
inference(cnf_transformation,[],[f2393]) ).
fof(f2393,plain,
! [X0,X1] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ),
inference(ennf_transformation,[],[f1373]) ).
fof(f1373,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = X0 ) ),
inference(rectify,[],[f874]) ).
fof(f874,axiom,
! [X7,X21] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X21
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X7) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X7)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X21
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X7) = X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__if) ).
fof(f21209,plain,
spl47_994,
inference(avatar_split_clause,[],[f5445,f21207]) ).
fof(f21207,plain,
( spl47_994
<=> ! [X4,X0,X3,X2,X1] :
( c_Polynomial_Osynthetic__div(X4,X3,X2) = X1
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),X3,c_Polynomial_Osmult(X4,X2,X1)) != c_Polynomial_OpCons(X4,X0,X1)
| ~ class_Rings_Ocomm__semiring__0(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_994])]) ).
fof(f5445,plain,
! [X2,X3,X0,X1,X4] :
( c_Polynomial_Osynthetic__div(X4,X3,X2) = X1
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),X3,c_Polynomial_Osmult(X4,X2,X1)) != c_Polynomial_OpCons(X4,X0,X1)
| ~ class_Rings_Ocomm__semiring__0(X4) ),
inference(cnf_transformation,[],[f3414]) ).
fof(f21205,plain,
spl47_993,
inference(avatar_split_clause,[],[f5363,f21203]) ).
fof(f21203,plain,
( spl47_993
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_993])]) ).
fof(f5363,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3319]) ).
fof(f3319,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(flattening,[],[f3318]) ).
fof(f3318,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2159]) ).
fof(f2159,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X0)) ) ),
inference(rectify,[],[f531]) ).
fof(f531,axiom,
! [X16,X17,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17)),X16))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X4),X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__left) ).
fof(f21201,plain,
spl47_992,
inference(avatar_split_clause,[],[f5362,f21199]) ).
fof(f21199,plain,
( spl47_992
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_992])]) ).
fof(f5362,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3317]) ).
fof(f3317,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(flattening,[],[f3316]) ).
fof(f3316,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2158]) ).
fof(f2158,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X0)) ) ),
inference(rectify,[],[f532]) ).
fof(f532,axiom,
! [X16,X17,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17)),X16))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X17),X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__right) ).
fof(f21197,plain,
spl47_991,
inference(avatar_split_clause,[],[f5361,f21195]) ).
fof(f21195,plain,
( spl47_991
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_991])]) ).
fof(f5361,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3315]) ).
fof(f3315,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(flattening,[],[f3314]) ).
fof(f3314,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2157]) ).
fof(f2157,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0)) ) ),
inference(rectify,[],[f103]) ).
fof(f103,axiom,
! [X13,X8,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),c_Polynomial_Osmult(X5,X4,X8)),X13))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),X8),X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd__cancel) ).
fof(f21193,plain,
spl47_990,
inference(avatar_split_clause,[],[f5360,f21191]) ).
fof(f21191,plain,
( spl47_990
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X3,X0,X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_990])]) ).
fof(f5360,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X3,X0,X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3313]) ).
fof(f3313,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X3,X0,X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(flattening,[],[f3312]) ).
fof(f3312,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X3,X0,X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2156]) ).
fof(f2156,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),X1))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_Osmult(X3,X0,X1))) ) ),
inference(rectify,[],[f104]) ).
fof(f104,axiom,
! [X4,X13,X8,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),X8),X13))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),X8),c_Polynomial_Osmult(X5,X4,X13))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult) ).
fof(f21189,plain,
( spl47_989
| ~ spl47_246
| ~ spl47_364 ),
inference(avatar_split_clause,[],[f8059,f7854,f7173,f21187]) ).
fof(f21187,plain,
( spl47_989
<=> ! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
| sP5(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_989])]) ).
fof(f7854,plain,
( spl47_364
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_364])]) ).
fof(f8059,plain,
( ! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
| sP5(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl47_246
| ~ spl47_364 ),
inference(superposition,[],[f7855,f7174]) ).
fof(f7855,plain,
( ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| sP5(X0,X1) )
| ~ spl47_364 ),
inference(avatar_component_clause,[],[f7854]) ).
fof(f21185,plain,
spl47_988,
inference(avatar_split_clause,[],[f5356,f21183]) ).
fof(f21183,plain,
( spl47_988
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_988])]) ).
fof(f5356,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3305]) ).
fof(f3305,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(flattening,[],[f3304]) ).
fof(f3304,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2152]) ).
fof(f2152,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))) ) ),
inference(rectify,[],[f528]) ).
fof(f528,axiom,
! [X17,X16,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X4),X16))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X16))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult) ).
fof(f21181,plain,
spl47_987,
inference(avatar_split_clause,[],[f5355,f21179]) ).
fof(f21179,plain,
( spl47_987
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_987])]) ).
fof(f5355,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3303]) ).
fof(f3303,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(flattening,[],[f3302]) ).
fof(f3302,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2151]) ).
fof(f2151,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),X1))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))) ) ),
inference(rectify,[],[f527]) ).
fof(f527,axiom,
! [X16,X17,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X4),X17))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X16))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult2) ).
fof(f21177,plain,
spl47_986,
inference(avatar_split_clause,[],[f5323,f21175]) ).
fof(f21175,plain,
( spl47_986
<=> ! [X0,X3,X2,X1] :
( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Osmult(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Polynomial_Opoly(X3,X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_986])]) ).
fof(f5323,plain,
! [X2,X3,X0,X1] :
( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Osmult(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Polynomial_Opoly(X3,X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f3267]) ).
fof(f3267,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Osmult(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Polynomial_Opoly(X3,X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f2119]) ).
fof(f2119,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Osmult(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
inference(rectify,[],[f603]) ).
fof(f603,axiom,
! [X6,X8,X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> hAPP(c_Polynomial_Opoly(X5,c_Polynomial_Osmult(X5,X4,X8)),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(c_Polynomial_Opoly(X5,X8),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__smult) ).
fof(f21173,plain,
spl47_985,
inference(avatar_split_clause,[],[f5322,f21171]) ).
fof(f21171,plain,
( spl47_985
<=> ! [X0,X3,X2,X1] :
( hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Osmult(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Polynomial_Ocoeff(X3,X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_985])]) ).
fof(f5322,plain,
! [X2,X3,X0,X1] :
( hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Osmult(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Polynomial_Ocoeff(X3,X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f3266]) ).
fof(f3266,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Osmult(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Polynomial_Ocoeff(X3,X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f2118]) ).
fof(f2118,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Osmult(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Polynomial_Ocoeff(X3,X1),X0)) ),
inference(rectify,[],[f803]) ).
fof(f803,axiom,
! [X7,X8,X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> hAPP(c_Polynomial_Ocoeff(X5,c_Polynomial_Osmult(X5,X4,X8)),X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),hAPP(c_Polynomial_Ocoeff(X5,X8),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__smult) ).
fof(f21169,plain,
spl47_984,
inference(avatar_split_clause,[],[f5321,f21167]) ).
fof(f21167,plain,
( spl47_984
<=> ! [X0,X3,X2,X1] :
( c_Polynomial_Osmult(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_Osmult(X3,X1,X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_984])]) ).
fof(f5321,plain,
! [X2,X3,X0,X1] :
( c_Polynomial_Osmult(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_Osmult(X3,X1,X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f3265]) ).
fof(f3265,plain,
! [X0,X1,X2,X3] :
( c_Polynomial_Osmult(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_Osmult(X3,X1,X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f2117]) ).
fof(f2117,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Polynomial_Osmult(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_Osmult(X3,X1,X0)) ),
inference(rectify,[],[f182]) ).
fof(f182,axiom,
! [X8,X17,X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Polynomial_Osmult(X5,c_Groups_Oplus__class_Oplus(X5,X4,X17),X8) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),c_Polynomial_Osmult(X5,X4,X8),c_Polynomial_Osmult(X5,X17,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__add__left) ).
fof(f21165,plain,
spl47_983,
inference(avatar_split_clause,[],[f5320,f21163]) ).
fof(f21163,plain,
( spl47_983
<=> ! [X0,X3,X2,X1] :
( c_Polynomial_Osynthetic__div(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Polynomial_OpCons(X3,hAPP(c_Polynomial_Opoly(X3,X1),X0),c_Polynomial_Osynthetic__div(X3,X1,X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_983])]) ).
fof(f5320,plain,
! [X2,X3,X0,X1] :
( c_Polynomial_Osynthetic__div(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Polynomial_OpCons(X3,hAPP(c_Polynomial_Opoly(X3,X1),X0),c_Polynomial_Osynthetic__div(X3,X1,X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f3264]) ).
fof(f3264,plain,
! [X0,X1,X2,X3] :
( c_Polynomial_Osynthetic__div(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Polynomial_OpCons(X3,hAPP(c_Polynomial_Opoly(X3,X1),X0),c_Polynomial_Osynthetic__div(X3,X1,X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f2116]) ).
fof(f2116,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Polynomial_Osynthetic__div(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Polynomial_OpCons(X3,hAPP(c_Polynomial_Opoly(X3,X1),X0),c_Polynomial_Osynthetic__div(X3,X1,X0)) ),
inference(rectify,[],[f117]) ).
fof(f117,axiom,
! [X16,X8,X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Polynomial_Osynthetic__div(X5,c_Polynomial_OpCons(X5,X4,X8),X16) = c_Polynomial_OpCons(X5,hAPP(c_Polynomial_Opoly(X5,X8),X16),c_Polynomial_Osynthetic__div(X5,X8,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__pCons) ).
fof(f21161,plain,
spl47_982,
inference(avatar_split_clause,[],[f5306,f21159]) ).
fof(f21159,plain,
( spl47_982
<=> ! [X0,X3,X2,X1] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Omonom(X3,X2,X1),c_Polynomial_Omonom(X3,X0,X1)) = c_Polynomial_Omonom(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),X1)
| ~ class_Groups_Ocomm__monoid__add(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_982])]) ).
fof(f5306,plain,
! [X2,X3,X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Omonom(X3,X2,X1),c_Polynomial_Omonom(X3,X0,X1)) = c_Polynomial_Omonom(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),X1)
| ~ class_Groups_Ocomm__monoid__add(X3) ),
inference(cnf_transformation,[],[f3249]) ).
fof(f3249,plain,
! [X0,X1,X2,X3] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Omonom(X3,X2,X1),c_Polynomial_Omonom(X3,X0,X1)) = c_Polynomial_Omonom(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),X1)
| ~ class_Groups_Ocomm__monoid__add(X3) ),
inference(ennf_transformation,[],[f2104]) ).
fof(f2104,plain,
! [X0,X1,X2,X3] :
( class_Groups_Ocomm__monoid__add(X3)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Omonom(X3,X2,X1),c_Polynomial_Omonom(X3,X0,X1)) = c_Polynomial_Omonom(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),X1) ),
inference(rectify,[],[f147]) ).
fof(f147,axiom,
! [X17,X7,X4,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),c_Polynomial_Omonom(X5,X4,X7),c_Polynomial_Omonom(X5,X17,X7)) = c_Polynomial_Omonom(X5,c_Groups_Oplus__class_Oplus(X5,X4,X17),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__monom) ).
fof(f21157,plain,
spl47_981,
inference(avatar_split_clause,[],[f5268,f21155]) ).
fof(f21155,plain,
( spl47_981
<=> ! [X0,X3,X2,X1] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Omonom(X3,X2,X1),c_Polynomial_Omonom(X3,X0,X1)) = c_Polynomial_Omonom(X3,c_Groups_Ominus__class_Ominus(X3,X2,X0),X1)
| ~ class_Groups_Oab__group__add(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_981])]) ).
fof(f5268,plain,
! [X2,X3,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Omonom(X3,X2,X1),c_Polynomial_Omonom(X3,X0,X1)) = c_Polynomial_Omonom(X3,c_Groups_Ominus__class_Ominus(X3,X2,X0),X1)
| ~ class_Groups_Oab__group__add(X3) ),
inference(cnf_transformation,[],[f3193]) ).
fof(f3193,plain,
! [X0,X1,X2,X3] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Omonom(X3,X2,X1),c_Polynomial_Omonom(X3,X0,X1)) = c_Polynomial_Omonom(X3,c_Groups_Ominus__class_Ominus(X3,X2,X0),X1)
| ~ class_Groups_Oab__group__add(X3) ),
inference(ennf_transformation,[],[f2071]) ).
fof(f2071,plain,
! [X0,X1,X2,X3] :
( class_Groups_Oab__group__add(X3)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Omonom(X3,X2,X1),c_Polynomial_Omonom(X3,X0,X1)) = c_Polynomial_Omonom(X3,c_Groups_Ominus__class_Ominus(X3,X2,X0),X1) ),
inference(rectify,[],[f773]) ).
fof(f773,axiom,
! [X17,X7,X4,X5] :
( class_Groups_Oab__group__add(X5)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5),c_Polynomial_Omonom(X5,X4,X7),c_Polynomial_Omonom(X5,X17,X7)) = c_Polynomial_Omonom(X5,c_Groups_Ominus__class_Ominus(X5,X4,X17),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__monom) ).
fof(f21153,plain,
spl47_980,
inference(avatar_split_clause,[],[f5247,f21151]) ).
fof(f21151,plain,
( spl47_980
<=> ! [X0,X3,X2,X1] :
( c_Polynomial_Osmult(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_Osmult(X3,X1,X0))
| ~ class_Rings_Ocomm__ring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_980])]) ).
fof(f5247,plain,
! [X2,X3,X0,X1] :
( c_Polynomial_Osmult(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_Osmult(X3,X1,X0))
| ~ class_Rings_Ocomm__ring(X3) ),
inference(cnf_transformation,[],[f3165]) ).
fof(f3165,plain,
! [X0,X1,X2,X3] :
( c_Polynomial_Osmult(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_Osmult(X3,X1,X0))
| ~ class_Rings_Ocomm__ring(X3) ),
inference(ennf_transformation,[],[f2054]) ).
fof(f2054,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__ring(X3)
=> c_Polynomial_Osmult(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X0),c_Polynomial_Osmult(X3,X1,X0)) ),
inference(rectify,[],[f776]) ).
fof(f776,axiom,
! [X8,X17,X4,X5] :
( class_Rings_Ocomm__ring(X5)
=> c_Polynomial_Osmult(X5,c_Groups_Ominus__class_Ominus(X5,X4,X17),X8) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5),c_Polynomial_Osmult(X5,X4,X8),c_Polynomial_Osmult(X5,X17,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__diff__left) ).
fof(f21149,plain,
spl47_979,
inference(avatar_split_clause,[],[f5186,f21147]) ).
fof(f21147,plain,
( spl47_979
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),c_Polynomial_Osmult(X1,X0,X2)),X3))
| ~ sP18(X3,X2,X1,X0)
| ~ sP19(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_979])]) ).
fof(f5186,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),c_Polynomial_Osmult(X1,X0,X2)),X3))
| ~ sP18(X3,X2,X1,X0)
| ~ sP19(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3839]) ).
fof(f3839,plain,
! [X0,X1,X2,X3] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),c_Polynomial_Osmult(X1,X0,X2)),X3))
| ~ sP18(X3,X2,X1,X0) )
& ( sP18(X3,X2,X1,X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),c_Polynomial_Osmult(X1,X0,X2)),X3)) ) )
| ~ sP19(X0,X1,X2,X3) ),
inference(rectify,[],[f3838]) ).
fof(f3838,plain,
! [X2,X3,X1,X0] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0))
| ~ sP18(X0,X1,X3,X2) )
& ( sP18(X0,X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0)) ) )
| ~ sP19(X2,X3,X1,X0) ),
inference(nnf_transformation,[],[f3506]) ).
fof(f3506,plain,
! [X2,X3,X1,X0] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0))
<=> sP18(X0,X1,X3,X2) )
| ~ sP19(X2,X3,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP19])]) ).
fof(f21145,plain,
( spl47_978
| ~ spl47_245
| ~ spl47_364 ),
inference(avatar_split_clause,[],[f8056,f7854,f7169,f21143]) ).
fof(f21143,plain,
( spl47_978
<=> ! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
| sP5(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_978])]) ).
fof(f8056,plain,
( ! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
| sP5(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) )
| ~ spl47_245
| ~ spl47_364 ),
inference(superposition,[],[f7855,f7170]) ).
fof(f21141,plain,
spl47_977,
inference(avatar_split_clause,[],[f5185,f21139]) ).
fof(f21139,plain,
( spl47_977
<=> ! [X0,X3,X2,X1] :
( sP18(X3,X2,X1,X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),c_Polynomial_Osmult(X1,X0,X2)),X3))
| ~ sP19(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_977])]) ).
fof(f5185,plain,
! [X2,X3,X0,X1] :
( sP18(X3,X2,X1,X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),c_Polynomial_Osmult(X1,X0,X2)),X3))
| ~ sP19(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3839]) ).
fof(f21137,plain,
spl47_976,
inference(avatar_split_clause,[],[f5151,f21135]) ).
fof(f21135,plain,
( spl47_976
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Rings_Oinverse__class_Odivide(X3,X1,X0)) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
| ~ class_Rings_Odivision__ring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_976])]) ).
fof(f5151,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Rings_Oinverse__class_Odivide(X3,X1,X0)) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
| ~ class_Rings_Odivision__ring(X3) ),
inference(cnf_transformation,[],[f3070]) ).
fof(f3070,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Rings_Oinverse__class_Odivide(X3,X1,X0)) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
| ~ class_Rings_Odivision__ring(X3) ),
inference(ennf_transformation,[],[f1997]) ).
fof(f1997,plain,
! [X0,X1,X2,X3] :
( class_Rings_Odivision__ring(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Rings_Oinverse__class_Odivide(X3,X1,X0)) = c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0) ),
inference(rectify,[],[f921]) ).
fof(f921,axiom,
! [X16,X17,X4,X5] :
( class_Rings_Odivision__ring(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Rings_Oinverse__class_Odivide(X5,X17,X16)) = c_Rings_Oinverse__class_Odivide(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__eq__right) ).
fof(f21133,plain,
spl47_975,
inference(avatar_split_clause,[],[f5045,f21131]) ).
fof(f21131,plain,
( spl47_975
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X1
| c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
| ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_975])]) ).
fof(f5045,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X1
| c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
| ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2) ),
inference(cnf_transformation,[],[f3778]) ).
fof(f21129,plain,
spl47_974,
inference(avatar_split_clause,[],[f5021,f21127]) ).
fof(f21127,plain,
( spl47_974
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_974])]) ).
fof(f5021,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(cnf_transformation,[],[f3006]) ).
fof(f3006,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(flattening,[],[f3005]) ).
fof(f3005,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(ennf_transformation,[],[f1915]) ).
fof(f1915,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0)) ) ),
inference(rectify,[],[f50]) ).
fof(f50,axiom,
! [X26,X10,X6] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X10))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X10),X26))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X26)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__trans) ).
fof(f21125,plain,
spl47_973,
inference(avatar_split_clause,[],[f5012,f21123]) ).
fof(f21123,plain,
( spl47_973
<=> ! [X2,X0,X1] :
( X0 = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_973])]) ).
fof(f5012,plain,
! [X2,X0,X1] :
( X0 = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(cnf_transformation,[],[f3767]) ).
fof(f3767,plain,
! [X0,X1,X2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)
| X0 != X1 )
& ( X0 = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(nnf_transformation,[],[f2999]) ).
fof(f2999,plain,
! [X0,X1,X2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)
<=> X0 = X1 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(ennf_transformation,[],[f1910]) ).
fof(f1910,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)
<=> X0 = X1 ) ),
inference(rectify,[],[f728]) ).
fof(f728,axiom,
! [X11,X14,X44] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X44)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X14) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X11)
<=> X11 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
fof(f21121,plain,
spl47_972,
inference(avatar_split_clause,[],[f4916,f21119]) ).
fof(f21119,plain,
( spl47_972
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),X1),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(X2,X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_972])]) ).
fof(f4916,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),X1),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(X2,X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(cnf_transformation,[],[f2886]) ).
fof(f2886,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),X1),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(X2,X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f1834]) ).
fof(f1834,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X2)),X1),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(X2,X1)),X0)) ),
inference(rectify,[],[f703]) ).
fof(f703,axiom,
! [X7,X8,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X5,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X5)),X8),X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(X5,X8)),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__power__le) ).
fof(f21117,plain,
spl47_971,
inference(avatar_split_clause,[],[f4902,f21115]) ).
fof(f21115,plain,
( spl47_971
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0)))
| ~ class_Rings_Ocomm__semiring__0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_971])]) ).
fof(f4902,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0)))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(cnf_transformation,[],[f2874]) ).
fof(f2874,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0)))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(ennf_transformation,[],[f1822]) ).
fof(f1822,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__0(X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))) ),
inference(rectify,[],[f626]) ).
fof(f626,axiom,
! [X13,X8,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X8),X13)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X5,X8),c_Polynomial_Odegree(X5,X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__mult__le) ).
fof(f21113,plain,
spl47_970,
inference(avatar_split_clause,[],[f4876,f21111]) ).
fof(f21111,plain,
( spl47_970
<=> ! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,X0) = c_Polynomial_Odegree(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| ~ class_Groups_Ocomm__monoid__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_970])]) ).
fof(f4876,plain,
! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,X0) = c_Polynomial_Odegree(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| ~ class_Groups_Ocomm__monoid__add(X2) ),
inference(cnf_transformation,[],[f2849]) ).
fof(f2849,plain,
! [X0,X1,X2] :
( c_Polynomial_Odegree(X2,X0) = c_Polynomial_Odegree(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| ~ class_Groups_Ocomm__monoid__add(X2) ),
inference(flattening,[],[f2848]) ).
fof(f2848,plain,
! [X0,X1,X2] :
( c_Polynomial_Odegree(X2,X0) = c_Polynomial_Odegree(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| ~ class_Groups_Ocomm__monoid__add(X2) ),
inference(ennf_transformation,[],[f1802]) ).
fof(f1802,plain,
! [X0,X1,X2] :
( class_Groups_Ocomm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
=> c_Polynomial_Odegree(X2,X0) = c_Polynomial_Odegree(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0)) ) ),
inference(rectify,[],[f179]) ).
fof(f179,axiom,
! [X13,X8,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5,X8),c_Polynomial_Odegree(X5,X13))
=> c_Polynomial_Odegree(X5,X13) = c_Polynomial_Odegree(X5,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),X8,X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__add__eq__right) ).
fof(f21109,plain,
spl47_969,
inference(avatar_split_clause,[],[f4875,f21107]) ).
fof(f21107,plain,
( spl47_969
<=> ! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,X0) = c_Polynomial_Odegree(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| ~ class_Groups_Ocomm__monoid__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_969])]) ).
fof(f4875,plain,
! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,X0) = c_Polynomial_Odegree(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| ~ class_Groups_Ocomm__monoid__add(X2) ),
inference(cnf_transformation,[],[f2847]) ).
fof(f2847,plain,
! [X0,X1,X2] :
( c_Polynomial_Odegree(X2,X0) = c_Polynomial_Odegree(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| ~ class_Groups_Ocomm__monoid__add(X2) ),
inference(flattening,[],[f2846]) ).
fof(f2846,plain,
! [X0,X1,X2] :
( c_Polynomial_Odegree(X2,X0) = c_Polynomial_Odegree(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
| ~ class_Groups_Ocomm__monoid__add(X2) ),
inference(ennf_transformation,[],[f1801]) ).
fof(f1801,plain,
! [X0,X1,X2] :
( class_Groups_Ocomm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,X0))
=> c_Polynomial_Odegree(X2,X0) = c_Polynomial_Odegree(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X0,X1)) ) ),
inference(rectify,[],[f178]) ).
fof(f178,axiom,
! [X8,X13,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5,X13),c_Polynomial_Odegree(X5,X8))
=> c_Polynomial_Odegree(X5,X8) = c_Polynomial_Odegree(X5,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),X8,X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__add__eq__left) ).
fof(f21105,plain,
spl47_968,
inference(avatar_split_clause,[],[f4456,f21103]) ).
fof(f21103,plain,
( spl47_968
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_968])]) ).
fof(f4456,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(cnf_transformation,[],[f3584]) ).
fof(f3584,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)),X1))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0 )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)),X1)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(nnf_transformation,[],[f2566]) ).
fof(f2566,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)),X1))
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(ennf_transformation,[],[f1534]) ).
fof(f1534,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)),X1))
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 ) ),
inference(rectify,[],[f707]) ).
fof(f707,axiom,
! [X11,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X14)),X14))
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel2) ).
fof(f21101,plain,
( spl47_967
| ~ spl47_121
| ~ spl47_359 ),
inference(avatar_split_clause,[],[f8049,f7834,f6636,f21098]) ).
fof(f21098,plain,
( spl47_967
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_967])]) ).
fof(f6636,plain,
( spl47_121
<=> class_Groups_Ozero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_121])]) ).
fof(f7834,plain,
( spl47_359
<=> ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Groups_Ozero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_359])]) ).
fof(f8049,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)))
| ~ spl47_121
| ~ spl47_359 ),
inference(resolution,[],[f7835,f6638]) ).
fof(f6638,plain,
( class_Groups_Ozero(tc_Int_Oint)
| ~ spl47_121 ),
inference(avatar_component_clause,[],[f6636]) ).
fof(f7835,plain,
( ! [X1] :
( ~ class_Groups_Ozero(X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) )
| ~ spl47_359 ),
inference(avatar_component_clause,[],[f7834]) ).
fof(f21096,plain,
spl47_966,
inference(avatar_split_clause,[],[f4454,f21094]) ).
fof(f21094,plain,
( spl47_966
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_966])]) ).
fof(f4454,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(cnf_transformation,[],[f3583]) ).
fof(f3583,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),X1))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0 )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),X1)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(nnf_transformation,[],[f2565]) ).
fof(f2565,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),X1))
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(ennf_transformation,[],[f1533]) ).
fof(f1533,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),X1))
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 ) ),
inference(rectify,[],[f706]) ).
fof(f706,axiom,
! [X11,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X11)),X14))
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel1) ).
fof(f21092,plain,
spl47_965,
inference(avatar_split_clause,[],[f4323,f21090]) ).
fof(f21090,plain,
( spl47_965
<=> ! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) = X0
| c_Groups_Oone__class_Oone(X1) = X0
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) != c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_965])]) ).
fof(f4323,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) = X0
| c_Groups_Oone__class_Oone(X1) = X0
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) != c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(cnf_transformation,[],[f3570]) ).
fof(f3570,plain,
! [X0,X1] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = c_Groups_Oone__class_Oone(X1)
| ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) != X0
& c_Groups_Oone__class_Oone(X1) != X0 ) )
& ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) = X0
| c_Groups_Oone__class_Oone(X1) = X0
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) != c_Groups_Oone__class_Oone(X1) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(flattening,[],[f3569]) ).
fof(f3569,plain,
! [X0,X1] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = c_Groups_Oone__class_Oone(X1)
| ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) != X0
& c_Groups_Oone__class_Oone(X1) != X0 ) )
& ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) = X0
| c_Groups_Oone__class_Oone(X1) = X0
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) != c_Groups_Oone__class_Oone(X1) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(nnf_transformation,[],[f2434]) ).
fof(f2434,plain,
! [X0,X1] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = c_Groups_Oone__class_Oone(X1)
<=> ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) = X0
| c_Groups_Oone__class_Oone(X1) = X0 ) )
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(ennf_transformation,[],[f1419]) ).
fof(f1419,plain,
! [X0,X1] :
( class_Rings_Oring__1__no__zero__divisors(X1)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = c_Groups_Oone__class_Oone(X1)
<=> ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) = X0
| c_Groups_Oone__class_Oone(X1) = X0 ) ) ),
inference(rectify,[],[f593]) ).
fof(f593,axiom,
! [X15,X5] :
( class_Rings_Oring__1__no__zero__divisors(X5)
=> ( c_Groups_Oone__class_Oone(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X15)
<=> ( c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Oone__class_Oone(X5)) = X15
| c_Groups_Oone__class_Oone(X5) = X15 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).
fof(f20389,plain,
( spl47_964
| ~ spl47_122
| ~ spl47_359 ),
inference(avatar_split_clause,[],[f8048,f7834,f6641,f20386]) ).
fof(f20386,plain,
( spl47_964
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_964])]) ).
fof(f6641,plain,
( spl47_122
<=> class_Groups_Ozero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_122])]) ).
fof(f8048,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)))
| ~ spl47_122
| ~ spl47_359 ),
inference(resolution,[],[f7835,f6643]) ).
fof(f6643,plain,
( class_Groups_Ozero(tc_Nat_Onat)
| ~ spl47_122 ),
inference(avatar_component_clause,[],[f6641]) ).
fof(f20239,plain,
( spl47_963
| ~ spl47_120
| ~ spl47_359 ),
inference(avatar_split_clause,[],[f8046,f7834,f6631,f20236]) ).
fof(f20236,plain,
( spl47_963
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_963])]) ).
fof(f6631,plain,
( spl47_120
<=> class_Groups_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_120])]) ).
fof(f8046,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
| ~ spl47_120
| ~ spl47_359 ),
inference(resolution,[],[f7835,f6633]) ).
fof(f6633,plain,
( class_Groups_Ozero(tc_Complex_Ocomplex)
| ~ spl47_120 ),
inference(avatar_component_clause,[],[f6631]) ).
fof(f19775,plain,
( spl47_962
| ~ spl47_295
| ~ spl47_356 ),
inference(avatar_split_clause,[],[f8041,f7822,f7409,f19773]) ).
fof(f19773,plain,
( spl47_962
<=> ! [X0] :
( ~ hBOOL(X0)
| ~ sP11(X0,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_962])]) ).
fof(f7409,plain,
( spl47_295
<=> ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_295])]) ).
fof(f8041,plain,
( ! [X0] :
( ~ hBOOL(X0)
| ~ sP11(X0,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)) )
| ~ spl47_295
| ~ spl47_356 ),
inference(superposition,[],[f7823,f7410]) ).
fof(f7410,plain,
( ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0
| ~ spl47_295 ),
inference(avatar_component_clause,[],[f7409]) ).
fof(f19722,plain,
spl47_961,
inference(avatar_split_clause,[],[f5997,f19720]) ).
fof(f19720,plain,
( spl47_961
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_961])]) ).
fof(f5997,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(forward_demodulation,[],[f5996,f4114]) ).
fof(f5996,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(forward_demodulation,[],[f5995,f4240]) ).
fof(f5995,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(forward_demodulation,[],[f5994,f4114]) ).
fof(f5994,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(forward_demodulation,[],[f5993,f4240]) ).
fof(f5993,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(forward_demodulation,[],[f5992,f4114]) ).
fof(f5992,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(forward_demodulation,[],[f5615,f4240]) ).
fof(f5615,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(definition_unfolding,[],[f4617,f4118,f4118,f4118]) ).
fof(f4617,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(cnf_transformation,[],[f3668]) ).
fof(f3668,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ) ),
inference(flattening,[],[f3667]) ).
fof(f3667,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ) ),
inference(nnf_transformation,[],[f1609]) ).
fof(f1609,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ) ),
inference(rectify,[],[f699]) ).
fof(f699,axiom,
! [X11,X14] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X11))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X11)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).
fof(f19718,plain,
spl47_960,
inference(avatar_split_clause,[],[f5937,f19716]) ).
fof(f19716,plain,
( spl47_960
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_960])]) ).
fof(f5937,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
inference(forward_demodulation,[],[f5936,f4114]) ).
fof(f5936,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
inference(forward_demodulation,[],[f5935,f4240]) ).
fof(f5935,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(forward_demodulation,[],[f5934,f4114]) ).
fof(f5934,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(forward_demodulation,[],[f5933,f4240]) ).
fof(f5933,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(forward_demodulation,[],[f5932,f4114]) ).
fof(f5932,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(forward_demodulation,[],[f5565,f4240]) ).
fof(f5565,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(definition_unfolding,[],[f4468,f4118,f4118,f4118]) ).
fof(f4468,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(cnf_transformation,[],[f2582]) ).
fof(f2582,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(flattening,[],[f2581]) ).
fof(f2581,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(ennf_transformation,[],[f1545]) ).
fof(f1545,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
inference(rectify,[],[f696]) ).
fof(f696,axiom,
! [X21,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__mult) ).
fof(f19714,plain,
spl47_959,
inference(avatar_split_clause,[],[f5649,f19712]) ).
fof(f19712,plain,
( spl47_959
<=> ! [X0,X3,X2,X1] :
( hAPP(c_Polynomial_Ocoeff(X3,X1),X0) = hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_OpCons(X3,X2,X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Groups_Ozero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_959])]) ).
fof(f5649,plain,
! [X2,X3,X0,X1] :
( hAPP(c_Polynomial_Ocoeff(X3,X1),X0) = hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_OpCons(X3,X2,X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Groups_Ozero(X3) ),
inference(definition_unfolding,[],[f5310,f4118]) ).
fof(f5310,plain,
! [X2,X3,X0,X1] :
( hAPP(c_Polynomial_Ocoeff(X3,X1),X0) = hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_OpCons(X3,X2,X1)),c_Nat_OSuc(X0))
| ~ class_Groups_Ozero(X3) ),
inference(cnf_transformation,[],[f3255]) ).
fof(f3255,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Ocoeff(X3,X1),X0) = hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_OpCons(X3,X2,X1)),c_Nat_OSuc(X0))
| ~ class_Groups_Ozero(X3) ),
inference(ennf_transformation,[],[f2108]) ).
fof(f2108,plain,
! [X0,X1,X2,X3] :
( class_Groups_Ozero(X3)
=> hAPP(c_Polynomial_Ocoeff(X3,X1),X0) = hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_OpCons(X3,X2,X1)),c_Nat_OSuc(X0)) ),
inference(rectify,[],[f802]) ).
fof(f802,axiom,
! [X7,X8,X4,X5] :
( class_Groups_Ozero(X5)
=> hAPP(c_Polynomial_Ocoeff(X5,X8),X7) = hAPP(c_Polynomial_Ocoeff(X5,c_Polynomial_OpCons(X5,X4,X8)),c_Nat_OSuc(X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__pCons__Suc) ).
fof(f19710,plain,
spl47_958,
inference(avatar_split_clause,[],[f5539,f19708]) ).
fof(f19708,plain,
( spl47_958
<=> ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_958])]) ).
fof(f5539,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0),
inference(definition_unfolding,[],[f4255,f4118]) ).
fof(f4255,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
inference(cnf_transformation,[],[f1371]) ).
fof(f1371,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
inference(rectify,[],[f685]) ).
fof(f685,axiom,
! [X7,X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(X21)),X7) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc) ).
fof(f19706,plain,
spl47_957,
inference(avatar_split_clause,[],[f5538,f19704]) ).
fof(f19704,plain,
( spl47_957
<=> ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_957])]) ).
fof(f5538,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(definition_unfolding,[],[f4254,f4118]) ).
fof(f4254,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
inference(cnf_transformation,[],[f1370]) ).
fof(f1370,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),
inference(rectify,[],[f684]) ).
fof(f684,axiom,
! [X7,X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),c_Nat_OSuc(X7)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
fof(f19702,plain,
spl47_956,
inference(avatar_split_clause,[],[f5423,f19700]) ).
fof(f19700,plain,
( spl47_956
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_956])]) ).
fof(f5423,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4) ),
inference(cnf_transformation,[],[f3394]) ).
fof(f3394,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4) ),
inference(flattening,[],[f3393]) ).
fof(f3393,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4) ),
inference(ennf_transformation,[],[f2204]) ).
fof(f2204,plain,
! [X0,X1,X2,X3,X4] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X3,X2)
=> ( c_Orderings_Oord__class_Oless(X4,X1,X0)
=> c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ) ) ),
inference(rectify,[],[f370]) ).
fof(f370,axiom,
! [X46,X16,X17,X4,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X17)
=> ( c_Orderings_Oord__class_Oless(X5,X16,X46)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X4,X16),c_Groups_Oplus__class_Oplus(X5,X17,X46)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).
fof(f19698,plain,
spl47_955,
inference(avatar_split_clause,[],[f5422,f19696]) ).
fof(f19696,plain,
( spl47_955
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_955])]) ).
fof(f5422,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4) ),
inference(cnf_transformation,[],[f3392]) ).
fof(f3392,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4) ),
inference(flattening,[],[f3391]) ).
fof(f3391,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4) ),
inference(ennf_transformation,[],[f2203]) ).
fof(f2203,plain,
! [X0,X1,X2,X3,X4] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X3,X2)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
=> c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ) ) ),
inference(rectify,[],[f385]) ).
fof(f385,axiom,
! [X46,X16,X17,X4,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X17)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X16,X46)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X4,X16),c_Groups_Oplus__class_Oplus(X5,X17,X46)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
fof(f19694,plain,
spl47_954,
inference(avatar_split_clause,[],[f5421,f19692]) ).
fof(f19692,plain,
( spl47_954
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_954])]) ).
fof(f5421,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4) ),
inference(cnf_transformation,[],[f3390]) ).
fof(f3390,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4) ),
inference(flattening,[],[f3389]) ).
fof(f3389,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4) ),
inference(ennf_transformation,[],[f2202]) ).
fof(f2202,plain,
! [X0,X1,X2,X3,X4] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
=> ( c_Orderings_Oord__class_Oless(X4,X1,X0)
=> c_Orderings_Oord__class_Oless(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ) ) ),
inference(rectify,[],[f384]) ).
fof(f384,axiom,
! [X46,X16,X17,X4,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X17)
=> ( c_Orderings_Oord__class_Oless(X5,X16,X46)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X4,X16),c_Groups_Oplus__class_Oplus(X5,X17,X46)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
fof(f19690,plain,
( spl47_953
| ~ spl47_294
| ~ spl47_356 ),
inference(avatar_split_clause,[],[f8040,f7822,f7405,f19688]) ).
fof(f19688,plain,
( spl47_953
<=> ! [X0] :
( ~ hBOOL(X0)
| ~ sP11(X0,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_953])]) ).
fof(f7405,plain,
( spl47_294
<=> ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_294])]) ).
fof(f8040,plain,
( ! [X0] :
( ~ hBOOL(X0)
| ~ sP11(X0,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)) )
| ~ spl47_294
| ~ spl47_356 ),
inference(superposition,[],[f7823,f7406]) ).
fof(f7406,plain,
( ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0
| ~ spl47_294 ),
inference(avatar_component_clause,[],[f7405]) ).
fof(f19686,plain,
spl47_952,
inference(avatar_split_clause,[],[f5418,f19684]) ).
fof(f19684,plain,
( spl47_952
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ class_Groups_Oordered__ab__semigroup__add(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_952])]) ).
fof(f5418,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ class_Groups_Oordered__ab__semigroup__add(X4) ),
inference(cnf_transformation,[],[f3384]) ).
fof(f3384,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ class_Groups_Oordered__ab__semigroup__add(X4) ),
inference(flattening,[],[f3383]) ).
fof(f3383,plain,
! [X0,X1,X2,X3,X4] :
( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ class_Groups_Oordered__ab__semigroup__add(X4) ),
inference(ennf_transformation,[],[f2199]) ).
fof(f2199,plain,
! [X0,X1,X2,X3,X4] :
( class_Groups_Oordered__ab__semigroup__add(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Oplus__class_Oplus(X4,X3,X1),c_Groups_Oplus__class_Oplus(X4,X2,X0)) ) ) ),
inference(rectify,[],[f363]) ).
fof(f363,axiom,
! [X46,X16,X17,X4,X5] :
( class_Groups_Oordered__ab__semigroup__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X17)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X16,X46)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X4,X16),c_Groups_Oplus__class_Oplus(X5,X17,X46)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mono) ).
fof(f19682,plain,
spl47_951,
inference(avatar_split_clause,[],[f5373,f19680]) ).
fof(f19680,plain,
( spl47_951
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ~ class_Orderings_Oord(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_951])]) ).
fof(f5373,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ~ class_Orderings_Oord(X3) ),
inference(cnf_transformation,[],[f3876]) ).
fof(f3876,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) )
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0) ) )
| ~ class_Orderings_Oord(X3) ),
inference(flattening,[],[f3875]) ).
fof(f3875,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) )
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0) ) )
| ~ class_Orderings_Oord(X3) ),
inference(nnf_transformation,[],[f3330]) ).
fof(f3330,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) ) )
| ~ class_Orderings_Oord(X3) ),
inference(ennf_transformation,[],[f2166]) ).
fof(f2166,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Oord(X3)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0) ) ) ),
inference(rectify,[],[f309]) ).
fof(f309,axiom,
! [X0,X1,X5,X31] :
( class_Orderings_Oord(X31)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X5,X31),X1,X0)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X31),X0,X1)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X31),X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).
fof(f19678,plain,
spl47_950,
inference(avatar_split_clause,[],[f5319,f19676]) ).
fof(f19676,plain,
( spl47_950
<=> ! [X0,X3,X2,X1] :
( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Opcompose(X3,X2,X1)),X0) = hAPP(c_Polynomial_Opoly(X3,X2),hAPP(c_Polynomial_Opoly(X3,X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_950])]) ).
fof(f5319,plain,
! [X2,X3,X0,X1] :
( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Opcompose(X3,X2,X1)),X0) = hAPP(c_Polynomial_Opoly(X3,X2),hAPP(c_Polynomial_Opoly(X3,X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f3263]) ).
fof(f3263,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Opcompose(X3,X2,X1)),X0) = hAPP(c_Polynomial_Opoly(X3,X2),hAPP(c_Polynomial_Opoly(X3,X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f2115]) ).
fof(f2115,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Opcompose(X3,X2,X1)),X0) = hAPP(c_Polynomial_Opoly(X3,X2),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
inference(rectify,[],[f693]) ).
fof(f693,axiom,
! [X6,X13,X8,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> hAPP(c_Polynomial_Opoly(X5,c_Polynomial_Opcompose(X5,X8,X13)),X6) = hAPP(c_Polynomial_Opoly(X5,X8),hAPP(c_Polynomial_Opoly(X5,X13),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pcompose) ).
fof(f19674,plain,
spl47_949,
inference(avatar_split_clause,[],[f5167,f19672]) ).
fof(f19672,plain,
( spl47_949
<=> ! [X0,X3,X2,X1] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,X0) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,c_Polynomial_Osmult(X3,X2,X0))
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_949])]) ).
fof(f5167,plain,
! [X2,X3,X0,X1] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,X0) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,c_Polynomial_Osmult(X3,X2,X0))
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(cnf_transformation,[],[f3089]) ).
fof(f3089,plain,
! [X0,X1,X2,X3] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,X0) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,c_Polynomial_Osmult(X3,X2,X0))
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(flattening,[],[f3088]) ).
fof(f3088,plain,
! [X0,X1,X2,X3] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,X0) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,c_Polynomial_Osmult(X3,X2,X0))
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Fields_Ofield(X3) ),
inference(ennf_transformation,[],[f2011]) ).
fof(f2011,plain,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( c_Groups_Ozero__class_Ozero(X3) != X2
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,X0) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,c_Polynomial_Osmult(X3,X2,X0)) ) ),
inference(rectify,[],[f988]) ).
fof(f988,axiom,
! [X10,X6,X4,X5] :
( class_Fields_Ofield(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X4
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X5),X6,X10) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X5),X6,c_Polynomial_Osmult(X5,X4,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__smult__right) ).
fof(f19670,plain,
spl47_948,
inference(avatar_split_clause,[],[f5150,f19668]) ).
fof(f19668,plain,
( spl47_948
<=> ! [X0,X3,X2,X1] :
( c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X0),c_Rings_Oinverse__class_Odivide(X3,X1,X0))
| ~ class_Rings_Odivision__ring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_948])]) ).
fof(f5150,plain,
! [X2,X3,X0,X1] :
( c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X0),c_Rings_Oinverse__class_Odivide(X3,X1,X0))
| ~ class_Rings_Odivision__ring(X3) ),
inference(cnf_transformation,[],[f3069]) ).
fof(f3069,plain,
! [X0,X1,X2,X3] :
( c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X0),c_Rings_Oinverse__class_Odivide(X3,X1,X0))
| ~ class_Rings_Odivision__ring(X3) ),
inference(ennf_transformation,[],[f1996]) ).
fof(f1996,plain,
! [X0,X1,X2,X3] :
( class_Rings_Odivision__ring(X3)
=> c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X0),c_Rings_Oinverse__class_Odivide(X3,X1,X0)) ),
inference(rectify,[],[f906]) ).
fof(f906,axiom,
! [X16,X17,X4,X5] :
( class_Rings_Odivision__ring(X5)
=> c_Rings_Oinverse__class_Odivide(X5,c_Groups_Oplus__class_Oplus(X5,X4,X17),X16) = c_Groups_Oplus__class_Oplus(X5,c_Rings_Oinverse__class_Odivide(X5,X4,X16),c_Rings_Oinverse__class_Odivide(X5,X17,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__distrib) ).
fof(f19666,plain,
spl47_947,
inference(avatar_split_clause,[],[f5149,f19664]) ).
fof(f19664,plain,
( spl47_947
<=> ! [X0,X3,X2,X1] :
( c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1),X0) = c_Groups_Ominus__class_Ominus(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X0),c_Rings_Oinverse__class_Odivide(X3,X1,X0))
| ~ class_Rings_Odivision__ring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_947])]) ).
fof(f5149,plain,
! [X2,X3,X0,X1] :
( c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1),X0) = c_Groups_Ominus__class_Ominus(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X0),c_Rings_Oinverse__class_Odivide(X3,X1,X0))
| ~ class_Rings_Odivision__ring(X3) ),
inference(cnf_transformation,[],[f3068]) ).
fof(f3068,plain,
! [X0,X1,X2,X3] :
( c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1),X0) = c_Groups_Ominus__class_Ominus(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X0),c_Rings_Oinverse__class_Odivide(X3,X1,X0))
| ~ class_Rings_Odivision__ring(X3) ),
inference(ennf_transformation,[],[f1995]) ).
fof(f1995,plain,
! [X0,X1,X2,X3] :
( class_Rings_Odivision__ring(X3)
=> c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1),X0) = c_Groups_Ominus__class_Ominus(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X0),c_Rings_Oinverse__class_Odivide(X3,X1,X0)) ),
inference(rectify,[],[f902]) ).
fof(f902,axiom,
! [X16,X17,X4,X5] :
( class_Rings_Odivision__ring(X5)
=> c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,X4,X17),X16) = c_Groups_Ominus__class_Ominus(X5,c_Rings_Oinverse__class_Odivide(X5,X4,X16),c_Rings_Oinverse__class_Odivide(X5,X17,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__divide__distrib) ).
fof(f19662,plain,
spl47_946,
inference(avatar_split_clause,[],[f5125,f19660]) ).
fof(f19660,plain,
( spl47_946
<=> ! [X0,X3,X2,X1] :
( c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X0),c_Rings_Oinverse__class_Odivide(X3,X1,X0))
| ~ class_RealVector_Oreal__normed__field(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_946])]) ).
fof(f5125,plain,
! [X2,X3,X0,X1] :
( c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X0),c_Rings_Oinverse__class_Odivide(X3,X1,X0))
| ~ class_RealVector_Oreal__normed__field(X3) ),
inference(cnf_transformation,[],[f3056]) ).
fof(f3056,plain,
! [X0,X1,X2,X3] :
( c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X0),c_Rings_Oinverse__class_Odivide(X3,X1,X0))
| ~ class_RealVector_Oreal__normed__field(X3) ),
inference(ennf_transformation,[],[f1987]) ).
fof(f1987,plain,
! [X0,X1,X2,X3] :
( class_RealVector_Oreal__normed__field(X3)
=> c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X0),c_Rings_Oinverse__class_Odivide(X3,X1,X0)) ),
inference(rectify,[],[f923]) ).
fof(f923,axiom,
! [X75,X10,X6,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> c_Rings_Oinverse__class_Odivide(X5,c_Groups_Oplus__class_Oplus(X5,X6,X10),X75) = c_Groups_Oplus__class_Oplus(X5,c_Rings_Oinverse__class_Odivide(X5,X6,X75),c_Rings_Oinverse__class_Odivide(X5,X10,X75)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Oadd) ).
fof(f19658,plain,
spl47_945,
inference(avatar_split_clause,[],[f5124,f19656]) ).
fof(f19656,plain,
( spl47_945
<=> ! [X0,X3,X2,X1] :
( c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1),X0) = c_Groups_Ominus__class_Ominus(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X0),c_Rings_Oinverse__class_Odivide(X3,X1,X0))
| ~ class_RealVector_Oreal__normed__field(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_945])]) ).
fof(f5124,plain,
! [X2,X3,X0,X1] :
( c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1),X0) = c_Groups_Ominus__class_Ominus(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X0),c_Rings_Oinverse__class_Odivide(X3,X1,X0))
| ~ class_RealVector_Oreal__normed__field(X3) ),
inference(cnf_transformation,[],[f3055]) ).
fof(f3055,plain,
! [X0,X1,X2,X3] :
( c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1),X0) = c_Groups_Ominus__class_Ominus(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X0),c_Rings_Oinverse__class_Odivide(X3,X1,X0))
| ~ class_RealVector_Oreal__normed__field(X3) ),
inference(ennf_transformation,[],[f1986]) ).
fof(f1986,plain,
! [X0,X1,X2,X3] :
( class_RealVector_Oreal__normed__field(X3)
=> c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ominus__class_Ominus(X3,X2,X1),X0) = c_Groups_Ominus__class_Ominus(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X0),c_Rings_Oinverse__class_Odivide(X3,X1,X0)) ),
inference(rectify,[],[f903]) ).
fof(f903,axiom,
! [X75,X10,X6,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ominus__class_Ominus(X5,X6,X10),X75) = c_Groups_Ominus__class_Ominus(X5,c_Rings_Oinverse__class_Odivide(X5,X6,X75),c_Rings_Oinverse__class_Odivide(X5,X10,X75)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Odiff) ).
fof(f19654,plain,
spl47_944,
inference(avatar_split_clause,[],[f5093,f19652]) ).
fof(f19652,plain,
( spl47_944
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| X0 = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_944])]) ).
fof(f5093,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| X0 = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0) ),
inference(cnf_transformation,[],[f3804]) ).
fof(f3804,plain,
! [X0,X1,X2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2
& X0 != X1 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| X0 = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0) ) ),
inference(flattening,[],[f3803]) ).
fof(f3803,plain,
! [X0,X1,X2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2
& X0 != X1 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| X0 = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0) ) ),
inference(nnf_transformation,[],[f1949]) ).
fof(f1949,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| X0 = X1 ) ),
inference(rectify,[],[f651]) ).
fof(f651,axiom,
! [X11,X14,X44] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X14) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X11)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X44
| X11 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel1) ).
fof(f19650,plain,
spl47_943,
inference(avatar_split_clause,[],[f5090,f19648]) ).
fof(f19648,plain,
( spl47_943
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| X0 = X2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_943])]) ).
fof(f5090,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| X0 = X2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) ),
inference(cnf_transformation,[],[f3802]) ).
fof(f3802,plain,
! [X0,X1,X2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
& X0 != X2 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| X0 = X2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) ) ),
inference(flattening,[],[f3801]) ).
fof(f3801,plain,
! [X0,X1,X2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
& X0 != X2 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| X0 = X2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) ) ),
inference(nnf_transformation,[],[f1948]) ).
fof(f1948,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| X0 = X2 ) ),
inference(rectify,[],[f650]) ).
fof(f650,axiom,
! [X11,X44,X14] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X44) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X44)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X44
| X11 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel2) ).
fof(f19646,plain,
( spl47_942
| ~ spl47_293
| ~ spl47_356 ),
inference(avatar_split_clause,[],[f8039,f7822,f7401,f19644]) ).
fof(f19644,plain,
( spl47_942
<=> ! [X0] :
( ~ hBOOL(X0)
| ~ sP11(c_Groups_Oone__class_Oone(tc_Nat_Onat),X0,c_Groups_Otimes__class_Otimes(tc_Nat_Onat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_942])]) ).
fof(f7401,plain,
( spl47_293
<=> ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_293])]) ).
fof(f8039,plain,
( ! [X0] :
( ~ hBOOL(X0)
| ~ sP11(c_Groups_Oone__class_Oone(tc_Nat_Onat),X0,c_Groups_Otimes__class_Otimes(tc_Nat_Onat)) )
| ~ spl47_293
| ~ spl47_356 ),
inference(superposition,[],[f7823,f7402]) ).
fof(f7402,plain,
( ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| ~ spl47_293 ),
inference(avatar_component_clause,[],[f7401]) ).
fof(f19642,plain,
spl47_941,
inference(avatar_split_clause,[],[f5043,f19640]) ).
fof(f19640,plain,
( spl47_941
<=> ! [X0,X6,X2,X1] :
( hBOOL(hAPP(X1,sK42(X0,X1,X2)))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X6)))
| ~ class_Rings_Osemiring__0(X2)
| ~ class_Rings_Odvd(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_941])]) ).
fof(f5043,plain,
! [X2,X0,X1,X6] :
( hBOOL(hAPP(X1,sK42(X0,X1,X2)))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X6)))
| ~ class_Rings_Osemiring__0(X2)
| ~ class_Rings_Odvd(X2) ),
inference(cnf_transformation,[],[f3776]) ).
fof(f19638,plain,
spl47_940,
inference(avatar_split_clause,[],[f4984,f19636]) ).
fof(f19636,plain,
( spl47_940
<=> ! [X2,X0,X1] :
( X0 = X1
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_940])]) ).
fof(f4984,plain,
! [X2,X0,X1] :
( X0 = X1
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f3759]) ).
fof(f3759,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)
| X0 != X1 )
& ( X0 = X1
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(nnf_transformation,[],[f2965]) ).
fof(f2965,plain,
! [X0,X1,X2] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)
<=> X0 = X1 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(flattening,[],[f2964]) ).
fof(f2964,plain,
! [X0,X1,X2] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)
<=> X0 = X1 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1888]) ).
fof(f1888,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)
<=> X0 = X1 ) ) ),
inference(rectify,[],[f785]) ).
fof(f785,axiom,
! [X11,X14,X44] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X14)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X11)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X14,X44) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X44)
<=> X11 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__diff__iff) ).
fof(f19634,plain,
spl47_939,
inference(avatar_split_clause,[],[f4901,f19632]) ).
fof(f19632,plain,
( spl47_939
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Opcompose(X2,X1,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(X2,X1)),c_Polynomial_Odegree(X2,X0)))
| ~ class_Rings_Ocomm__semiring__0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_939])]) ).
fof(f4901,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Opcompose(X2,X1,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(X2,X1)),c_Polynomial_Odegree(X2,X0)))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(cnf_transformation,[],[f2873]) ).
fof(f2873,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Opcompose(X2,X1,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(X2,X1)),c_Polynomial_Odegree(X2,X0)))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(ennf_transformation,[],[f1821]) ).
fof(f1821,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__0(X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Opcompose(X2,X1,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(X2,X1)),c_Polynomial_Odegree(X2,X0))) ),
inference(rectify,[],[f676]) ).
fof(f676,axiom,
! [X13,X8,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X5,c_Polynomial_Opcompose(X5,X8,X13)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(X5,X8)),c_Polynomial_Odegree(X5,X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__pcompose__le) ).
fof(f19630,plain,
spl47_938,
inference(avatar_split_clause,[],[f4766,f19628]) ).
fof(f19628,plain,
( spl47_938
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,X1,X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Groups_Oordered__comm__monoid__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_938])]) ).
fof(f4766,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,X1,X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(cnf_transformation,[],[f2728]) ).
fof(f2728,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,X1,X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(flattening,[],[f2727]) ).
fof(f2727,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,X1,X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(ennf_transformation,[],[f1722]) ).
fof(f1722,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__comm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X0)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,X1,X0)) ) ) ),
inference(rectify,[],[f381]) ).
fof(f381,axiom,
! [X17,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X17)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,X4,X17)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).
fof(f19626,plain,
spl47_937,
inference(avatar_split_clause,[],[f4764,f19624]) ).
fof(f19624,plain,
( spl47_937
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__comm__monoid__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_937])]) ).
fof(f4764,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(cnf_transformation,[],[f2724]) ).
fof(f2724,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(flattening,[],[f2723]) ).
fof(f2723,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(ennf_transformation,[],[f1720]) ).
fof(f1720,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__comm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
inference(rectify,[],[f380]) ).
fof(f380,axiom,
! [X17,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,c_Groups_Ozero__class_Ozero(X5))
=> ( c_Orderings_Oord__class_Oless(X5,X17,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X4,X17),c_Groups_Ozero__class_Ozero(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__neg) ).
fof(f19622,plain,
spl47_936,
inference(avatar_split_clause,[],[f4763,f19620]) ).
fof(f19620,plain,
( spl47_936
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__comm__monoid__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_936])]) ).
fof(f4763,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(cnf_transformation,[],[f2722]) ).
fof(f2722,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(flattening,[],[f2721]) ).
fof(f2721,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(ennf_transformation,[],[f1719]) ).
fof(f1719,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__comm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
inference(rectify,[],[f305]) ).
fof(f305,axiom,
! [X17,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,c_Groups_Ozero__class_Ozero(X5))
=> ( c_Orderings_Oord__class_Oless__eq(X5,X17,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X4,X17),c_Groups_Ozero__class_Ozero(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
fof(f19618,plain,
spl47_935,
inference(avatar_split_clause,[],[f4757,f19616]) ).
fof(f19616,plain,
( spl47_935
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__comm__monoid__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_935])]) ).
fof(f4757,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(cnf_transformation,[],[f2714]) ).
fof(f2714,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(flattening,[],[f2713]) ).
fof(f2713,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(ennf_transformation,[],[f1715]) ).
fof(f1715,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__comm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
inference(rectify,[],[f306]) ).
fof(f306,axiom,
! [X17,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,c_Groups_Ozero__class_Ozero(X5))
=> ( c_Orderings_Oord__class_Oless(X5,X17,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X4,X17),c_Groups_Ozero__class_Ozero(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
fof(f19614,plain,
spl47_934,
inference(avatar_split_clause,[],[f4756,f19612]) ).
fof(f19612,plain,
( spl47_934
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__comm__monoid__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_934])]) ).
fof(f4756,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(cnf_transformation,[],[f2712]) ).
fof(f2712,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(flattening,[],[f2711]) ).
fof(f2711,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(ennf_transformation,[],[f1714]) ).
fof(f1714,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__comm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
inference(rectify,[],[f373]) ).
fof(f373,axiom,
! [X17,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,c_Groups_Ozero__class_Ozero(X5))
=> ( c_Orderings_Oord__class_Oless__eq(X5,X17,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X4,X17),c_Groups_Ozero__class_Ozero(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(f19610,plain,
spl47_933,
inference(avatar_split_clause,[],[f4659,f19608]) ).
fof(f19608,plain,
( spl47_933
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)))
| ~ class_Rings_Olinordered__ring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_933])]) ).
fof(f4659,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)))
| ~ class_Rings_Olinordered__ring(X2) ),
inference(cnf_transformation,[],[f2642]) ).
fof(f2642,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)))
| ~ class_Rings_Olinordered__ring(X2) ),
inference(ennf_transformation,[],[f1662]) ).
fof(f1662,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__ring(X2)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0))) ),
inference(rectify,[],[f617]) ).
fof(f617,axiom,
! [X10,X6,X5] :
( class_Rings_Olinordered__ring(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).
fof(f19606,plain,
spl47_932,
inference(avatar_split_clause,[],[f4658,f19604]) ).
fof(f19604,plain,
( spl47_932
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__ring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_932])]) ).
fof(f4658,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__ring(X2) ),
inference(cnf_transformation,[],[f2641]) ).
fof(f2641,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__ring(X2) ),
inference(ennf_transformation,[],[f1661]) ).
fof(f1661,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__ring(X2)
=> ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)),c_Groups_Ozero__class_Ozero(X2)) ),
inference(rectify,[],[f619]) ).
fof(f619,axiom,
! [X10,X6,X5] :
( class_Rings_Olinordered__ring(X5)
=> ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X10),X10)),c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).
fof(f19602,plain,
( spl47_931
| ~ spl47_292
| ~ spl47_356 ),
inference(avatar_split_clause,[],[f8038,f7822,f7397,f19600]) ).
fof(f19600,plain,
( spl47_931
<=> ! [X0] :
( ~ hBOOL(X0)
| ~ sP11(c_Groups_Oone__class_Oone(tc_Int_Oint),X0,c_Groups_Otimes__class_Otimes(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_931])]) ).
fof(f7397,plain,
( spl47_292
<=> ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_292])]) ).
fof(f8038,plain,
( ! [X0] :
( ~ hBOOL(X0)
| ~ sP11(c_Groups_Oone__class_Oone(tc_Int_Oint),X0,c_Groups_Otimes__class_Otimes(tc_Int_Oint)) )
| ~ spl47_292
| ~ spl47_356 ),
inference(superposition,[],[f7823,f7398]) ).
fof(f7398,plain,
( ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0
| ~ spl47_292 ),
inference(avatar_component_clause,[],[f7397]) ).
fof(f19598,plain,
spl47_930,
inference(avatar_split_clause,[],[f4614,f19596]) ).
fof(f19596,plain,
( spl47_930
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_930])]) ).
fof(f4614,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(cnf_transformation,[],[f3666]) ).
fof(f3666,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ) ),
inference(flattening,[],[f3665]) ).
fof(f3665,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ) ),
inference(nnf_transformation,[],[f1608]) ).
fof(f1608,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
inference(rectify,[],[f682]) ).
fof(f682,axiom,
! [X11,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X11))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X11)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
fof(f19594,plain,
spl47_929,
inference(avatar_split_clause,[],[f4444,f19592]) ).
fof(f19592,plain,
( spl47_929
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_929])]) ).
fof(f4444,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(cnf_transformation,[],[f2552]) ).
fof(f2552,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(flattening,[],[f2551]) ).
fof(f2551,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(ennf_transformation,[],[f1525]) ).
fof(f1525,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)) ) ),
inference(rectify,[],[f657]) ).
fof(f657,axiom,
! [X10,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X10)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X6),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
fof(f19396,plain,
( spl47_928
| ~ spl47_345
| ~ spl47_356 ),
inference(avatar_split_clause,[],[f8029,f7822,f7778,f19394]) ).
fof(f19394,plain,
( spl47_928
<=> ! [X0,X1] :
( ~ sP11(X0,c_Groups_Oone__class_Oone(X1),c_Rings_Odvd__class_Odvd(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_928])]) ).
fof(f7778,plain,
( spl47_345
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Oone__class_Oone(X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_345])]) ).
fof(f8029,plain,
( ! [X0,X1] :
( ~ sP11(X0,c_Groups_Oone__class_Oone(X1),c_Rings_Odvd__class_Odvd(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) )
| ~ spl47_345
| ~ spl47_356 ),
inference(resolution,[],[f7823,f7779]) ).
fof(f7779,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Oone__class_Oone(X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) )
| ~ spl47_345 ),
inference(avatar_component_clause,[],[f7778]) ).
fof(f19235,plain,
( spl47_927
| ~ spl47_344
| ~ spl47_356 ),
inference(avatar_split_clause,[],[f8028,f7822,f7774,f19233]) ).
fof(f19233,plain,
( spl47_927
<=> ! [X0,X1] :
( ~ sP11(c_Groups_Ozero__class_Ozero(X0),X1,c_Rings_Odvd__class_Odvd(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_927])]) ).
fof(f7774,plain,
( spl47_344
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_344])]) ).
fof(f8028,plain,
( ! [X0,X1] :
( ~ sP11(c_Groups_Ozero__class_Ozero(X0),X1,c_Rings_Odvd__class_Odvd(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) )
| ~ spl47_344
| ~ spl47_356 ),
inference(resolution,[],[f7823,f7775]) ).
fof(f7775,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Ocomm__semiring__1(X1) )
| ~ spl47_344 ),
inference(avatar_component_clause,[],[f7774]) ).
fof(f18790,plain,
( ~ spl47_51
| ~ spl47_926
| ~ spl47_222
| ~ spl47_350 ),
inference(avatar_split_clause,[],[f7964,f7798,f7074,f18787,f6286]) ).
fof(f6286,plain,
( spl47_51
<=> class_Orderings_Olinorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_51])]) ).
fof(f18787,plain,
( spl47_926
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_926])]) ).
fof(f7074,plain,
( spl47_222
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_222])]) ).
fof(f7798,plain,
( spl47_350
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_350])]) ).
fof(f7964,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Orderings_Olinorder(tc_Int_Oint)
| ~ spl47_222
| ~ spl47_350 ),
inference(resolution,[],[f7799,f7076]) ).
fof(f7076,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl47_222 ),
inference(avatar_component_clause,[],[f7074]) ).
fof(f7799,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl47_350 ),
inference(avatar_component_clause,[],[f7798]) ).
fof(f18785,plain,
spl47_925,
inference(avatar_split_clause,[],[f5931,f18783]) ).
fof(f18783,plain,
( spl47_925
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_925])]) ).
fof(f5931,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(forward_demodulation,[],[f5930,f4114]) ).
fof(f5930,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(forward_demodulation,[],[f5929,f4240]) ).
fof(f5929,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(forward_demodulation,[],[f5928,f4114]) ).
fof(f5928,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(forward_demodulation,[],[f5564,f4240]) ).
fof(f5564,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(definition_unfolding,[],[f4467,f4118,f4118]) ).
fof(f4467,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(cnf_transformation,[],[f2580]) ).
fof(f2580,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(flattening,[],[f2579]) ).
fof(f2579,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(ennf_transformation,[],[f1544]) ).
fof(f1544,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ) ),
inference(rectify,[],[f697]) ).
fof(f697,axiom,
! [X21,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).
fof(f18781,plain,
spl47_924,
inference(avatar_split_clause,[],[f5927,f18779]) ).
fof(f18779,plain,
( spl47_924
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_924])]) ).
fof(f5927,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
inference(forward_demodulation,[],[f5926,f4114]) ).
fof(f5926,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
inference(forward_demodulation,[],[f5925,f4240]) ).
fof(f5925,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(forward_demodulation,[],[f5924,f4114]) ).
fof(f5924,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(forward_demodulation,[],[f5563,f4240]) ).
fof(f5563,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(definition_unfolding,[],[f4466,f4118,f4118]) ).
fof(f4466,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(cnf_transformation,[],[f2578]) ).
fof(f2578,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(flattening,[],[f2577]) ).
fof(f2577,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(ennf_transformation,[],[f1543]) ).
fof(f1543,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
inference(rectify,[],[f698]) ).
fof(f698,axiom,
! [X21,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).
fof(f18777,plain,
spl47_923,
inference(avatar_split_clause,[],[f5917,f18775]) ).
fof(f18775,plain,
( spl47_923
<=> ! [X0,X1] :
( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK33(X0,X1))))
| ~ hBOOL(hAPP(X1,X0))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_923])]) ).
fof(f5917,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK33(X0,X1))))
| ~ hBOOL(hAPP(X1,X0))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(forward_demodulation,[],[f4440,f4240]) ).
fof(f4440,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK33(X0,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(X1,X0))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(cnf_transformation,[],[f3580]) ).
fof(f3580,plain,
! [X0,X1] :
( ( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK33(X0,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [X3] :
( ~ hBOOL(hAPP(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,sK33(X0,X1)) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK33(X0,X1),X0) )
| ~ hBOOL(hAPP(X1,X0))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f2546,f3579]) ).
fof(f3579,plain,
! [X0,X1] :
( ? [X2] :
( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [X3] :
( ~ hBOOL(hAPP(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) )
=> ( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK33(X0,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [X3] :
( ~ hBOOL(hAPP(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,sK33(X0,X1)) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK33(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f2546,plain,
! [X0,X1] :
( ? [X2] :
( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [X3] :
( ~ hBOOL(hAPP(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) )
| ~ hBOOL(hAPP(X1,X0))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(flattening,[],[f2545]) ).
fof(f2545,plain,
! [X0,X1] :
( ? [X2] :
( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [X3] :
( ~ hBOOL(hAPP(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) )
| ~ hBOOL(hAPP(X1,X0))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(ennf_transformation,[],[f1521]) ).
fof(f1521,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X1,X0))
=> ? [X2] :
( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
=> ~ hBOOL(hAPP(X1,X3)) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) ) ) ),
inference(rectify,[],[f753]) ).
fof(f753,axiom,
! [X11,X39] :
( ~ hBOOL(hAPP(X39,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X39,X11))
=> ? [X45] :
( hBOOL(hAPP(X39,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X45,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [X78] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X78,X45)
=> ~ hBOOL(hAPP(X39,X78)) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X45,X11) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).
fof(f18773,plain,
spl47_922,
inference(avatar_split_clause,[],[f5768,f18771]) ).
fof(f18771,plain,
( spl47_922
<=> ! [X2,X0] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X0)),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Rings_Oidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_922])]) ).
fof(f5768,plain,
! [X2,X0] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X0)),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Rings_Oidom(X2) ),
inference(equality_resolution,[],[f4838]) ).
fof(f4838,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X0)
| c_Groups_Ouminus__class_Ouminus(X2,X0) != X1
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f3731]) ).
fof(f18769,plain,
spl47_921,
inference(avatar_split_clause,[],[f5631,f18767]) ).
fof(f18767,plain,
( spl47_921
<=> ! [X2,X0,X1] :
( c_Polynomial_OpCons(X2,c_Groups_Ozero__class_Ozero(X2),c_Polynomial_Omonom(X2,X1,X0)) = c_Polynomial_Omonom(X2,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Groups_Ozero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_921])]) ).
fof(f5631,plain,
! [X2,X0,X1] :
( c_Polynomial_OpCons(X2,c_Groups_Ozero__class_Ozero(X2),c_Polynomial_Omonom(X2,X1,X0)) = c_Polynomial_Omonom(X2,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Groups_Ozero(X2) ),
inference(definition_unfolding,[],[f4880,f4118]) ).
fof(f4880,plain,
! [X2,X0,X1] :
( c_Polynomial_Omonom(X2,X1,c_Nat_OSuc(X0)) = c_Polynomial_OpCons(X2,c_Groups_Ozero__class_Ozero(X2),c_Polynomial_Omonom(X2,X1,X0))
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f2853]) ).
fof(f2853,plain,
! [X0,X1,X2] :
( c_Polynomial_Omonom(X2,X1,c_Nat_OSuc(X0)) = c_Polynomial_OpCons(X2,c_Groups_Ozero__class_Ozero(X2),c_Polynomial_Omonom(X2,X1,X0))
| ~ class_Groups_Ozero(X2) ),
inference(ennf_transformation,[],[f1806]) ).
fof(f1806,plain,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> c_Polynomial_Omonom(X2,X1,c_Nat_OSuc(X0)) = c_Polynomial_OpCons(X2,c_Groups_Ozero__class_Ozero(X2),c_Polynomial_Omonom(X2,X1,X0)) ),
inference(rectify,[],[f132]) ).
fof(f132,axiom,
! [X7,X4,X5] :
( class_Groups_Ozero(X5)
=> c_Polynomial_Omonom(X5,X4,c_Nat_OSuc(X7)) = c_Polynomial_OpCons(X5,c_Groups_Ozero__class_Ozero(X5),c_Polynomial_Omonom(X5,X4,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__Suc) ).
fof(f18765,plain,
spl47_920,
inference(avatar_split_clause,[],[f5556,f18763]) ).
fof(f18763,plain,
( spl47_920
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_920])]) ).
fof(f5556,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(definition_unfolding,[],[f4458,f4118,f4118]) ).
fof(f4458,plain,
! [X0,X1] :
( c_Nat_OSuc(X0) = X1
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
inference(cnf_transformation,[],[f2568]) ).
fof(f2568,plain,
! [X0,X1] :
( c_Nat_OSuc(X0) = X1
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
inference(flattening,[],[f2567]) ).
fof(f2567,plain,
! [X0,X1] :
( c_Nat_OSuc(X0) = X1
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
inference(ennf_transformation,[],[f1535]) ).
fof(f1535,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> c_Nat_OSuc(X0) = X1 ) ),
inference(rectify,[],[f99]) ).
fof(f99,axiom,
! [X7,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,c_Nat_OSuc(X7))
=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X7)
=> c_Nat_OSuc(X7) = X21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucE) ).
fof(f18761,plain,
spl47_919,
inference(avatar_split_clause,[],[f5553,f18759]) ).
fof(f18759,plain,
( spl47_919
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_919])]) ).
fof(f5553,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f4437,f4118,f4118]) ).
fof(f4437,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
| c_Nat_OSuc(X1) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2544]) ).
fof(f2544,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
| c_Nat_OSuc(X1) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(flattening,[],[f2543]) ).
fof(f2543,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
| c_Nat_OSuc(X1) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1520]) ).
fof(f1520,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> ( c_Nat_OSuc(X1) != X0
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ) ),
inference(rectify,[],[f224]) ).
fof(f224,axiom,
! [X7,X21] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X7)
=> ( c_Nat_OSuc(X21) != X7
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X21),X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).
fof(f18757,plain,
spl47_918,
inference(avatar_split_clause,[],[f5455,f18755]) ).
fof(f18755,plain,
( spl47_918
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,X4),X2,X1),X0) = c_Groups_Ominus__class_Ominus(X4,hAPP(X2,X0),hAPP(X1,X0))
| ~ class_Groups_Ominus(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_918])]) ).
fof(f5455,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,X4),X2,X1),X0) = c_Groups_Ominus__class_Ominus(X4,hAPP(X2,X0),hAPP(X1,X0))
| ~ class_Groups_Ominus(X4) ),
inference(cnf_transformation,[],[f3429]) ).
fof(f3429,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,X4),X2,X1),X0) = c_Groups_Ominus__class_Ominus(X4,hAPP(X2,X0),hAPP(X1,X0))
| ~ class_Groups_Ominus(X4) ),
inference(ennf_transformation,[],[f2228]) ).
fof(f2228,plain,
! [X0,X1,X2,X3,X4] :
( class_Groups_Ominus(X4)
=> hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,X4),X2,X1),X0) = c_Groups_Ominus__class_Ominus(X4,hAPP(X2,X0),hAPP(X1,X0)) ),
inference(rectify,[],[f782]) ).
fof(f782,axiom,
! [X15,X79,X58,X31,X5] :
( class_Groups_Ominus(X5)
=> hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31,X5),X58,X79),X15) = c_Groups_Ominus__class_Ominus(X5,hAPP(X58,X15),hAPP(X79,X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__apply) ).
fof(f18753,plain,
spl47_917,
inference(avatar_split_clause,[],[f5417,f18751]) ).
fof(f18751,plain,
( spl47_917
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ~ class_Groups_Oordered__ab__group__add(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_917])]) ).
fof(f5417,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0)
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ~ class_Groups_Oordered__ab__group__add(X4) ),
inference(cnf_transformation,[],[f3889]) ).
fof(f3889,plain,
! [X0,X1,X2,X3,X4] :
( ( ( c_Orderings_Oord__class_Oless(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X4,X1,X0) )
& ( c_Orderings_Oord__class_Oless(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X4,X3,X2) ) )
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ~ class_Groups_Oordered__ab__group__add(X4) ),
inference(nnf_transformation,[],[f3382]) ).
fof(f3382,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Orderings_Oord__class_Oless(X4,X3,X2)
<=> c_Orderings_Oord__class_Oless(X4,X1,X0) )
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ~ class_Groups_Oordered__ab__group__add(X4) ),
inference(flattening,[],[f3381]) ).
fof(f3381,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Orderings_Oord__class_Oless(X4,X3,X2)
<=> c_Orderings_Oord__class_Oless(X4,X1,X0) )
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ~ class_Groups_Oordered__ab__group__add(X4) ),
inference(ennf_transformation,[],[f2198]) ).
fof(f2198,plain,
! [X0,X1,X2,X3,X4] :
( class_Groups_Oordered__ab__group__add(X4)
=> ( c_Groups_Ominus__class_Ominus(X4,X3,X2) = c_Groups_Ominus__class_Ominus(X4,X1,X0)
=> ( c_Orderings_Oord__class_Oless(X4,X3,X2)
<=> c_Orderings_Oord__class_Oless(X4,X1,X0) ) ) ),
inference(rectify,[],[f796]) ).
fof(f796,axiom,
! [X52,X24,X29,X12,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Groups_Ominus__class_Ominus(X5,X12,X29) = c_Groups_Ominus__class_Ominus(X5,X24,X52)
=> ( c_Orderings_Oord__class_Oless(X5,X12,X29)
<=> c_Orderings_Oord__class_Oless(X5,X24,X52) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).
fof(f18749,plain,
spl47_916,
inference(avatar_split_clause,[],[f5415,f18747]) ).
fof(f18747,plain,
( spl47_916
<=> ! [X4,X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ~ class_Groups_Oordered__ab__group__add(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_916])]) ).
fof(f5415,plain,
! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ~ class_Groups_Oordered__ab__group__add(X4) ),
inference(cnf_transformation,[],[f3888]) ).
fof(f3888,plain,
! [X0,X1,X2,X3,X4] :
( ( ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(X4,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X2) ) )
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ~ class_Groups_Oordered__ab__group__add(X4) ),
inference(nnf_transformation,[],[f3380]) ).
fof(f3380,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
<=> c_Orderings_Oord__class_Oless__eq(X4,X1,X0) )
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ~ class_Groups_Oordered__ab__group__add(X4) ),
inference(flattening,[],[f3379]) ).
fof(f3379,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
<=> c_Orderings_Oord__class_Oless__eq(X4,X1,X0) )
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ~ class_Groups_Oordered__ab__group__add(X4) ),
inference(ennf_transformation,[],[f2197]) ).
fof(f2197,plain,
! [X0,X1,X2,X3,X4] :
( class_Groups_Oordered__ab__group__add(X4)
=> ( c_Groups_Ominus__class_Ominus(X4,X3,X2) = c_Groups_Ominus__class_Ominus(X4,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X3,X2)
<=> c_Orderings_Oord__class_Oless__eq(X4,X1,X0) ) ) ),
inference(rectify,[],[f797]) ).
fof(f797,axiom,
! [X52,X24,X29,X12,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Groups_Ominus__class_Ominus(X5,X12,X29) = c_Groups_Ominus__class_Ominus(X5,X24,X52)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,X29)
<=> c_Orderings_Oord__class_Oless__eq(X5,X24,X52) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).
fof(f18741,plain,
spl47_915,
inference(avatar_split_clause,[],[f5404,f18739]) ).
fof(f18739,plain,
( spl47_915
<=> ! [X4,X0,X3,X2,X1] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X2),X0) = X4
| ~ sP25(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_915])]) ).
fof(f5404,plain,
! [X2,X3,X0,X1,X4] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X2),X0) = X4
| ~ sP25(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f3884]) ).
fof(f18737,plain,
spl47_914,
inference(avatar_split_clause,[],[f5318,f18735]) ).
fof(f18735,plain,
( spl47_914
<=> ! [X0,X3,X2,X1] :
( hAPP(c_Polynomial_Opoly(X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X2,X1)),X0) = hAPP(c_Polynomial_Opoly(X3,X2),c_Groups_Oplus__class_Oplus(X3,X1,X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_914])]) ).
fof(f5318,plain,
! [X2,X3,X0,X1] :
( hAPP(c_Polynomial_Opoly(X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X2,X1)),X0) = hAPP(c_Polynomial_Opoly(X3,X2),c_Groups_Oplus__class_Oplus(X3,X1,X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f3262]) ).
fof(f3262,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Opoly(X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X2,X1)),X0) = hAPP(c_Polynomial_Opoly(X3,X2),c_Groups_Oplus__class_Oplus(X3,X1,X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f2114]) ).
fof(f2114,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(c_Polynomial_Opoly(X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X2,X1)),X0) = hAPP(c_Polynomial_Opoly(X3,X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)) ),
inference(rectify,[],[f207]) ).
fof(f207,axiom,
! [X6,X35,X8,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> hAPP(c_Polynomial_Opoly(X5,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5,X8,X35)),X6) = hAPP(c_Polynomial_Opoly(X5,X8),c_Groups_Oplus__class_Oplus(X5,X35,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__offset__poly) ).
fof(f18733,plain,
spl47_913,
inference(avatar_split_clause,[],[f5317,f18731]) ).
fof(f18731,plain,
( spl47_913
<=> ! [X0,X3,X2,X1] :
( c_Polynomial_Osmult(X3,X2,c_Polynomial_Osmult(X3,X1,X0)) = c_Polynomial_Osmult(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
| ~ class_Rings_Ocomm__semiring__0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_913])]) ).
fof(f5317,plain,
! [X2,X3,X0,X1] :
( c_Polynomial_Osmult(X3,X2,c_Polynomial_Osmult(X3,X1,X0)) = c_Polynomial_Osmult(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f3261]) ).
fof(f3261,plain,
! [X0,X1,X2,X3] :
( c_Polynomial_Osmult(X3,X2,c_Polynomial_Osmult(X3,X1,X0)) = c_Polynomial_Osmult(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f2113]) ).
fof(f2113,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Polynomial_Osmult(X3,X2,c_Polynomial_Osmult(X3,X1,X0)) = c_Polynomial_Osmult(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0) ),
inference(rectify,[],[f543]) ).
fof(f543,axiom,
! [X8,X17,X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Polynomial_Osmult(X5,X4,c_Polynomial_Osmult(X5,X17,X8)) = c_Polynomial_Osmult(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__smult) ).
fof(f18729,plain,
spl47_912,
inference(avatar_split_clause,[],[f5316,f18727]) ).
fof(f18727,plain,
( spl47_912
<=> ! [X0,X3,X2,X1] :
( c_Polynomial_Osmult(X3,X2,c_Polynomial_Omonom(X3,X1,X0)) = c_Polynomial_Omonom(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
| ~ class_Rings_Ocomm__semiring__0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_912])]) ).
fof(f5316,plain,
! [X2,X3,X0,X1] :
( c_Polynomial_Osmult(X3,X2,c_Polynomial_Omonom(X3,X1,X0)) = c_Polynomial_Omonom(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f3260]) ).
fof(f3260,plain,
! [X0,X1,X2,X3] :
( c_Polynomial_Osmult(X3,X2,c_Polynomial_Omonom(X3,X1,X0)) = c_Polynomial_Omonom(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f2112]) ).
fof(f2112,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Polynomial_Osmult(X3,X2,c_Polynomial_Omonom(X3,X1,X0)) = c_Polynomial_Omonom(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0) ),
inference(rectify,[],[f604]) ).
fof(f604,axiom,
! [X7,X17,X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Polynomial_Osmult(X5,X4,c_Polynomial_Omonom(X5,X17,X7)) = c_Polynomial_Omonom(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__monom) ).
fof(f18725,plain,
spl47_911,
inference(avatar_split_clause,[],[f5166,f18723]) ).
fof(f18723,plain,
( spl47_911
<=> ! [X0,X3,X2,X1] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),X0) = c_Polynomial_Osmult(X3,X2,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,X0))
| ~ class_Fields_Ofield(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_911])]) ).
fof(f5166,plain,
! [X2,X3,X0,X1] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),X0) = c_Polynomial_Osmult(X3,X2,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,X0))
| ~ class_Fields_Ofield(X3) ),
inference(cnf_transformation,[],[f3087]) ).
fof(f3087,plain,
! [X0,X1,X2,X3] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),X0) = c_Polynomial_Osmult(X3,X2,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,X0))
| ~ class_Fields_Ofield(X3) ),
inference(ennf_transformation,[],[f2010]) ).
fof(f2010,plain,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),X0) = c_Polynomial_Osmult(X3,X2,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X1,X0)) ),
inference(rectify,[],[f987]) ).
fof(f987,axiom,
! [X10,X6,X4,X5] :
( class_Fields_Ofield(X5)
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X5),c_Polynomial_Osmult(X5,X4,X6),X10) = c_Polynomial_Osmult(X5,X4,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X5),X6,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__smult__left) ).
fof(f18721,plain,
spl47_910,
inference(avatar_split_clause,[],[f5108,f18719]) ).
fof(f18719,plain,
( spl47_910
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_910])]) ).
fof(f5108,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ),
inference(cnf_transformation,[],[f3814]) ).
fof(f3814,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ) ),
inference(flattening,[],[f3813]) ).
fof(f3813,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ) ),
inference(nnf_transformation,[],[f1954]) ).
fof(f1954,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ) ),
inference(rectify,[],[f681]) ).
fof(f681,axiom,
! [X11,X14,X44] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X11))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X11)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X44) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
fof(f18717,plain,
spl47_909,
inference(avatar_split_clause,[],[f5105,f18715]) ).
fof(f18715,plain,
( spl47_909
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_909])]) ).
fof(f5105,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
inference(cnf_transformation,[],[f3812]) ).
fof(f3812,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
inference(flattening,[],[f3811]) ).
fof(f3811,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
inference(nnf_transformation,[],[f1953]) ).
fof(f1953,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
inference(rectify,[],[f680]) ).
fof(f680,axiom,
! [X11,X44,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X44),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X44))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X11)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X44) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
fof(f18713,plain,
spl47_908,
inference(avatar_split_clause,[],[f5103,f18711]) ).
fof(f18711,plain,
( spl47_908
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_908])]) ).
fof(f5103,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(cnf_transformation,[],[f3810]) ).
fof(f3810,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ) ),
inference(flattening,[],[f3809]) ).
fof(f3809,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ) ),
inference(nnf_transformation,[],[f3054]) ).
fof(f3054,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ) ),
inference(ennf_transformation,[],[f1952]) ).
fof(f1952,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(rectify,[],[f702]) ).
fof(f702,axiom,
! [X11,X14,X44] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X11))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X44)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
fof(f18709,plain,
spl47_907,
inference(avatar_split_clause,[],[f5100,f18707]) ).
fof(f18707,plain,
( spl47_907
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_907])]) ).
fof(f5100,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(cnf_transformation,[],[f3808]) ).
fof(f18705,plain,
spl47_906,
inference(avatar_split_clause,[],[f4978,f18703]) ).
fof(f18703,plain,
( spl47_906
<=> ! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_906])]) ).
fof(f4978,plain,
! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2956]) ).
fof(f2956,plain,
! [X0,X1,X2] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1882]) ).
fof(f1882,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X0) ),
inference(rectify,[],[f816]) ).
fof(f816,axiom,
! [X32,X33,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X33)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,X20),X32) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X32),X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).
fof(f18701,plain,
( ~ spl47_51
| ~ spl47_905
| ~ spl47_222
| ~ spl47_349 ),
inference(avatar_split_clause,[],[f7954,f7794,f7074,f18698,f6286]) ).
fof(f18698,plain,
( spl47_905
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_905])]) ).
fof(f7794,plain,
( spl47_349
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_349])]) ).
fof(f7954,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Orderings_Olinorder(tc_Int_Oint)
| ~ spl47_222
| ~ spl47_349 ),
inference(resolution,[],[f7795,f7076]) ).
fof(f7795,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl47_349 ),
inference(avatar_component_clause,[],[f7794]) ).
fof(f18696,plain,
spl47_904,
inference(avatar_split_clause,[],[f4976,f18694]) ).
fof(f18694,plain,
( spl47_904
<=> ! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_904])]) ).
fof(f4976,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2954]) ).
fof(f2954,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1880]) ).
fof(f1880,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(rectify,[],[f815]) ).
fof(f815,axiom,
! [X32,X33,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X33)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,X20)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X33),X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc) ).
fof(f18692,plain,
spl47_903,
inference(avatar_split_clause,[],[f4975,f18690]) ).
fof(f18690,plain,
( spl47_903
<=> ! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_903])]) ).
fof(f4975,plain,
! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2953]) ).
fof(f2953,plain,
! [X0,X1,X2] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1879]) ).
fof(f1879,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1) ),
inference(rectify,[],[f807]) ).
fof(f807,axiom,
! [X32,X33,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X33)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,X20)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X20),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__right) ).
fof(f18688,plain,
spl47_902,
inference(avatar_split_clause,[],[f4921,f18686]) ).
fof(f18686,plain,
( spl47_902
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_902])]) ).
fof(f4921,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(cnf_transformation,[],[f2892]) ).
fof(f2892,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1)))
| ( c_Groups_Oone__class_Oone(X2) != X0
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(flattening,[],[f2891]) ).
fof(f2891,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1)))
| ( c_Groups_Oone__class_Oone(X2) != X0
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f1839]) ).
fof(f1839,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> ( ( c_Groups_Oone__class_Oone(X2) = X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X0),X1))) ) ),
inference(rectify,[],[f247]) ).
fof(f247,axiom,
! [X6,X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( ( c_Groups_Oone__class_Oone(X5) = X6
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7) )
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X7))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power) ).
fof(f18684,plain,
spl47_901,
inference(avatar_split_clause,[],[f4865,f18682]) ).
fof(f18682,plain,
( spl47_901
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Ozero__class_Ozero(X2) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Ono__zero__divisors(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_901])]) ).
fof(f4865,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Ozero__class_Ozero(X2) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Ono__zero__divisors(X2) ),
inference(cnf_transformation,[],[f2836]) ).
fof(f2836,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Ozero__class_Ozero(X2) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Ono__zero__divisors(X2) ),
inference(flattening,[],[f2835]) ).
fof(f2835,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Ozero__class_Ozero(X2) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Ono__zero__divisors(X2) ),
inference(ennf_transformation,[],[f1793]) ).
fof(f1793,plain,
! [X0,X1,X2] :
( class_Rings_Ono__zero__divisors(X2)
=> ( c_Groups_Ozero__class_Ozero(X2) != X1
=> ( c_Groups_Ozero__class_Ozero(X2) != X0
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2) ) ) ),
inference(rectify,[],[f517]) ).
fof(f517,axiom,
! [X17,X4,X5] :
( class_Rings_Ono__zero__divisors(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X4
=> ( c_Groups_Ozero__class_Ozero(X5) != X17
=> c_Groups_Ozero__class_Ozero(X5) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_no__zero__divisors) ).
fof(f18680,plain,
spl47_900,
inference(avatar_split_clause,[],[f4850,f18678]) ).
fof(f18678,plain,
( spl47_900
<=> ! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_OpCons(X2,X1,X0)) = c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0))
| ~ class_Groups_Oab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_900])]) ).
fof(f4850,plain,
! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_OpCons(X2,X1,X0)) = c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0))
| ~ class_Groups_Oab__group__add(X2) ),
inference(cnf_transformation,[],[f2810]) ).
fof(f2810,plain,
! [X0,X1,X2] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_OpCons(X2,X1,X0)) = c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0))
| ~ class_Groups_Oab__group__add(X2) ),
inference(ennf_transformation,[],[f1779]) ).
fof(f1779,plain,
! [X0,X1,X2] :
( class_Groups_Oab__group__add(X2)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_OpCons(X2,X1,X0)) = c_Polynomial_OpCons(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0)) ),
inference(rectify,[],[f403]) ).
fof(f403,axiom,
! [X8,X4,X31] :
( class_Groups_Oab__group__add(X31)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X31),c_Polynomial_OpCons(X31,X4,X8)) = c_Polynomial_OpCons(X31,c_Groups_Ouminus__class_Ouminus(X31,X4),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X31),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I2_J) ).
fof(f18676,plain,
spl47_899,
inference(avatar_split_clause,[],[f4833,f18674]) ).
fof(f18674,plain,
( spl47_899
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_Osmult(X2,X1,X0)
| ~ class_Rings_Oidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_899])]) ).
fof(f4833,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_Osmult(X2,X1,X0)
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f3729]) ).
fof(f3729,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,X1,X0)
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
& c_Groups_Ozero__class_Ozero(X2) != X1 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_Osmult(X2,X1,X0) ) )
| ~ class_Rings_Oidom(X2) ),
inference(flattening,[],[f3728]) ).
fof(f3728,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,X1,X0)
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
& c_Groups_Ozero__class_Ozero(X2) != X1 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_Osmult(X2,X1,X0) ) )
| ~ class_Rings_Oidom(X2) ),
inference(nnf_transformation,[],[f2800]) ).
fof(f2800,plain,
! [X0,X1,X2] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,X1,X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1 ) )
| ~ class_Rings_Oidom(X2) ),
inference(ennf_transformation,[],[f1769]) ).
fof(f1769,plain,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,X1,X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1 ) ) ),
inference(rectify,[],[f109]) ).
fof(f109,axiom,
! [X9,X12,X5] :
( class_Rings_Oidom(X5)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_Osmult(X5,X12,X9)
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X9
| c_Groups_Ozero__class_Ozero(X5) = X12 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__eq__0__iff) ).
fof(f18672,plain,
spl47_898,
inference(avatar_split_clause,[],[f4742,f18670]) ).
fof(f18670,plain,
( spl47_898
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0)
| ~ class_Rings_Oring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_898])]) ).
fof(f4742,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0)
| ~ class_Rings_Oring(X2) ),
inference(cnf_transformation,[],[f2699]) ).
fof(f2699,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0)
| ~ class_Rings_Oring(X2) ),
inference(ennf_transformation,[],[f1703]) ).
fof(f1703,plain,
! [X0,X1,X2] :
( class_Rings_Oring(X2)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0) ),
inference(rectify,[],[f500]) ).
fof(f500,axiom,
! [X17,X4,X5] :
( class_Rings_Oring(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ouminus__class_Ouminus(X5,X17)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ouminus__class_Ouminus(X5,X4)),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__commute) ).
fof(f18668,plain,
spl47_897,
inference(avatar_split_clause,[],[f4741,f18666]) ).
fof(f18666,plain,
( spl47_897
<=> ! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0)
| ~ class_Rings_Oring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_897])]) ).
fof(f4741,plain,
! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0)
| ~ class_Rings_Oring(X2) ),
inference(cnf_transformation,[],[f2698]) ).
fof(f2698,plain,
! [X0,X1,X2] :
( c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0)
| ~ class_Rings_Oring(X2) ),
inference(ennf_transformation,[],[f1702]) ).
fof(f1702,plain,
! [X0,X1,X2] :
( class_Rings_Oring(X2)
=> c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0) ),
inference(rectify,[],[f499]) ).
fof(f499,axiom,
! [X17,X4,X5] :
( class_Rings_Oring(X5)
=> c_Groups_Ouminus__class_Ouminus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ouminus__class_Ouminus(X5,X4)),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__left) ).
fof(f18664,plain,
spl47_896,
inference(avatar_split_clause,[],[f4740,f18662]) ).
fof(f18662,plain,
( spl47_896
<=> ! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Rings_Oring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_896])]) ).
fof(f4740,plain,
! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Rings_Oring(X2) ),
inference(cnf_transformation,[],[f2697]) ).
fof(f2697,plain,
! [X0,X1,X2] :
( c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Rings_Oring(X2) ),
inference(ennf_transformation,[],[f1701]) ).
fof(f1701,plain,
! [X0,X1,X2] :
( class_Rings_Oring(X2)
=> c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(rectify,[],[f498]) ).
fof(f498,axiom,
! [X17,X4,X5] :
( class_Rings_Oring(X5)
=> c_Groups_Ouminus__class_Ouminus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ouminus__class_Ouminus(X5,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__right) ).
fof(f18660,plain,
spl47_895,
inference(avatar_split_clause,[],[f4739,f18658]) ).
fof(f18658,plain,
( spl47_895
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Rings_Oring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_895])]) ).
fof(f4739,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Rings_Oring(X2) ),
inference(cnf_transformation,[],[f2696]) ).
fof(f2696,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Rings_Oring(X2) ),
inference(ennf_transformation,[],[f1700]) ).
fof(f1700,plain,
! [X0,X1,X2] :
( class_Rings_Oring(X2)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(rectify,[],[f501]) ).
fof(f501,axiom,
! [X17,X4,X5] :
( class_Rings_Oring(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ouminus__class_Ouminus(X5,X4)),c_Groups_Ouminus__class_Ouminus(X5,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__minus) ).
fof(f18656,plain,
( spl47_894
| ~ spl47_42
| ~ spl47_342 ),
inference(avatar_split_clause,[],[f7902,f7766,f6241,f18654]) ).
fof(f18654,plain,
( spl47_894
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_894])]) ).
fof(f6241,plain,
( spl47_42
<=> class_Divides_Osemiring__div(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_42])]) ).
fof(f7766,plain,
( spl47_342
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Divides_Osemiring__div(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_342])]) ).
fof(f7902,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ spl47_42
| ~ spl47_342 ),
inference(resolution,[],[f7767,f6243]) ).
fof(f6243,plain,
( class_Divides_Osemiring__div(tc_Nat_Onat)
| ~ spl47_42 ),
inference(avatar_component_clause,[],[f6241]) ).
fof(f7767,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X1)
| c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
| ~ spl47_342 ),
inference(avatar_component_clause,[],[f7766]) ).
fof(f18652,plain,
spl47_893,
inference(avatar_split_clause,[],[f4727,f18650]) ).
fof(f18650,plain,
( spl47_893
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oring__no__zero__divisors(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_893])]) ).
fof(f4727,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(cnf_transformation,[],[f3704]) ).
fof(f3704,plain,
! [X0,X1,X2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
| ( c_Groups_Ozero__class_Ozero(X2) != X0
& c_Groups_Ozero__class_Ozero(X2) != X1 ) )
& ( c_Groups_Ozero__class_Ozero(X2) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2) ) )
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(flattening,[],[f3703]) ).
fof(f3703,plain,
! [X0,X1,X2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
| ( c_Groups_Ozero__class_Ozero(X2) != X0
& c_Groups_Ozero__class_Ozero(X2) != X1 ) )
& ( c_Groups_Ozero__class_Ozero(X2) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2) ) )
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(nnf_transformation,[],[f2681]) ).
fof(f2681,plain,
! [X0,X1,X2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
<=> ( c_Groups_Ozero__class_Ozero(X2) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1 ) )
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(ennf_transformation,[],[f1691]) ).
fof(f1691,plain,
! [X0,X1,X2] :
( class_Rings_Oring__no__zero__divisors(X2)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
<=> ( c_Groups_Ozero__class_Ozero(X2) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1 ) ) ),
inference(rectify,[],[f516]) ).
fof(f516,axiom,
! [X29,X12,X5] :
( class_Rings_Oring__no__zero__divisors(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X29)
<=> ( c_Groups_Ozero__class_Ozero(X5) = X29
| c_Groups_Ozero__class_Ozero(X5) = X12 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
fof(f18648,plain,
spl47_892,
inference(avatar_split_clause,[],[f4657,f18646]) ).
fof(f18646,plain,
( spl47_892
<=> ! [X2,X0,X1] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1),X0) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X1,X0))
| ~ class_Fields_Ofield(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_892])]) ).
fof(f4657,plain,
! [X2,X0,X1] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1),X0) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X1,X0))
| ~ class_Fields_Ofield(X2) ),
inference(cnf_transformation,[],[f2640]) ).
fof(f2640,plain,
! [X0,X1,X2] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1),X0) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X1,X0))
| ~ class_Fields_Ofield(X2) ),
inference(ennf_transformation,[],[f1660]) ).
fof(f1660,plain,
! [X0,X1,X2] :
( class_Fields_Ofield(X2)
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1),X0) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X1,X0)) ),
inference(rectify,[],[f986]) ).
fof(f986,axiom,
! [X10,X6,X5] :
( class_Fields_Ofield(X5)
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X5),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5),X6),X10) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X5),X6,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__mod__minus__left) ).
fof(f18644,plain,
spl47_891,
inference(avatar_split_clause,[],[f4653,f18642]) ).
fof(f18642,plain,
( spl47_891
<=> ! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0)
| ~ class_RealVector_Oreal__normed__algebra(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_891])]) ).
fof(f4653,plain,
! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0)
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(cnf_transformation,[],[f2636]) ).
fof(f2636,plain,
! [X0,X1,X2] :
( c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0)
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(ennf_transformation,[],[f1656]) ).
fof(f1656,plain,
! [X0,X1,X2] :
( class_RealVector_Oreal__normed__algebra(X2)
=> c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0) ),
inference(rectify,[],[f750]) ).
fof(f750,axiom,
! [X17,X4,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> c_Groups_Ouminus__class_Ouminus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ouminus__class_Ouminus(X5,X4)),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__left) ).
fof(f18640,plain,
spl47_890,
inference(avatar_split_clause,[],[f4652,f18638]) ).
fof(f18638,plain,
( spl47_890
<=> ! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_RealVector_Oreal__normed__algebra(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_890])]) ).
fof(f4652,plain,
! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(cnf_transformation,[],[f2635]) ).
fof(f2635,plain,
! [X0,X1,X2] :
( c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(ennf_transformation,[],[f1655]) ).
fof(f1655,plain,
! [X0,X1,X2] :
( class_RealVector_Oreal__normed__algebra(X2)
=> c_Groups_Ouminus__class_Ouminus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(rectify,[],[f731]) ).
fof(f731,axiom,
! [X17,X4,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> c_Groups_Ouminus__class_Ouminus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ouminus__class_Ouminus(X5,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__right) ).
fof(f18636,plain,
spl47_889,
inference(avatar_split_clause,[],[f4649,f18634]) ).
fof(f18634,plain,
( spl47_889
<=> ! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,c_Rings_Oinverse__class_Odivide(X2,X0,X1)) = c_Rings_Oinverse__class_Odivide(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1))
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Odivision__ring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_889])]) ).
fof(f4649,plain,
! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,c_Rings_Oinverse__class_Odivide(X2,X0,X1)) = c_Rings_Oinverse__class_Odivide(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1))
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Odivision__ring(X2) ),
inference(cnf_transformation,[],[f2632]) ).
fof(f2632,plain,
! [X0,X1,X2] :
( c_Groups_Ouminus__class_Ouminus(X2,c_Rings_Oinverse__class_Odivide(X2,X0,X1)) = c_Rings_Oinverse__class_Odivide(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1))
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Odivision__ring(X2) ),
inference(flattening,[],[f2631]) ).
fof(f2631,plain,
! [X0,X1,X2] :
( c_Groups_Ouminus__class_Ouminus(X2,c_Rings_Oinverse__class_Odivide(X2,X0,X1)) = c_Rings_Oinverse__class_Odivide(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1))
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Odivision__ring(X2) ),
inference(ennf_transformation,[],[f1653]) ).
fof(f1653,plain,
! [X0,X1,X2] :
( class_Rings_Odivision__ring(X2)
=> ( c_Groups_Ozero__class_Ozero(X2) != X1
=> c_Groups_Ouminus__class_Ouminus(X2,c_Rings_Oinverse__class_Odivide(X2,X0,X1)) = c_Rings_Oinverse__class_Odivide(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) ) ),
inference(rectify,[],[f915]) ).
fof(f915,axiom,
! [X4,X17,X5] :
( class_Rings_Odivision__ring(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X17
=> c_Groups_Ouminus__class_Ouminus(X5,c_Rings_Oinverse__class_Odivide(X5,X4,X17)) = c_Rings_Oinverse__class_Odivide(X5,X4,c_Groups_Ouminus__class_Ouminus(X5,X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__minus__divide__right) ).
fof(f18632,plain,
spl47_888,
inference(avatar_split_clause,[],[f4648,f18630]) ).
fof(f18630,plain,
( spl47_888
<=> ! [X2,X0,X1] :
( c_Rings_Oinverse__class_Odivide(X2,X0,X1) = c_Rings_Oinverse__class_Odivide(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Odivision__ring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_888])]) ).
fof(f4648,plain,
! [X2,X0,X1] :
( c_Rings_Oinverse__class_Odivide(X2,X0,X1) = c_Rings_Oinverse__class_Odivide(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Odivision__ring(X2) ),
inference(cnf_transformation,[],[f2630]) ).
fof(f2630,plain,
! [X0,X1,X2] :
( c_Rings_Oinverse__class_Odivide(X2,X0,X1) = c_Rings_Oinverse__class_Odivide(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Odivision__ring(X2) ),
inference(flattening,[],[f2629]) ).
fof(f2629,plain,
! [X0,X1,X2] :
( c_Rings_Oinverse__class_Odivide(X2,X0,X1) = c_Rings_Oinverse__class_Odivide(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Odivision__ring(X2) ),
inference(ennf_transformation,[],[f1652]) ).
fof(f1652,plain,
! [X0,X1,X2] :
( class_Rings_Odivision__ring(X2)
=> ( c_Groups_Ozero__class_Ozero(X2) != X1
=> c_Rings_Oinverse__class_Odivide(X2,X0,X1) = c_Rings_Oinverse__class_Odivide(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1)) ) ),
inference(rectify,[],[f916]) ).
fof(f916,axiom,
! [X4,X17,X5] :
( class_Rings_Odivision__ring(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X17
=> c_Rings_Oinverse__class_Odivide(X5,X4,X17) = c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),c_Groups_Ouminus__class_Ouminus(X5,X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__minus__divide__divide) ).
fof(f18628,plain,
spl47_887,
inference(avatar_split_clause,[],[f4606,f18626]) ).
fof(f18626,plain,
( spl47_887
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_887])]) ).
fof(f4606,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f3662]) ).
fof(f3662,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ) ),
inference(flattening,[],[f3661]) ).
fof(f3661,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ) ),
inference(nnf_transformation,[],[f1606]) ).
fof(f1606,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(rectify,[],[f307]) ).
fof(f307,axiom,
! [X11,X15] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X15),X11))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).
fof(f18624,plain,
spl47_886,
inference(avatar_split_clause,[],[f4439,f18622]) ).
fof(f18622,plain,
( spl47_886
<=> ! [X0,X1,X3] :
( ~ hBOOL(hAPP(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,sK33(X0,X1))
| ~ hBOOL(hAPP(X1,X0))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_886])]) ).
fof(f4439,plain,
! [X3,X0,X1] :
( ~ hBOOL(hAPP(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,sK33(X0,X1))
| ~ hBOOL(hAPP(X1,X0))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(cnf_transformation,[],[f3580]) ).
fof(f18614,plain,
( spl47_885
| ~ spl47_41
| ~ spl47_342 ),
inference(avatar_split_clause,[],[f7901,f7766,f6236,f18612]) ).
fof(f18612,plain,
( spl47_885
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_885])]) ).
fof(f6236,plain,
( spl47_41
<=> class_Divides_Osemiring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_41])]) ).
fof(f7901,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ spl47_41
| ~ spl47_342 ),
inference(resolution,[],[f7767,f6238]) ).
fof(f6238,plain,
( class_Divides_Osemiring__div(tc_Int_Oint)
| ~ spl47_41 ),
inference(avatar_component_clause,[],[f6236]) ).
fof(f18200,plain,
( spl47_884
| ~ spl47_3
| ~ spl47_340 ),
inference(avatar_split_clause,[],[f7899,f7758,f6046,f18198]) ).
fof(f18198,plain,
( spl47_884
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_884])]) ).
fof(f6046,plain,
( spl47_3
<=> class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_3])]) ).
fof(f7758,plain,
( spl47_340
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_RealVector_Oreal__normed__field(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_340])]) ).
fof(f7899,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0)
| ~ spl47_3
| ~ spl47_340 ),
inference(resolution,[],[f7759,f6048]) ).
fof(f6048,plain,
( class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex)
| ~ spl47_3 ),
inference(avatar_component_clause,[],[f6046]) ).
fof(f7759,plain,
( ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__field(X1)
| c_Groups_Ozero__class_Ozero(X1) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
| ~ spl47_340 ),
inference(avatar_component_clause,[],[f7758]) ).
fof(f17808,plain,
( spl47_883
| ~ spl47_2
| ~ spl47_338 ),
inference(avatar_split_clause,[],[f7898,f7749,f6041,f17806]) ).
fof(f17806,plain,
( spl47_883
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_883])]) ).
fof(f6041,plain,
( spl47_2
<=> class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_2])]) ).
fof(f7749,plain,
( spl47_338
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Rings_Oinverse__class_Odivide(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_338])]) ).
fof(f7898,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ spl47_2
| ~ spl47_338 ),
inference(resolution,[],[f7750,f6043]) ).
fof(f6043,plain,
( class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex)
| ~ spl47_2 ),
inference(avatar_component_clause,[],[f6041]) ).
fof(f7750,plain,
( ! [X0,X1] :
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Groups_Ozero__class_Ozero(X1) = c_Rings_Oinverse__class_Odivide(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
| ~ spl47_338 ),
inference(avatar_component_clause,[],[f7749]) ).
fof(f17623,plain,
( spl47_882
| ~ spl47_127
| ~ spl47_334 ),
inference(avatar_split_clause,[],[f7879,f7733,f6666,f17620]) ).
fof(f17620,plain,
( spl47_882
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_882])]) ).
fof(f6666,plain,
( spl47_127
<=> class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_127])]) ).
fof(f7733,plain,
( spl47_334
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_334])]) ).
fof(f7879,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Int_Oint)))
| ~ spl47_127
| ~ spl47_334 ),
inference(resolution,[],[f7734,f6668]) ).
fof(f6668,plain,
( class_Rings_Ocomm__semiring__1(tc_Int_Oint)
| ~ spl47_127 ),
inference(avatar_component_clause,[],[f6666]) ).
fof(f7734,plain,
( ! [X0] :
( ~ class_Rings_Ocomm__semiring__1(X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0))) )
| ~ spl47_334 ),
inference(avatar_component_clause,[],[f7733]) ).
fof(f17479,plain,
spl47_881,
inference(avatar_split_clause,[],[f5914,f17477]) ).
fof(f17477,plain,
( spl47_881
<=> ! [X0,X1] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(X1,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
| ~ class_Groups_Ozero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_881])]) ).
fof(f5914,plain,
! [X0,X1] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(X1,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
| ~ class_Groups_Ozero(X1) ),
inference(forward_demodulation,[],[f5541,f4240]) ).
fof(f5541,plain,
! [X0,X1] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X1,X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
| ~ class_Groups_Ozero(X1) ),
inference(definition_unfolding,[],[f4367,f4118]) ).
fof(f4367,plain,
! [X0,X1] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0) = c_Nat_OSuc(c_Polynomial_Odegree(X1,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
| ~ class_Groups_Ozero(X1) ),
inference(cnf_transformation,[],[f2472]) ).
fof(f2472,plain,
! [X0,X1] :
( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0) = c_Nat_OSuc(c_Polynomial_Odegree(X1,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X0 ) )
| ~ class_Groups_Ozero(X1) ),
inference(ennf_transformation,[],[f1457]) ).
fof(f1457,plain,
! [X0,X1] :
( class_Groups_Ozero(X1)
=> ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X0
=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0) = c_Nat_OSuc(c_Polynomial_Odegree(X1,X0)) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0) ) ) ),
inference(rectify,[],[f28]) ).
fof(f28,axiom,
! [X8,X5] :
( class_Groups_Ozero(X5)
=> ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) != X8
=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X5,X8) = c_Nat_OSuc(c_Polynomial_Odegree(X5,X8)) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X8
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X5,X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psize__def) ).
fof(f17475,plain,
spl47_880,
inference(avatar_split_clause,[],[f5802,f17473]) ).
fof(f17473,plain,
( spl47_880
<=> ! [X2,X1] :
( c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_880])]) ).
fof(f5802,plain,
! [X2,X1] :
( c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2) ),
inference(equality_resolution,[],[f5046]) ).
fof(f5046,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
| ~ class_Rings_Ozero__neq__one(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Power_Opower(X2) ),
inference(cnf_transformation,[],[f3778]) ).
fof(f17471,plain,
( spl47_879
| ~ spl47_128
| ~ spl47_334 ),
inference(avatar_split_clause,[],[f7878,f7733,f6671,f17468]) ).
fof(f17468,plain,
( spl47_879
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_879])]) ).
fof(f6671,plain,
( spl47_128
<=> class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_128])]) ).
fof(f7878,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Nat_Onat)))
| ~ spl47_128
| ~ spl47_334 ),
inference(resolution,[],[f7734,f6673]) ).
fof(f6673,plain,
( class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
| ~ spl47_128 ),
inference(avatar_component_clause,[],[f6671]) ).
fof(f17466,plain,
spl47_878,
inference(avatar_split_clause,[],[f5586,f17464]) ).
fof(f17464,plain,
( spl47_878
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK38(X0,X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_878])]) ).
fof(f5586,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK38(X0,X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(definition_unfolding,[],[f4536,f4118]) ).
fof(f4536,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK38(X0,X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
inference(cnf_transformation,[],[f3624]) ).
fof(f17462,plain,
spl47_877,
inference(avatar_split_clause,[],[f5566,f17460]) ).
fof(f17460,plain,
( spl47_877
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_877])]) ).
fof(f5566,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
inference(definition_unfolding,[],[f4483,f4118]) ).
fof(f4483,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_OSuc(X0))
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
inference(cnf_transformation,[],[f2603]) ).
fof(f2603,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_OSuc(X0))
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
inference(flattening,[],[f2602]) ).
fof(f2602,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_OSuc(X0))
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
inference(ennf_transformation,[],[f1556]) ).
fof(f1556,plain,
! [X0,X1] :
( ( class_Rings_Osemiring__0(X1)
& class_Power_Opower(X1) )
=> c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_OSuc(X0)) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X7,X5] :
( ( class_Rings_Osemiring__0(X5)
& class_Power_Opower(X5) )
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Ozero__class_Ozero(X5)),c_Nat_OSuc(X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__Suc) ).
fof(f17458,plain,
spl47_876,
inference(avatar_split_clause,[],[f5403,f17456]) ).
fof(f17456,plain,
( spl47_876
<=> ! [X2,X4,X0,X3,X1] :
( c_Polynomial_Opdivmod__rel(X3,X0,X2,X1,X4)
| ~ sP25(X4,X3,X2,X1,X0)
| ~ sP26(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_876])]) ).
fof(f5403,plain,
! [X2,X3,X0,X1,X4] :
( c_Polynomial_Opdivmod__rel(X3,X0,X2,X1,X4)
| ~ sP25(X4,X3,X2,X1,X0)
| ~ sP26(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f3881]) ).
fof(f3881,plain,
! [X0,X1,X2,X3,X4] :
( ( ( c_Polynomial_Opdivmod__rel(X3,X0,X2,X1,X4)
| ~ sP25(X4,X3,X2,X1,X0) )
& ( sP25(X4,X3,X2,X1,X0)
| ~ c_Polynomial_Opdivmod__rel(X3,X0,X2,X1,X4) ) )
| ~ sP26(X0,X1,X2,X3,X4) ),
inference(rectify,[],[f3880]) ).
fof(f3880,plain,
! [X3,X1,X2,X4,X0] :
( ( ( c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
| ~ sP25(X0,X4,X2,X1,X3) )
& ( sP25(X0,X4,X2,X1,X3)
| ~ c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0) ) )
| ~ sP26(X3,X1,X2,X4,X0) ),
inference(nnf_transformation,[],[f3516]) ).
fof(f3516,plain,
! [X3,X1,X2,X4,X0] :
( ( c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
<=> sP25(X0,X4,X2,X1,X3) )
| ~ sP26(X3,X1,X2,X4,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP26])]) ).
fof(f17454,plain,
spl47_875,
inference(avatar_split_clause,[],[f5402,f17452]) ).
fof(f17452,plain,
( spl47_875
<=> ! [X4,X0,X3,X2,X1] :
( sP25(X4,X3,X2,X1,X0)
| ~ c_Polynomial_Opdivmod__rel(X3,X0,X2,X1,X4)
| ~ sP26(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_875])]) ).
fof(f5402,plain,
! [X2,X3,X0,X1,X4] :
( sP25(X4,X3,X2,X1,X0)
| ~ c_Polynomial_Opdivmod__rel(X3,X0,X2,X1,X4)
| ~ sP26(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f3881]) ).
fof(f17450,plain,
spl47_874,
inference(avatar_split_clause,[],[f5389,f17448]) ).
fof(f17448,plain,
( spl47_874
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_874])]) ).
fof(f5389,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(cnf_transformation,[],[f3362]) ).
fof(f3362,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(flattening,[],[f3361]) ).
fof(f3361,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(ennf_transformation,[],[f2183]) ).
fof(f2183,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ) ),
inference(rectify,[],[f321]) ).
fof(f321,axiom,
! [X43,X20,X33,X32] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32,X33)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X43)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X20),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X43)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).
fof(f17446,plain,
spl47_873,
inference(avatar_split_clause,[],[f5388,f17444]) ).
fof(f17444,plain,
( spl47_873
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_873])]) ).
fof(f5388,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2) ),
inference(cnf_transformation,[],[f3360]) ).
fof(f3360,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2) ),
inference(flattening,[],[f3359]) ).
fof(f3359,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2) ),
inference(ennf_transformation,[],[f2182]) ).
fof(f2182,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0)) ) ),
inference(rectify,[],[f476]) ).
fof(f476,axiom,
! [X26,X50,X48,X51] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X51,X48)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X26)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X51,X50),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X48,X26)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).
fof(f17442,plain,
spl47_872,
inference(avatar_split_clause,[],[f5386,f17440]) ).
fof(f17440,plain,
( spl47_872
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_872])]) ).
fof(f5386,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(cnf_transformation,[],[f3356]) ).
fof(f3356,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(flattening,[],[f3355]) ).
fof(f3355,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(ennf_transformation,[],[f2180]) ).
fof(f2180,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ) ),
inference(rectify,[],[f332]) ).
fof(f332,axiom,
! [X43,X20,X33,X32] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32,X33)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X43)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X20),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X43)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).
fof(f17438,plain,
spl47_871,
inference(avatar_split_clause,[],[f5286,f17436]) ).
fof(f17436,plain,
( spl47_871
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Rings_Olinordered__semidom(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_871])]) ).
fof(f5286,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(cnf_transformation,[],[f3222]) ).
fof(f3222,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(flattening,[],[f3221]) ).
fof(f3221,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(ennf_transformation,[],[f2086]) ).
fof(f2086,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless(X3,X1,X0)
=> c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ) ) ),
inference(rectify,[],[f140]) ).
fof(f140,axiom,
! [X16,X17,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> ( c_Orderings_Oord__class_Oless(X5,X17,X16)
=> c_Orderings_Oord__class_Oless(X5,X17,c_Groups_Oplus__class_Oplus(X5,X4,X16)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).
fof(f17434,plain,
spl47_870,
inference(avatar_split_clause,[],[f5255,f17432]) ).
fof(f17432,plain,
( spl47_870
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_870])]) ).
fof(f5255,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X3) ),
inference(cnf_transformation,[],[f3178]) ).
fof(f3178,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X3) ),
inference(flattening,[],[f3177]) ).
fof(f3177,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X3) ),
inference(ennf_transformation,[],[f2062]) ).
fof(f2062,plain,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__comm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
=> c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ) ) ),
inference(rectify,[],[f303]) ).
fof(f303,axiom,
! [X16,X17,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X17,X16)
=> c_Orderings_Oord__class_Oless(X5,X17,c_Groups_Oplus__class_Oplus(X5,X4,X16)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
fof(f17430,plain,
spl47_869,
inference(avatar_split_clause,[],[f5254,f17428]) ).
fof(f17428,plain,
( spl47_869
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_869])]) ).
fof(f5254,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X3) ),
inference(cnf_transformation,[],[f3176]) ).
fof(f3176,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X3) ),
inference(flattening,[],[f3175]) ).
fof(f3175,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X3) ),
inference(ennf_transformation,[],[f2061]) ).
fof(f2061,plain,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__comm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless(X3,X1,X0)
=> c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ) ) ),
inference(rectify,[],[f304]) ).
fof(f304,axiom,
! [X16,X17,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> ( c_Orderings_Oord__class_Oless(X5,X17,X16)
=> c_Orderings_Oord__class_Oless(X5,X17,c_Groups_Oplus__class_Oplus(X5,X4,X16)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
fof(f17426,plain,
( spl47_868
| ~ spl47_126
| ~ spl47_334 ),
inference(avatar_split_clause,[],[f7876,f7733,f6661,f17423]) ).
fof(f17423,plain,
( spl47_868
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_868])]) ).
fof(f7876,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
| ~ spl47_126
| ~ spl47_334 ),
inference(resolution,[],[f7734,f6663]) ).
fof(f6663,plain,
( class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ~ spl47_126 ),
inference(avatar_component_clause,[],[f6661]) ).
fof(f17421,plain,
spl47_867,
inference(avatar_split_clause,[],[f5253,f17419]) ).
fof(f17419,plain,
( spl47_867
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_867])]) ).
fof(f5253,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X3) ),
inference(cnf_transformation,[],[f3174]) ).
fof(f3174,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X3) ),
inference(flattening,[],[f3173]) ).
fof(f3173,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X3) ),
inference(ennf_transformation,[],[f2060]) ).
fof(f2060,plain,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__comm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X0,X2)) ) ) ),
inference(rectify,[],[f374]) ).
fof(f374,axiom,
! [X4,X17,X16,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X16)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X17,X4)
=> c_Orderings_Oord__class_Oless__eq(X5,X17,c_Groups_Oplus__class_Oplus(X5,X4,X16)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing2) ).
fof(f17417,plain,
spl47_866,
inference(avatar_split_clause,[],[f5252,f17415]) ).
fof(f17415,plain,
( spl47_866
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_866])]) ).
fof(f5252,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X3) ),
inference(cnf_transformation,[],[f3172]) ).
fof(f3172,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X3) ),
inference(flattening,[],[f3171]) ).
fof(f3171,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X3) ),
inference(ennf_transformation,[],[f2059]) ).
fof(f2059,plain,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__comm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ) ) ),
inference(rectify,[],[f375]) ).
fof(f375,axiom,
! [X16,X17,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X17,X16)
=> c_Orderings_Oord__class_Oless__eq(X5,X17,c_Groups_Oplus__class_Oplus(X5,X4,X16)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing) ).
fof(f17413,plain,
spl47_865,
inference(avatar_split_clause,[],[f5109,f17411]) ).
fof(f17411,plain,
( spl47_865
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_865])]) ).
fof(f5109,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ),
inference(cnf_transformation,[],[f3814]) ).
fof(f17409,plain,
spl47_864,
inference(avatar_split_clause,[],[f5106,f17407]) ).
fof(f17407,plain,
( spl47_864
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_864])]) ).
fof(f5106,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
inference(cnf_transformation,[],[f3812]) ).
fof(f17405,plain,
spl47_863,
inference(avatar_split_clause,[],[f5073,f17403]) ).
fof(f17403,plain,
( spl47_863
<=> ! [X2,X0,X1] :
( sP13(X0,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK45(X0,X1,X2)) = X1
| ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_863])]) ).
fof(f5073,plain,
! [X2,X0,X1] :
( sP13(X0,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK45(X0,X1,X2)) = X1
| ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(cnf_transformation,[],[f3793]) ).
fof(f3793,plain,
! [X0,X1,X2] :
( ( sP13(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK45(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK45(X0,X1,X2)) = X1 )
| ( ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
& ( ( ! [X4] :
( hBOOL(hAPP(X0,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X1 )
& ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
| ~ sP13(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK45])],[f3791,f3792]) ).
fof(f3792,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(X0,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) = X1 )
=> ( ~ hBOOL(hAPP(X0,sK45(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK45(X0,X1,X2)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f3791,plain,
! [X0,X1,X2] :
( ( sP13(X0,X1,X2)
| ? [X3] :
( ~ hBOOL(hAPP(X0,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) = X1 )
| ( ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
& ( ( ! [X4] :
( hBOOL(hAPP(X0,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X1 )
& ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
| ~ sP13(X0,X1,X2) ) ),
inference(rectify,[],[f3790]) ).
fof(f3790,plain,
! [X2,X1,X0] :
( ( sP13(X2,X1,X0)
| ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X1 )
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) )
& ( ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) )
| ~ sP13(X2,X1,X0) ) ),
inference(flattening,[],[f3789]) ).
fof(f3789,plain,
! [X2,X1,X0] :
( ( sP13(X2,X1,X0)
| ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X1 )
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) )
& ( ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) )
| ~ sP13(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f3497]) ).
fof(f3497,plain,
! [X2,X1,X0] :
( sP13(X2,X1,X0)
<=> ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f17401,plain,
spl47_862,
inference(avatar_split_clause,[],[f5065,f17399]) ).
fof(f17399,plain,
( spl47_862
<=> ! [X2,X0,X1] :
( sP12(X0,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK44(X0,X1,X2)) = X1
| ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_862])]) ).
fof(f5065,plain,
! [X2,X0,X1] :
( sP12(X0,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK44(X0,X1,X2)) = X1
| ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(cnf_transformation,[],[f3787]) ).
fof(f3787,plain,
! [X0,X1,X2] :
( ( sP12(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK44(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK44(X0,X1,X2)) = X1 )
| ( ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
& ( ( ! [X4] :
( hBOOL(hAPP(X0,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X1 )
& ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
| ~ sP12(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44])],[f3785,f3786]) ).
fof(f3786,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(X0,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) = X1 )
=> ( ~ hBOOL(hAPP(X0,sK44(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK44(X0,X1,X2)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f3785,plain,
! [X0,X1,X2] :
( ( sP12(X0,X1,X2)
| ? [X3] :
( ~ hBOOL(hAPP(X0,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) = X1 )
| ( ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
& ( ( ! [X4] :
( hBOOL(hAPP(X0,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X1 )
& ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
| ~ sP12(X0,X1,X2) ) ),
inference(rectify,[],[f3784]) ).
fof(f3784,plain,
! [X2,X1,X0] :
( ( sP12(X2,X1,X0)
| ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X1 )
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) )
& ( ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) )
| ~ sP12(X2,X1,X0) ) ),
inference(flattening,[],[f3783]) ).
fof(f3783,plain,
! [X2,X1,X0] :
( ( sP12(X2,X1,X0)
| ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X1 )
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) )
& ( ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) )
| ~ sP12(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f3495]) ).
fof(f3495,plain,
! [X2,X1,X0] :
( sP12(X2,X1,X0)
<=> ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f17397,plain,
spl47_861,
inference(avatar_split_clause,[],[f5004,f17395]) ).
fof(f17395,plain,
( spl47_861
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_861])]) ).
fof(f5004,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2986]) ).
fof(f2986,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(flattening,[],[f2985]) ).
fof(f2985,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1903]) ).
fof(f1903,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) ) ),
inference(rectify,[],[f790]) ).
fof(f790,axiom,
! [X43,X7,X21] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X7)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X43)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X43,X7),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X43,X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
fof(f17393,plain,
spl47_860,
inference(avatar_split_clause,[],[f5002,f17391]) ).
fof(f17391,plain,
( spl47_860
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_860])]) ).
fof(f5002,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2982]) ).
fof(f2982,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(flattening,[],[f2981]) ).
fof(f2981,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1901]) ).
fof(f1901,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ) ),
inference(rectify,[],[f821]) ).
fof(f821,axiom,
! [X16,X17,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X17)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,X4)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X16),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono) ).
fof(f17389,plain,
spl47_859,
inference(avatar_split_clause,[],[f4992,f17387]) ).
fof(f17387,plain,
( spl47_859
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_859])]) ).
fof(f4992,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f3763]) ).
fof(f3763,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(nnf_transformation,[],[f2971]) ).
fof(f2971,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1892]) ).
fof(f1892,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1) ) ),
inference(rectify,[],[f812]) ).
fof(f812,axiom,
! [X80,X81,X44] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X81)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X80,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X81,X44))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X80,X44),X81) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv2) ).
fof(f17385,plain,
spl47_858,
inference(avatar_split_clause,[],[f4974,f17383]) ).
fof(f17383,plain,
( spl47_858
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_858])]) ).
fof(f4974,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2952]) ).
fof(f2952,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1878]) ).
fof(f1878,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(rectify,[],[f662]) ).
fof(f662,axiom,
! [X20,X33,X32] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32,X33)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
fof(f17381,plain,
( spl47_857
| ~ spl47_121
| ~ spl47_333 ),
inference(avatar_split_clause,[],[f7870,f7729,f6636,f17378]) ).
fof(f17378,plain,
( spl47_857
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_857])]) ).
fof(f7729,plain,
( spl47_333
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Groups_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_333])]) ).
fof(f7870,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)))
| ~ spl47_121
| ~ spl47_333 ),
inference(resolution,[],[f7730,f6638]) ).
fof(f7730,plain,
( ! [X0] :
( ~ class_Groups_Ozero(X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) )
| ~ spl47_333 ),
inference(avatar_component_clause,[],[f7729]) ).
fof(f17376,plain,
spl47_856,
inference(avatar_split_clause,[],[f4973,f17374]) ).
fof(f17374,plain,
( spl47_856
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_856])]) ).
fof(f4973,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2951]) ).
fof(f2951,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1877]) ).
fof(f1877,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)) ),
inference(rectify,[],[f661]) ).
fof(f661,axiom,
! [X20,X33,X32] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32,X33)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X32),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
fof(f17372,plain,
spl47_855,
inference(avatar_split_clause,[],[f4900,f17370]) ).
fof(f17370,plain,
( spl47_855
<=> ! [X2,X0,X1] :
( c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0)
| ~ class_Rings_Ocomm__semiring__0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_855])]) ).
fof(f4900,plain,
! [X2,X0,X1] :
( c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0)
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(cnf_transformation,[],[f2872]) ).
fof(f2872,plain,
! [X0,X1,X2] :
( c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0)
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(ennf_transformation,[],[f1820]) ).
fof(f1820,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__0(X2)
=> c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0) ),
inference(rectify,[],[f128]) ).
fof(f128,axiom,
! [X35,X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Polynomial_OpCons(X5,X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5,c_Polynomial_OpCons(X5,X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__single) ).
fof(f17368,plain,
spl47_854,
inference(avatar_split_clause,[],[f4849,f17366]) ).
fof(f17366,plain,
( spl47_854
<=> ! [X2,X0,X1] :
( hAPP(c_Polynomial_Ocoeff(X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1)),X0) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(c_Polynomial_Ocoeff(X2,X1),X0))
| ~ class_Groups_Oab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_854])]) ).
fof(f4849,plain,
! [X2,X0,X1] :
( hAPP(c_Polynomial_Ocoeff(X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1)),X0) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(c_Polynomial_Ocoeff(X2,X1),X0))
| ~ class_Groups_Oab__group__add(X2) ),
inference(cnf_transformation,[],[f2809]) ).
fof(f2809,plain,
! [X0,X1,X2] :
( hAPP(c_Polynomial_Ocoeff(X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1)),X0) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(c_Polynomial_Ocoeff(X2,X1),X0))
| ~ class_Groups_Oab__group__add(X2) ),
inference(ennf_transformation,[],[f1778]) ).
fof(f1778,plain,
! [X0,X1,X2] :
( class_Groups_Oab__group__add(X2)
=> hAPP(c_Polynomial_Ocoeff(X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1)),X0) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(c_Polynomial_Ocoeff(X2,X1),X0)) ),
inference(rectify,[],[f842]) ).
fof(f842,axiom,
! [X7,X8,X5] :
( class_Groups_Oab__group__add(X5)
=> hAPP(c_Polynomial_Ocoeff(X5,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5),X8)),X7) = c_Groups_Ouminus__class_Ouminus(X5,hAPP(c_Polynomial_Ocoeff(X5,X8),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__minus) ).
fof(f17364,plain,
spl47_853,
inference(avatar_split_clause,[],[f4755,f17362]) ).
fof(f17362,plain,
( spl47_853
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| ~ class_Rings_Ocomm__ring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_853])]) ).
fof(f4755,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(cnf_transformation,[],[f3707]) ).
fof(f3707,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0)) ) )
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(nnf_transformation,[],[f2710]) ).
fof(f2710,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0)) )
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(ennf_transformation,[],[f1713]) ).
fof(f1713,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__ring__1(X2)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0)) ) ),
inference(rectify,[],[f423]) ).
fof(f423,axiom,
! [X25,X15,X5] :
( class_Rings_Ocomm__ring__1(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),c_Groups_Ouminus__class_Ouminus(X5,X15)),X25))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X15),X25)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__dvd__iff) ).
fof(f17360,plain,
spl47_852,
inference(avatar_split_clause,[],[f4754,f17358]) ).
fof(f17358,plain,
( spl47_852
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0))
| ~ class_Rings_Ocomm__ring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_852])]) ).
fof(f4754,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),c_Groups_Ouminus__class_Ouminus(X2,X1)),X0))
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(cnf_transformation,[],[f3707]) ).
fof(f17356,plain,
spl47_851,
inference(avatar_split_clause,[],[f4753,f17354]) ).
fof(f17354,plain,
( spl47_851
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| ~ class_Rings_Ocomm__ring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_851])]) ).
fof(f4753,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(cnf_transformation,[],[f3706]) ).
fof(f3706,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0))) ) )
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(nnf_transformation,[],[f2709]) ).
fof(f2709,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0)) )
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(ennf_transformation,[],[f1712]) ).
fof(f1712,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__ring__1(X2)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0)) ) ),
inference(rectify,[],[f422]) ).
fof(f422,axiom,
! [X25,X15,X5] :
( class_Rings_Ocomm__ring__1(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X15),c_Groups_Ouminus__class_Ouminus(X5,X25)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X15),X25)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__minus__iff) ).
fof(f17352,plain,
spl47_850,
inference(avatar_split_clause,[],[f4752,f17350]) ).
fof(f17350,plain,
( spl47_850
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)))
| ~ class_Rings_Ocomm__ring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_850])]) ).
fof(f4752,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),c_Groups_Ouminus__class_Ouminus(X2,X0)))
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(cnf_transformation,[],[f3706]) ).
fof(f17348,plain,
spl47_849,
inference(avatar_split_clause,[],[f4749,f17346]) ).
fof(f17346,plain,
( spl47_849
<=> ! [X2,X0,X1] :
( hAPP(c_Polynomial_Opoly(X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1)),X0) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(c_Polynomial_Opoly(X2,X1),X0))
| ~ class_Rings_Ocomm__ring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_849])]) ).
fof(f4749,plain,
! [X2,X0,X1] :
( hAPP(c_Polynomial_Opoly(X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1)),X0) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(c_Polynomial_Opoly(X2,X1),X0))
| ~ class_Rings_Ocomm__ring(X2) ),
inference(cnf_transformation,[],[f2706]) ).
fof(f2706,plain,
! [X0,X1,X2] :
( hAPP(c_Polynomial_Opoly(X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1)),X0) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(c_Polynomial_Opoly(X2,X1),X0))
| ~ class_Rings_Ocomm__ring(X2) ),
inference(ennf_transformation,[],[f1709]) ).
fof(f1709,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__ring(X2)
=> hAPP(c_Polynomial_Opoly(X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X1)),X0) = c_Groups_Ouminus__class_Ouminus(X2,hAPP(c_Polynomial_Opoly(X2,X1),X0)) ),
inference(rectify,[],[f402]) ).
fof(f402,axiom,
! [X6,X8,X5] :
( class_Rings_Ocomm__ring(X5)
=> hAPP(c_Polynomial_Opoly(X5,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5),X8)),X6) = c_Groups_Ouminus__class_Ouminus(X5,hAPP(c_Polynomial_Opoly(X5,X8),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__minus) ).
fof(f17344,plain,
spl47_848,
inference(avatar_split_clause,[],[f4679,f17342]) ).
fof(f17342,plain,
( spl47_848
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ sP9(X2,X1,X0)
| ~ sP10(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_848])]) ).
fof(f4679,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ sP9(X2,X1,X0)
| ~ sP10(X0,X1,X2) ),
inference(cnf_transformation,[],[f3680]) ).
fof(f3680,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ sP9(X2,X1,X0) )
& ( sP9(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2),c_Groups_Ozero__class_Ozero(X1)) ) )
| ~ sP10(X0,X1,X2) ),
inference(rectify,[],[f3679]) ).
fof(f3679,plain,
! [X1,X2,X0] :
( ( ( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
| ~ sP9(X0,X2,X1) )
& ( sP9(X0,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2)) ) )
| ~ sP10(X1,X2,X0) ),
inference(nnf_transformation,[],[f3491]) ).
fof(f3491,plain,
! [X1,X2,X0] :
( ( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
<=> sP9(X0,X2,X1) )
| ~ sP10(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f17340,plain,
spl47_847,
inference(avatar_split_clause,[],[f4678,f17338]) ).
fof(f17338,plain,
( spl47_847
<=> ! [X2,X0,X1] :
( sP9(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ sP10(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_847])]) ).
fof(f4678,plain,
! [X2,X0,X1] :
( sP9(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ sP10(X0,X1,X2) ),
inference(cnf_transformation,[],[f3680]) ).
fof(f17336,plain,
( spl47_846
| ~ spl47_122
| ~ spl47_333 ),
inference(avatar_split_clause,[],[f7869,f7729,f6641,f17333]) ).
fof(f17333,plain,
( spl47_846
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_846])]) ).
fof(f7869,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Nat_Onat)))
| ~ spl47_122
| ~ spl47_333 ),
inference(resolution,[],[f7730,f6643]) ).
fof(f17331,plain,
spl47_845,
inference(avatar_split_clause,[],[f4670,f17329]) ).
fof(f17329,plain,
( spl47_845
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1))
| ~ sP7(X2,X1,X0)
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_845])]) ).
fof(f4670,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1))
| ~ sP7(X2,X1,X0)
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f3675]) ).
fof(f3675,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1))
| ~ sP7(X2,X1,X0) )
& ( sP7(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)) ) )
| ~ sP8(X0,X1,X2) ),
inference(rectify,[],[f3674]) ).
fof(f3674,plain,
! [X1,X0,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
| ~ sP7(X2,X0,X1) )
& ( sP7(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ) )
| ~ sP8(X1,X0,X2) ),
inference(nnf_transformation,[],[f3488]) ).
fof(f3488,plain,
! [X1,X0,X2] :
( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
<=> sP7(X2,X0,X1) )
| ~ sP8(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f17327,plain,
spl47_844,
inference(avatar_split_clause,[],[f4669,f17325]) ).
fof(f4669,plain,
! [X2,X0,X1] :
( sP7(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1))
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f3675]) ).
fof(f17323,plain,
spl47_843,
inference(avatar_split_clause,[],[f4586,f17321]) ).
fof(f17321,plain,
( spl47_843
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_843])]) ).
fof(f4586,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(cnf_transformation,[],[f3649]) ).
fof(f3649,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ) ),
inference(flattening,[],[f3648]) ).
fof(f3648,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ) ),
inference(nnf_transformation,[],[f1599]) ).
fof(f1599,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
inference(rectify,[],[f342]) ).
fof(f342,axiom,
! [X11,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X11))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X11)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).
fof(f17319,plain,
spl47_842,
inference(avatar_split_clause,[],[f4485,f17317]) ).
fof(f17317,plain,
( spl47_842
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_842])]) ).
fof(f4485,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
inference(cnf_transformation,[],[f2605]) ).
fof(f2605,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
& ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
inference(flattening,[],[f2604]) ).
fof(f2604,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
& ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
| ~ class_Rings_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
inference(ennf_transformation,[],[f1557]) ).
fof(f1557,plain,
! [X0,X1] :
( ( class_Rings_Osemiring__0(X1)
& class_Power_Opower(X1) )
=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
=> c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X0) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
=> c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X0) ) ) ),
inference(rectify,[],[f280]) ).
fof(f280,axiom,
! [X7,X5] :
( ( class_Rings_Osemiring__0(X5)
& class_Power_Opower(X5) )
=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X7
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Ozero__class_Ozero(X5)),X7) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X7
=> c_Groups_Oone__class_Oone(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Ozero__class_Ozero(X5)),X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__left) ).
fof(f17315,plain,
spl47_841,
inference(avatar_split_clause,[],[f4448,f17313]) ).
fof(f17313,plain,
( spl47_841
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_841])]) ).
fof(f4448,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(cnf_transformation,[],[f3582]) ).
fof(f3582,plain,
! [X0,X1] :
( ( ( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X1 )
& ( ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X1 )
| c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(flattening,[],[f3581]) ).
fof(f3581,plain,
! [X0,X1] :
( ( ( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X1 )
& ( ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X1 )
| c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(nnf_transformation,[],[f2557]) ).
fof(f2557,plain,
! [X0,X1] :
( ( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
<=> ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X1 ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(ennf_transformation,[],[f1528]) ).
fof(f1528,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
=> ( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
<=> ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X1 ) ) ),
inference(rectify,[],[f687]) ).
fof(f687,axiom,
! [X11,X14] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X14)
=> ( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14),X11)
<=> ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X11
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
fof(f17311,plain,
spl47_840,
inference(avatar_split_clause,[],[f4447,f17309]) ).
fof(f17309,plain,
( spl47_840
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_840])]) ).
fof(f4447,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(cnf_transformation,[],[f3582]) ).
fof(f17307,plain,
spl47_839,
inference(avatar_split_clause,[],[f4443,f17305]) ).
fof(f17305,plain,
( spl47_839
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_839])]) ).
fof(f4443,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(cnf_transformation,[],[f2550]) ).
fof(f2550,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(flattening,[],[f2549]) ).
fof(f2549,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(ennf_transformation,[],[f1524]) ).
fof(f1524,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) ) ),
inference(rectify,[],[f710]) ).
fof(f710,axiom,
! [X10,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X10)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X6,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
fof(f17303,plain,
spl47_838,
inference(avatar_split_clause,[],[f4396,f17301]) ).
fof(f17301,plain,
( spl47_838
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1))),X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_838])]) ).
fof(f4396,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1))),X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2499]) ).
fof(f2499,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1))),X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1483]) ).
fof(f1483,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Groups_Oplus__class_Oplus(X1,X0,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1))),X0) ),
inference(rectify,[],[f586]) ).
fof(f586,axiom,
! [X21,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,X21,X21) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oplus__class_Oplus(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Oone__class_Oone(X5))),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(f17236,plain,
( spl47_837
| ~ spl47_120
| ~ spl47_333 ),
inference(avatar_split_clause,[],[f7867,f7729,f6631,f17233]) ).
fof(f17233,plain,
( spl47_837
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_837])]) ).
fof(f7867,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
| ~ spl47_120
| ~ spl47_333 ),
inference(resolution,[],[f7730,f6633]) ).
fof(f17148,plain,
( spl47_836
| ~ spl47_279
| ~ spl47_302 ),
inference(avatar_split_clause,[],[f7595,f7437,f7319,f17146]) ).
fof(f17146,plain,
( spl47_836
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_836])]) ).
fof(f7319,plain,
( spl47_279
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_279])]) ).
fof(f7437,plain,
( spl47_302
<=> ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_302])]) ).
fof(f7595,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ~ spl47_279
| ~ spl47_302 ),
inference(superposition,[],[f7320,f7438]) ).
fof(f7438,plain,
( ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
| ~ spl47_302 ),
inference(avatar_component_clause,[],[f7437]) ).
fof(f7320,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl47_279 ),
inference(avatar_component_clause,[],[f7319]) ).
fof(f17004,plain,
( spl47_835
| ~ spl47_280
| ~ spl47_302 ),
inference(avatar_split_clause,[],[f7594,f7437,f7323,f17002]) ).
fof(f17002,plain,
( spl47_835
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_835])]) ).
fof(f7323,plain,
( spl47_280
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_280])]) ).
fof(f7594,plain,
( ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X0)
| ~ spl47_280
| ~ spl47_302 ),
inference(superposition,[],[f7324,f7438]) ).
fof(f7324,plain,
( ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ spl47_280 ),
inference(avatar_component_clause,[],[f7323]) ).
fof(f16773,plain,
( spl47_834
| ~ spl47_281
| ~ spl47_302 ),
inference(avatar_split_clause,[],[f7593,f7437,f7327,f16771]) ).
fof(f16771,plain,
( spl47_834
<=> ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_834])]) ).
fof(f7327,plain,
( spl47_281
<=> ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_281])]) ).
fof(f7593,plain,
( ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))
| ~ spl47_281
| ~ spl47_302 ),
inference(superposition,[],[f7328,f7438]) ).
fof(f7328,plain,
( ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ spl47_281 ),
inference(avatar_component_clause,[],[f7327]) ).
fof(f16655,plain,
( spl47_833
| ~ spl47_282
| ~ spl47_301 ),
inference(avatar_split_clause,[],[f7576,f7433,f7331,f16653]) ).
fof(f16653,plain,
( spl47_833
<=> ! [X0] : c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_833])]) ).
fof(f7331,plain,
( spl47_282
<=> ! [X1] : c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_282])]) ).
fof(f7433,plain,
( spl47_301
<=> ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_301])]) ).
fof(f7576,plain,
( ! [X0] : c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0))
| ~ spl47_282
| ~ spl47_301 ),
inference(superposition,[],[f7332,f7434]) ).
fof(f7434,plain,
( ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)
| ~ spl47_301 ),
inference(avatar_component_clause,[],[f7433]) ).
fof(f7332,plain,
( ! [X1] : c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl47_282 ),
inference(avatar_component_clause,[],[f7331]) ).
fof(f16614,plain,
( spl47_832
| ~ spl47_301
| ~ spl47_789 ),
inference(avatar_split_clause,[],[f16420,f16417,f7433,f16612]) ).
fof(f16612,plain,
( spl47_832
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_832])]) ).
fof(f16417,plain,
( spl47_789
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_789])]) ).
fof(f16420,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ~ spl47_301
| ~ spl47_789 ),
inference(forward_demodulation,[],[f16418,f7434]) ).
fof(f16418,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ~ spl47_789 ),
inference(avatar_component_clause,[],[f16417]) ).
fof(f16610,plain,
( spl47_831
| ~ spl47_301
| ~ spl47_788 ),
inference(avatar_split_clause,[],[f16415,f16412,f7433,f16608]) ).
fof(f16608,plain,
( spl47_831
<=> ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_831])]) ).
fof(f16412,plain,
( spl47_788
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_788])]) ).
fof(f16415,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ~ spl47_301
| ~ spl47_788 ),
inference(forward_demodulation,[],[f16413,f7434]) ).
fof(f16413,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ~ spl47_788 ),
inference(avatar_component_clause,[],[f16412]) ).
fof(f16606,plain,
spl47_830,
inference(avatar_split_clause,[],[f6019,f16604]) ).
fof(f16604,plain,
( spl47_830
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X1,X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(X2,X0)))
| ~ class_Groups_Ozero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_830])]) ).
fof(f6019,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X1,X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(X2,X0)))
| ~ class_Groups_Ozero(X2) ),
inference(forward_demodulation,[],[f5630,f4240]) ).
fof(f5630,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X1,X0)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Groups_Ozero(X2) ),
inference(definition_unfolding,[],[f4879,f4118]) ).
fof(f4879,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X1,X0)),c_Nat_OSuc(c_Polynomial_Odegree(X2,X0)))
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f2852]) ).
fof(f2852,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X1,X0)),c_Nat_OSuc(c_Polynomial_Odegree(X2,X0)))
| ~ class_Groups_Ozero(X2) ),
inference(ennf_transformation,[],[f1805]) ).
fof(f1805,plain,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_OpCons(X2,X1,X0)),c_Nat_OSuc(c_Polynomial_Odegree(X2,X0))) ),
inference(rectify,[],[f91]) ).
fof(f91,axiom,
! [X8,X4,X5] :
( class_Groups_Ozero(X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X5,c_Polynomial_OpCons(X5,X4,X8)),c_Nat_OSuc(c_Polynomial_Odegree(X5,X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__pCons__le) ).
fof(f16602,plain,
spl47_829,
inference(avatar_split_clause,[],[f5979,f16600]) ).
fof(f16600,plain,
( spl47_829
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_829])]) ).
fof(f5979,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(forward_demodulation,[],[f5978,f4114]) ).
fof(f5978,plain,
! [X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(forward_demodulation,[],[f5977,f4240]) ).
fof(f5977,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(forward_demodulation,[],[f5976,f4114]) ).
fof(f5976,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(forward_demodulation,[],[f5611,f4240]) ).
fof(f5611,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(definition_unfolding,[],[f4598,f4118,f4118]) ).
fof(f4598,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0) ),
inference(cnf_transformation,[],[f3657]) ).
fof(f3657,plain,
! [X0,X1] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
| ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0) ) ),
inference(flattening,[],[f3656]) ).
fof(f3656,plain,
! [X0,X1] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
| ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0) ) ),
inference(nnf_transformation,[],[f1603]) ).
fof(f1603,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
<=> ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X14,X15] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X15),X14)
<=> ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X15
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
fof(f16598,plain,
spl47_828,
inference(avatar_split_clause,[],[f5903,f16596]) ).
fof(f16596,plain,
( spl47_828
<=> ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_828])]) ).
fof(f5903,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(forward_demodulation,[],[f5902,f4114]) ).
fof(f5902,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(forward_demodulation,[],[f5901,f5515]) ).
fof(f5515,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(definition_unfolding,[],[f4119,f4118]) ).
fof(f4119,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f1243]) ).
fof(f1243,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(rectify,[],[f317]) ).
fof(f317,axiom,
! [X7] : c_Nat_OSuc(X7) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(f5901,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(forward_demodulation,[],[f5900,f5515]) ).
fof(f5900,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(forward_demodulation,[],[f5899,f4114]) ).
fof(f5899,plain,
! [X0] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(forward_demodulation,[],[f5522,f5515]) ).
fof(f5522,plain,
! [X0] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(definition_unfolding,[],[f4213,f4118,f4118,f4118]) ).
fof(f4213,plain,
! [X0] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(cnf_transformation,[],[f2390]) ).
fof(f2390,plain,
! [X0] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(flattening,[],[f2389]) ).
fof(f2389,plain,
! [X0] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(ennf_transformation,[],[f1337]) ).
fof(f1337,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
=> ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(rectify,[],[f308]) ).
fof(f308,axiom,
! [X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
=> ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X6
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).
fof(f16594,plain,
spl47_827,
inference(avatar_split_clause,[],[f5888,f16592]) ).
fof(f16592,plain,
( spl47_827
<=> ! [X2] :
( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__comm__monoid__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_827])]) ).
fof(f5888,plain,
! [X2] :
( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(duplicate_literal_removal,[],[f5749]) ).
fof(f5749,plain,
! [X2] :
( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(equality_resolution,[],[f5748]) ).
fof(f5748,plain,
! [X2,X1] :
( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| c_Groups_Ozero__class_Ozero(X2) != X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(equality_resolution,[],[f4761]) ).
fof(f4761,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(X2) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(cnf_transformation,[],[f3709]) ).
fof(f16590,plain,
spl47_826,
inference(avatar_split_clause,[],[f5845,f16588]) ).
fof(f16588,plain,
( spl47_826
<=> ! [X2,X1,X3] :
( sP18(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_826])]) ).
fof(f5845,plain,
! [X2,X3,X1] :
( sP18(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)))) ),
inference(equality_resolution,[],[f5192]) ).
fof(f5192,plain,
! [X2,X3,X0,X1] :
( sP18(X0,X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0 ),
inference(cnf_transformation,[],[f3842]) ).
fof(f3842,plain,
! [X0,X1,X2,X3] :
( ( sP18(X0,X1,X2,X3)
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
& c_Groups_Ozero__class_Ozero(X2) != X3 )
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
& c_Groups_Ozero__class_Ozero(X2) = X3 ) )
& ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
| c_Groups_Ozero__class_Ozero(X2) = X3 )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Groups_Ozero__class_Ozero(X2) != X3 ) )
| ~ sP18(X0,X1,X2,X3) ) ),
inference(rectify,[],[f3841]) ).
fof(f3841,plain,
! [X0,X1,X3,X2] :
( ( sP18(X0,X1,X3,X2)
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
& c_Groups_Ozero__class_Ozero(X3) != X2 )
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != X0
& c_Groups_Ozero__class_Ozero(X3) = X2 ) )
& ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
| c_Groups_Ozero__class_Ozero(X3) = X2 )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X0
| c_Groups_Ozero__class_Ozero(X3) != X2 ) )
| ~ sP18(X0,X1,X3,X2) ) ),
inference(flattening,[],[f3840]) ).
fof(f3840,plain,
! [X0,X1,X3,X2] :
( ( sP18(X0,X1,X3,X2)
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
& c_Groups_Ozero__class_Ozero(X3) != X2 )
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != X0
& c_Groups_Ozero__class_Ozero(X3) = X2 ) )
& ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
| c_Groups_Ozero__class_Ozero(X3) = X2 )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X0
| c_Groups_Ozero__class_Ozero(X3) != X2 ) )
| ~ sP18(X0,X1,X3,X2) ) ),
inference(nnf_transformation,[],[f3505]) ).
fof(f3505,plain,
! [X0,X1,X3,X2] :
( sP18(X0,X1,X3,X2)
<=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
| c_Groups_Ozero__class_Ozero(X3) = X2 )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X0
| c_Groups_Ozero__class_Ozero(X3) != X2 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).
fof(f16586,plain,
spl47_825,
inference(avatar_split_clause,[],[f5838,f16584]) ).
fof(f16584,plain,
( spl47_825
<=> ! [X2,X0,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Rings_Oinverse__class_Odivide(X3,X0,X2)),X2) = X0
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Rings_Odivision__ring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_825])]) ).
fof(f5838,plain,
! [X2,X3,X0] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Rings_Oinverse__class_Odivide(X3,X0,X2)),X2) = X0
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Rings_Odivision__ring(X3) ),
inference(equality_resolution,[],[f5154]) ).
fof(f5154,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2) = X0
| c_Rings_Oinverse__class_Odivide(X3,X0,X2) != X1
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Rings_Odivision__ring(X3) ),
inference(cnf_transformation,[],[f3831]) ).
fof(f3831,plain,
! [X0,X1,X2,X3] :
( ( ( c_Rings_Oinverse__class_Odivide(X3,X0,X2) = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2) != X0 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2) = X0
| c_Rings_Oinverse__class_Odivide(X3,X0,X2) != X1 ) )
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Rings_Odivision__ring(X3) ),
inference(nnf_transformation,[],[f3076]) ).
fof(f3076,plain,
! [X0,X1,X2,X3] :
( ( c_Rings_Oinverse__class_Odivide(X3,X0,X2) = X1
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2) = X0 )
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Rings_Odivision__ring(X3) ),
inference(flattening,[],[f3075]) ).
fof(f3075,plain,
! [X0,X1,X2,X3] :
( ( c_Rings_Oinverse__class_Odivide(X3,X0,X2) = X1
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2) = X0 )
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Rings_Odivision__ring(X3) ),
inference(ennf_transformation,[],[f2000]) ).
fof(f2000,plain,
! [X0,X1,X2,X3] :
( class_Rings_Odivision__ring(X3)
=> ( c_Groups_Ozero__class_Ozero(X3) != X2
=> ( c_Rings_Oinverse__class_Odivide(X3,X0,X2) = X1
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2) = X0 ) ) ),
inference(rectify,[],[f920]) ).
fof(f920,axiom,
! [X29,X12,X24,X5] :
( class_Rings_Odivision__ring(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X24
=> ( c_Rings_Oinverse__class_Odivide(X5,X29,X24) = X12
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X24) = X29 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__eq__divide__eq) ).
fof(f16582,plain,
spl47_824,
inference(avatar_split_clause,[],[f5835,f16580]) ).
fof(f16580,plain,
( spl47_824
<=> ! [X2,X1,X3] :
( c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2),X2) = X1
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Rings_Odivision__ring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_824])]) ).
fof(f5835,plain,
! [X2,X3,X1] :
( c_Rings_Oinverse__class_Odivide(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2),X2) = X1
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Rings_Odivision__ring(X3) ),
inference(equality_resolution,[],[f5152]) ).
fof(f5152,plain,
! [X2,X3,X0,X1] :
( c_Rings_Oinverse__class_Odivide(X3,X0,X2) = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2) != X0
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Rings_Odivision__ring(X3) ),
inference(cnf_transformation,[],[f3072]) ).
fof(f3072,plain,
! [X0,X1,X2,X3] :
( c_Rings_Oinverse__class_Odivide(X3,X0,X2) = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2) != X0
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Rings_Odivision__ring(X3) ),
inference(flattening,[],[f3071]) ).
fof(f3071,plain,
! [X0,X1,X2,X3] :
( c_Rings_Oinverse__class_Odivide(X3,X0,X2) = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2) != X0
| c_Groups_Ozero__class_Ozero(X3) = X2
| ~ class_Rings_Odivision__ring(X3) ),
inference(ennf_transformation,[],[f1998]) ).
fof(f1998,plain,
! [X0,X1,X2,X3] :
( class_Rings_Odivision__ring(X3)
=> ( c_Groups_Ozero__class_Ozero(X3) != X2
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X2) = X0
=> c_Rings_Oinverse__class_Odivide(X3,X0,X2) = X1 ) ) ),
inference(rectify,[],[f917]) ).
fof(f917,axiom,
! [X17,X4,X16,X5] :
( class_Rings_Odivision__ring(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X16
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X16) = X17
=> c_Rings_Oinverse__class_Odivide(X5,X17,X16) = X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__imp) ).
fof(f16559,plain,
spl47_823,
inference(avatar_split_clause,[],[f5666,f16557]) ).
fof(f16557,plain,
( spl47_823
<=> ! [X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_823])]) ).
fof(f5666,plain,
! [X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(equality_resolution,[],[f4325]) ).
fof(f4325,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = c_Groups_Oone__class_Oone(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) != X0
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(cnf_transformation,[],[f3570]) ).
fof(f16555,plain,
spl47_822,
inference(avatar_split_clause,[],[f5497,f16553]) ).
fof(f16553,plain,
( spl47_822
<=> ! [X6,X4,X3,X0,X5,X2,X1] :
( X0 = X2
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X1,X0)
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
| ~ class_Fields_Ofield(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_822])]) ).
fof(f5497,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( X0 = X2
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X1,X0)
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
| ~ class_Fields_Ofield(X6) ),
inference(cnf_transformation,[],[f3470]) ).
fof(f3470,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( X0 = X2
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X1,X0)
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
| ~ class_Fields_Ofield(X6) ),
inference(flattening,[],[f3469]) ).
fof(f3469,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( X0 = X2
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X1,X0)
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
| ~ class_Fields_Ofield(X6) ),
inference(ennf_transformation,[],[f2257]) ).
fof(f2257,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( class_Fields_Ofield(X6)
=> ( c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
=> ( c_Polynomial_Opdivmod__rel(X6,X5,X4,X1,X0)
=> X0 = X2 ) ) ),
inference(rectify,[],[f738]) ).
fof(f738,axiom,
! [X71,X72,X73,X74,X10,X6,X5] :
( class_Fields_Ofield(X5)
=> ( c_Polynomial_Opdivmod__rel(X5,X6,X10,X74,X73)
=> ( c_Polynomial_Opdivmod__rel(X5,X6,X10,X72,X71)
=> X71 = X73 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__unique__mod) ).
fof(f16551,plain,
spl47_821,
inference(avatar_split_clause,[],[f5496,f16549]) ).
fof(f16549,plain,
( spl47_821
<=> ! [X5,X6,X4,X2,X0,X3,X1] :
( X1 = X3
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X1,X0)
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
| ~ class_Fields_Ofield(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_821])]) ).
fof(f5496,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( X1 = X3
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X1,X0)
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
| ~ class_Fields_Ofield(X6) ),
inference(cnf_transformation,[],[f3468]) ).
fof(f3468,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( X1 = X3
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X1,X0)
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
| ~ class_Fields_Ofield(X6) ),
inference(flattening,[],[f3467]) ).
fof(f3467,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( X1 = X3
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X1,X0)
| ~ c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
| ~ class_Fields_Ofield(X6) ),
inference(ennf_transformation,[],[f2256]) ).
fof(f2256,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( class_Fields_Ofield(X6)
=> ( c_Polynomial_Opdivmod__rel(X6,X5,X4,X3,X2)
=> ( c_Polynomial_Opdivmod__rel(X6,X5,X4,X1,X0)
=> X1 = X3 ) ) ),
inference(rectify,[],[f739]) ).
fof(f739,axiom,
! [X71,X72,X73,X74,X10,X6,X5] :
( class_Fields_Ofield(X5)
=> ( c_Polynomial_Opdivmod__rel(X5,X6,X10,X74,X73)
=> ( c_Polynomial_Opdivmod__rel(X5,X6,X10,X72,X71)
=> X72 = X74 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__unique__div) ).
fof(f16547,plain,
spl47_820,
inference(avatar_split_clause,[],[f5390,f16545]) ).
fof(f16545,plain,
( spl47_820
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_820])]) ).
fof(f5390,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(cnf_transformation,[],[f3364]) ).
fof(f3364,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(flattening,[],[f3363]) ).
fof(f3363,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(ennf_transformation,[],[f2184]) ).
fof(f2184,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(rectify,[],[f320]) ).
fof(f320,axiom,
! [X7,X21,X43,X20] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X43)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X43) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X7)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
fof(f16543,plain,
spl47_819,
inference(avatar_split_clause,[],[f5341,f16541]) ).
fof(f16541,plain,
( spl47_819
<=> ! [X0,X3,X2,X1] :
( c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_819])]) ).
fof(f5341,plain,
! [X2,X3,X0,X1] :
( c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3287]) ).
fof(f3287,plain,
! [X0,X1,X2,X3] :
( c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2137]) ).
fof(f2137,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),X1) ),
inference(rectify,[],[f443]) ).
fof(f443,axiom,
! [X16,X17,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Oplus__class_Oplus(X5,X4,X17),X16) = c_Groups_Oplus__class_Oplus(X5,c_Groups_Oplus__class_Oplus(X5,X4,X16),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(f16539,plain,
spl47_818,
inference(avatar_split_clause,[],[f5339,f16537]) ).
fof(f16537,plain,
( spl47_818
<=> ! [X0,X3,X2,X1] :
( c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_818])]) ).
fof(f5339,plain,
! [X2,X3,X0,X1] :
( c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3285]) ).
fof(f3285,plain,
! [X0,X1,X2,X3] :
( c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2135]) ).
fof(f2135,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) ),
inference(rectify,[],[f445]) ).
fof(f445,axiom,
! [X46,X16,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Oplus__class_Oplus(X5,X16,X46)) = c_Groups_Oplus__class_Oplus(X5,c_Groups_Oplus__class_Oplus(X5,X4,X16),X46) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(f16535,plain,
spl47_817,
inference(avatar_split_clause,[],[f5338,f16533]) ).
fof(f16533,plain,
( spl47_817
<=> ! [X0,X3,X2,X1] :
( c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_817])]) ).
fof(f5338,plain,
! [X2,X3,X0,X1] :
( c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3284]) ).
fof(f3284,plain,
! [X0,X1,X2,X3] :
( c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2134]) ).
fof(f2134,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ),
inference(rectify,[],[f446]) ).
fof(f446,axiom,
! [X46,X16,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Oplus__class_Oplus(X5,X16,X46)) = c_Groups_Oplus__class_Oplus(X5,X16,c_Groups_Oplus__class_Oplus(X5,X4,X46)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(f16531,plain,
spl47_816,
inference(avatar_split_clause,[],[f5291,f16529]) ).
fof(f16529,plain,
( spl47_816
<=> ! [X0,X3,X2,X1] :
( c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0))
| ~ class_Groups_Oab__semigroup__add(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_816])]) ).
fof(f5291,plain,
! [X2,X3,X0,X1] :
( c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0))
| ~ class_Groups_Oab__semigroup__add(X3) ),
inference(cnf_transformation,[],[f3231]) ).
fof(f3231,plain,
! [X0,X1,X2,X3] :
( c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0))
| ~ class_Groups_Oab__semigroup__add(X3) ),
inference(ennf_transformation,[],[f2091]) ).
fof(f2091,plain,
! [X0,X1,X2,X3] :
( class_Groups_Oab__semigroup__add(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) ),
inference(rectify,[],[f347]) ).
fof(f347,axiom,
! [X16,X17,X4,X5] :
( class_Groups_Oab__semigroup__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Oplus__class_Oplus(X5,X4,X17),X16) = c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Oplus__class_Oplus(X5,X17,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(f16527,plain,
spl47_815,
inference(avatar_split_clause,[],[f5191,f16525]) ).
fof(f5191,plain,
! [X2,X3,X0,X1] :
( sP18(X0,X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
| c_Groups_Ozero__class_Ozero(X2) = X3 ),
inference(cnf_transformation,[],[f3842]) ).
fof(f16523,plain,
spl47_814,
inference(avatar_split_clause,[],[f5188,f16521]) ).
fof(f16521,plain,
( spl47_814
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
| c_Groups_Ozero__class_Ozero(X2) = X3
| ~ sP18(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_814])]) ).
fof(f5188,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X1),X0))
| c_Groups_Ozero__class_Ozero(X2) = X3
| ~ sP18(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3842]) ).
fof(f16518,plain,
spl47_813,
inference(avatar_split_clause,[],[f5142,f16516]) ).
fof(f16516,plain,
( spl47_813
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2) = X3
| c_Groups_Ozero__class_Ozero(X1) = X2
| ~ sP16(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_813])]) ).
fof(f5142,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2) = X3
| c_Groups_Ozero__class_Ozero(X1) = X2
| ~ sP16(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3830]) ).
fof(f3830,plain,
! [X0,X1,X2,X3] :
( ( sP16(X0,X1,X2,X3)
| ( c_Groups_Ozero__class_Ozero(X1) != X0
& c_Groups_Ozero__class_Ozero(X1) = X2 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2) != X3
& c_Groups_Ozero__class_Ozero(X1) != X2 ) )
& ( ( ( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != X2 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2) = X3
| c_Groups_Ozero__class_Ozero(X1) = X2 ) )
| ~ sP16(X0,X1,X2,X3) ) ),
inference(rectify,[],[f3829]) ).
fof(f3829,plain,
! [X0,X3,X1,X2] :
( ( sP16(X0,X3,X1,X2)
| ( c_Groups_Ozero__class_Ozero(X3) != X0
& c_Groups_Ozero__class_Ozero(X3) = X1 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1) != X2
& c_Groups_Ozero__class_Ozero(X3) != X1 ) )
& ( ( ( c_Groups_Ozero__class_Ozero(X3) = X0
| c_Groups_Ozero__class_Ozero(X3) != X1 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1) = X2
| c_Groups_Ozero__class_Ozero(X3) = X1 ) )
| ~ sP16(X0,X3,X1,X2) ) ),
inference(flattening,[],[f3828]) ).
fof(f3828,plain,
! [X0,X3,X1,X2] :
( ( sP16(X0,X3,X1,X2)
| ( c_Groups_Ozero__class_Ozero(X3) != X0
& c_Groups_Ozero__class_Ozero(X3) = X1 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1) != X2
& c_Groups_Ozero__class_Ozero(X3) != X1 ) )
& ( ( ( c_Groups_Ozero__class_Ozero(X3) = X0
| c_Groups_Ozero__class_Ozero(X3) != X1 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1) = X2
| c_Groups_Ozero__class_Ozero(X3) = X1 ) )
| ~ sP16(X0,X3,X1,X2) ) ),
inference(nnf_transformation,[],[f3502]) ).
fof(f3502,plain,
! [X0,X3,X1,X2] :
( sP16(X0,X3,X1,X2)
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = X0
| c_Groups_Ozero__class_Ozero(X3) != X1 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1) = X2
| c_Groups_Ozero__class_Ozero(X3) = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f16514,plain,
spl47_812,
inference(avatar_split_clause,[],[f5133,f16512]) ).
fof(f16512,plain,
( spl47_812
<=> ! [X0,X3,X2,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2) = X3
| c_Groups_Ozero__class_Ozero(X1) = X2
| ~ sP14(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_812])]) ).
fof(f5133,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2) = X3
| c_Groups_Ozero__class_Ozero(X1) = X2
| ~ sP14(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3825]) ).
fof(f3825,plain,
! [X0,X1,X2,X3] :
( ( sP14(X0,X1,X2,X3)
| ( c_Groups_Ozero__class_Ozero(X1) != X0
& c_Groups_Ozero__class_Ozero(X1) = X2 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2) != X3
& c_Groups_Ozero__class_Ozero(X1) != X2 ) )
& ( ( ( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != X2 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2) = X3
| c_Groups_Ozero__class_Ozero(X1) = X2 ) )
| ~ sP14(X0,X1,X2,X3) ) ),
inference(rectify,[],[f3824]) ).
fof(f3824,plain,
! [X2,X3,X0,X1] :
( ( sP14(X2,X3,X0,X1)
| ( c_Groups_Ozero__class_Ozero(X3) != X2
& c_Groups_Ozero__class_Ozero(X3) = X0 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0) != X1
& c_Groups_Ozero__class_Ozero(X3) != X0 ) )
& ( ( ( c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Ozero__class_Ozero(X3) != X0 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0) = X1
| c_Groups_Ozero__class_Ozero(X3) = X0 ) )
| ~ sP14(X2,X3,X0,X1) ) ),
inference(flattening,[],[f3823]) ).
fof(f3823,plain,
! [X2,X3,X0,X1] :
( ( sP14(X2,X3,X0,X1)
| ( c_Groups_Ozero__class_Ozero(X3) != X2
& c_Groups_Ozero__class_Ozero(X3) = X0 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0) != X1
& c_Groups_Ozero__class_Ozero(X3) != X0 ) )
& ( ( ( c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Ozero__class_Ozero(X3) != X0 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0) = X1
| c_Groups_Ozero__class_Ozero(X3) = X0 ) )
| ~ sP14(X2,X3,X0,X1) ) ),
inference(nnf_transformation,[],[f3499]) ).
fof(f3499,plain,
! [X2,X3,X0,X1] :
( sP14(X2,X3,X0,X1)
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Ozero__class_Ozero(X3) != X0 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0) = X1
| c_Groups_Ozero__class_Ozero(X3) = X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f16510,plain,
spl47_811,
inference(avatar_split_clause,[],[f5072,f16508]) ).
fof(f16508,plain,
( spl47_811
<=> ! [X2,X0,X1] :
( sP13(X0,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK45(X0,X1,X2)) = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_811])]) ).
fof(f5072,plain,
! [X2,X0,X1] :
( sP13(X0,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK45(X0,X1,X2)) = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(cnf_transformation,[],[f3793]) ).
fof(f16506,plain,
spl47_810,
inference(avatar_split_clause,[],[f5064,f16504]) ).
fof(f16504,plain,
( spl47_810
<=> ! [X2,X0,X1] :
( sP12(X0,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK44(X0,X1,X2)) = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_810])]) ).
fof(f5064,plain,
! [X2,X0,X1] :
( sP12(X0,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK44(X0,X1,X2)) = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(cnf_transformation,[],[f3787]) ).
fof(f16502,plain,
spl47_809,
inference(avatar_split_clause,[],[f5056,f16500]) ).
fof(f16500,plain,
( spl47_809
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| sP11(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_809])]) ).
fof(f5056,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| sP11(X2,X1,X0) ),
inference(cnf_transformation,[],[f3494]) ).
fof(f3494,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) )
| ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& X1 = X2 )
| sP11(X2,X1,X0) ),
inference(definition_folding,[],[f3048,f3493]) ).
fof(f3493,plain,
! [X2,X1,X0] :
( ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
| ~ sP11(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f3048,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) )
| ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& X1 = X2 )
| ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
inference(flattening,[],[f3047]) ).
fof(f3047,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(X0,X1),X2))
| ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) )
| ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& X1 = X2 )
| ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
inference(ennf_transformation,[],[f1938]) ).
fof(f1938,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> hBOOL(hAPP(hAPP(X0,X1),X2)) )
=> ( ( X1 = X2
=> hBOOL(hAPP(hAPP(X0,X1),X2)) )
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
=> hBOOL(hAPP(hAPP(X0,X1),X2)) )
=> hBOOL(hAPP(hAPP(X0,X1),X2)) ) ) ),
inference(rectify,[],[f176]) ).
fof(f176,axiom,
! [X39,X11,X14] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X11)
=> hBOOL(hAPP(hAPP(X39,X11),X14)) )
=> ( ( X11 = X14
=> hBOOL(hAPP(hAPP(X39,X11),X14)) )
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X14)
=> hBOOL(hAPP(hAPP(X39,X11),X14)) )
=> hBOOL(hAPP(hAPP(X39,X11),X14)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).
fof(f16498,plain,
spl47_808,
inference(avatar_split_clause,[],[f4862,f16496]) ).
fof(f16496,plain,
( spl47_808
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_808])]) ).
fof(f4862,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(cnf_transformation,[],[f2830]) ).
fof(f2830,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(flattening,[],[f2829]) ).
fof(f2829,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(ennf_transformation,[],[f1790]) ).
fof(f1790,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ) ),
inference(rectify,[],[f252]) ).
fof(f252,axiom,
! [X7,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).
fof(f16494,plain,
spl47_807,
inference(avatar_split_clause,[],[f4855,f16492]) ).
fof(f16492,plain,
( spl47_807
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_807])]) ).
fof(f4855,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(cnf_transformation,[],[f2816]) ).
fof(f2816,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(flattening,[],[f2815]) ).
fof(f2815,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(ennf_transformation,[],[f1783]) ).
fof(f1783,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ) ),
inference(rectify,[],[f108]) ).
fof(f108,axiom,
! [X7,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power) ).
fof(f16490,plain,
spl47_806,
inference(avatar_split_clause,[],[f4854,f16488]) ).
fof(f16488,plain,
( spl47_806
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_806])]) ).
fof(f4854,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(cnf_transformation,[],[f2814]) ).
fof(f2814,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(flattening,[],[f2813]) ).
fof(f2813,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(ennf_transformation,[],[f1782]) ).
fof(f1782,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),X1)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)) ) ),
inference(rectify,[],[f253]) ).
fof(f253,axiom,
! [X7,X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5),X4)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__power) ).
fof(f16486,plain,
spl47_805,
inference(avatar_split_clause,[],[f4848,f16484]) ).
fof(f16484,plain,
( spl47_805
<=> ! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Oab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_805])]) ).
fof(f4848,plain,
! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Oab__group__add(X2) ),
inference(cnf_transformation,[],[f2808]) ).
fof(f2808,plain,
! [X0,X1,X2] :
( c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Oab__group__add(X2) ),
inference(ennf_transformation,[],[f1777]) ).
fof(f1777,plain,
! [X0,X1,X2] :
( class_Groups_Oab__group__add(X2)
=> c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(rectify,[],[f418]) ).
fof(f418,axiom,
! [X17,X4,X5] :
( class_Groups_Oab__group__add(X5)
=> c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Oplus__class_Oplus(X5,X4,X17)) = c_Groups_Oplus__class_Oplus(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),c_Groups_Ouminus__class_Ouminus(X5,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__distrib) ).
fof(f16482,plain,
spl47_804,
inference(avatar_split_clause,[],[f4847,f16480]) ).
fof(f16480,plain,
( spl47_804
<=> ! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Oab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_804])]) ).
fof(f4847,plain,
! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Oab__group__add(X2) ),
inference(cnf_transformation,[],[f2807]) ).
fof(f2807,plain,
! [X0,X1,X2] :
( c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Oab__group__add(X2) ),
inference(ennf_transformation,[],[f1776]) ).
fof(f1776,plain,
! [X0,X1,X2] :
( class_Groups_Oab__group__add(X2)
=> c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(rectify,[],[f901]) ).
fof(f901,axiom,
! [X17,X4,X5] :
( class_Groups_Oab__group__add(X5)
=> c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Ominus__class_Ominus(X5,X4,X17)) = c_Groups_Ominus__class_Ominus(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),c_Groups_Ouminus__class_Ouminus(X5,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Limits_Ominus__diff__minus) ).
fof(f16477,plain,
spl47_803,
inference(avatar_split_clause,[],[f4832,f16475]) ).
fof(f16475,plain,
( spl47_803
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Oorder(X2,X0,X1)
| ~ class_Rings_Oidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_803])]) ).
fof(f4832,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Oorder(X2,X0,X1)
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f3727]) ).
fof(f16473,plain,
spl47_802,
inference(avatar_split_clause,[],[f4804,f16471]) ).
fof(f16471,plain,
( spl47_802
<=> ! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ class_Groups_Ogroup__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_802])]) ).
fof(f4804,plain,
! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ class_Groups_Ogroup__add(X2) ),
inference(cnf_transformation,[],[f2775]) ).
fof(f2775,plain,
! [X0,X1,X2] :
( c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f1751]) ).
fof(f1751,plain,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1)) ),
inference(rectify,[],[f419]) ).
fof(f419,axiom,
! [X17,X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Oplus__class_Oplus(X5,X4,X17)) = c_Groups_Oplus__class_Oplus(X5,c_Groups_Ouminus__class_Ouminus(X5,X17),c_Groups_Ouminus__class_Ouminus(X5,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add) ).
fof(f16469,plain,
spl47_801,
inference(avatar_split_clause,[],[f4748,f16467]) ).
fof(f16467,plain,
( spl47_801
<=> ! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X0)) = c_Polynomial_Osmult(X2,X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0))
| ~ class_Rings_Ocomm__ring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_801])]) ).
fof(f4748,plain,
! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X0)) = c_Polynomial_Osmult(X2,X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0))
| ~ class_Rings_Ocomm__ring(X2) ),
inference(cnf_transformation,[],[f2705]) ).
fof(f2705,plain,
! [X0,X1,X2] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X0)) = c_Polynomial_Osmult(X2,X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0))
| ~ class_Rings_Ocomm__ring(X2) ),
inference(ennf_transformation,[],[f1708]) ).
fof(f1708,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__ring(X2)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X0)) = c_Polynomial_Osmult(X2,X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0)) ),
inference(rectify,[],[f426]) ).
fof(f426,axiom,
! [X8,X4,X5] :
( class_Rings_Ocomm__ring(X5)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5),c_Polynomial_Osmult(X5,X4,X8)) = c_Polynomial_Osmult(X5,X4,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__minus__right) ).
fof(f16465,plain,
spl47_800,
inference(avatar_split_clause,[],[f4718,f16463]) ).
fof(f16463,plain,
( spl47_800
<=> ! [X2,X0,X1] :
( c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0)
| ~ class_Rings_Olinordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_800])]) ).
fof(f4718,plain,
! [X2,X0,X1] :
( c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(cnf_transformation,[],[f3699]) ).
fof(f3699,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0)
| ( ~ c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
& X0 != X1 ) )
& ( c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0) ) )
| ~ class_Rings_Olinordered__idom(X2) ),
inference(flattening,[],[f3698]) ).
fof(f3698,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0)
| ( ~ c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
& X0 != X1 ) )
& ( c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0) ) )
| ~ class_Rings_Olinordered__idom(X2) ),
inference(nnf_transformation,[],[f2678]) ).
fof(f2678,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0)
<=> ( c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
| X0 = X1 ) )
| ~ class_Rings_Olinordered__idom(X2) ),
inference(ennf_transformation,[],[f1688]) ).
fof(f1688,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0)
<=> ( c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
| X0 = X1 ) ) ),
inference(rectify,[],[f886]) ).
fof(f886,axiom,
! [X25,X15,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X5),X15,X25)
<=> ( c_Polynomial_Opos__poly(X5,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5),X25,X15))
| X15 = X25 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__poly__def) ).
fof(f16461,plain,
spl47_799,
inference(avatar_split_clause,[],[f4715,f16459]) ).
fof(f16459,plain,
( spl47_799
<=> ! [X2,X0,X1] :
( c_Polynomial_Opos__poly(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0))
| ~ c_Polynomial_Opos__poly(X2,X0)
| ~ c_Polynomial_Opos__poly(X2,X1)
| ~ class_Rings_Olinordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_799])]) ).
fof(f4715,plain,
! [X2,X0,X1] :
( c_Polynomial_Opos__poly(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0))
| ~ c_Polynomial_Opos__poly(X2,X0)
| ~ c_Polynomial_Opos__poly(X2,X1)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(cnf_transformation,[],[f2673]) ).
fof(f2673,plain,
! [X0,X1,X2] :
( c_Polynomial_Opos__poly(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0))
| ~ c_Polynomial_Opos__poly(X2,X0)
| ~ c_Polynomial_Opos__poly(X2,X1)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(flattening,[],[f2672]) ).
fof(f2672,plain,
! [X0,X1,X2] :
( c_Polynomial_Opos__poly(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0))
| ~ c_Polynomial_Opos__poly(X2,X0)
| ~ c_Polynomial_Opos__poly(X2,X1)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(ennf_transformation,[],[f1685]) ).
fof(f1685,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Polynomial_Opos__poly(X2,X1)
=> ( c_Polynomial_Opos__poly(X2,X0)
=> c_Polynomial_Opos__poly(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X1),X0)) ) ) ),
inference(rectify,[],[f539]) ).
fof(f539,axiom,
! [X13,X8,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Polynomial_Opos__poly(X5,X8)
=> ( c_Polynomial_Opos__poly(X5,X13)
=> c_Polynomial_Opos__poly(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X8),X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__mult) ).
fof(f16457,plain,
spl47_798,
inference(avatar_split_clause,[],[f4605,f16455]) ).
fof(f16455,plain,
( spl47_798
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_798])]) ).
fof(f4605,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f3660]) ).
fof(f3660,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))) ) ),
inference(nnf_transformation,[],[f1605]) ).
fof(f1605,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) ),
inference(rectify,[],[f328]) ).
fof(f328,axiom,
! [X11,X44] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X44),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X44)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X44),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__reduce) ).
fof(f16453,plain,
spl47_797,
inference(avatar_split_clause,[],[f4604,f16451]) ).
fof(f16451,plain,
( spl47_797
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_797])]) ).
fof(f4604,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))) ),
inference(cnf_transformation,[],[f3660]) ).
fof(f16449,plain,
spl47_796,
inference(avatar_split_clause,[],[f4595,f16447]) ).
fof(f16447,plain,
( spl47_796
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_796])]) ).
fof(f4595,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ),
inference(cnf_transformation,[],[f3655]) ).
fof(f3655,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ) ),
inference(flattening,[],[f3654]) ).
fof(f3654,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ) ),
inference(nnf_transformation,[],[f1602]) ).
fof(f1602,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) ),
inference(rectify,[],[f652]) ).
fof(f652,axiom,
! [X11,X14] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X11)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X11
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__is__0) ).
fof(f16445,plain,
spl47_795,
inference(avatar_split_clause,[],[f4469,f16443]) ).
fof(f16443,plain,
( spl47_795
<=> ! [X0,X1] :
( X0 = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_795])]) ).
fof(f4469,plain,
! [X0,X1] :
( X0 = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2584]) ).
fof(f2584,plain,
! [X0,X1] :
( X0 = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ),
inference(flattening,[],[f2583]) ).
fof(f2583,plain,
! [X0,X1] :
( X0 = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1546]) ).
fof(f1546,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)
=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)
=> X0 = X1 ) ),
inference(rectify,[],[f795]) ).
fof(f795,axiom,
! [X7,X21] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X7)
=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X21)
=> X7 = X21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).
fof(f16441,plain,
spl47_794,
inference(avatar_split_clause,[],[f4453,f16439]) ).
fof(f16439,plain,
( spl47_794
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_794])]) ).
fof(f4453,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(cnf_transformation,[],[f2564]) ).
fof(f2564,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(flattening,[],[f2563]) ).
fof(f2563,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(ennf_transformation,[],[f1532]) ).
fof(f1532,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
inference(rectify,[],[f259]) ).
fof(f259,axiom,
! [X21,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X21),X7))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__pos__nat) ).
fof(f16436,plain,
spl47_793,
inference(avatar_split_clause,[],[f4452,f16434]) ).
fof(f16434,plain,
( spl47_793
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_793])]) ).
fof(f4452,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(cnf_transformation,[],[f2562]) ).
fof(f2562,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(flattening,[],[f2561]) ).
fof(f2561,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(ennf_transformation,[],[f1531]) ).
fof(f1531,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0) ) ),
inference(rectify,[],[f830]) ).
fof(f830,axiom,
! [X21,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X7),X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less) ).
fof(f16432,plain,
spl47_792,
inference(avatar_split_clause,[],[f4409,f16430]) ).
fof(f16430,plain,
( spl47_792
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_792])]) ).
fof(f4409,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| X0 = X1 ),
inference(cnf_transformation,[],[f2513]) ).
fof(f2513,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| X0 = X1 ),
inference(flattening,[],[f2512]) ).
fof(f2512,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| X0 = X1 ),
inference(ennf_transformation,[],[f1494]) ).
fof(f1494,plain,
! [X0,X1] :
( X0 != X1
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) ) ) ),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
! [X17,X4] :
( X4 != X17
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4),X17))
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X17),X4))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4),X17)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oneq__le__trans) ).
fof(f16428,plain,
spl47_791,
inference(avatar_split_clause,[],[f4368,f16426]) ).
fof(f16426,plain,
( spl47_791
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
| ~ class_Groups_Ozero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_791])]) ).
fof(f4368,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
| ~ class_Groups_Ozero(X1) ),
inference(cnf_transformation,[],[f2474]) ).
fof(f2474,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
| ~ class_Groups_Ozero(X1) ),
inference(flattening,[],[f2473]) ).
fof(f2473,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
| ~ class_Groups_Ozero(X1) ),
inference(ennf_transformation,[],[f1458]) ).
fof(f1458,plain,
! [X0,X1] :
( class_Groups_Ozero(X1)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X0
=> c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0)) ) ),
inference(rectify,[],[f869]) ).
fof(f869,axiom,
! [X8,X5] :
( class_Groups_Ozero(X5)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) != X8
=> c_Groups_Ozero__class_Ozero(X5) != hAPP(c_Polynomial_Ocoeff(X5,X8),c_Polynomial_Odegree(X5,X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leading__coeff__neq__0) ).
fof(f16424,plain,
spl47_790,
inference(avatar_split_clause,[],[f4256,f16422]) ).
fof(f16422,plain,
( spl47_790
<=> ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X0) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_790])]) ).
fof(f4256,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X0) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)),
inference(cnf_transformation,[],[f1372]) ).
fof(f1372,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X0) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)),
inference(rectify,[],[f647]) ).
fof(f647,axiom,
! [X48,X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X26)),X48) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X48)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zminus) ).
fof(f16419,plain,
spl47_789,
inference(avatar_split_clause,[],[f4230,f16417]) ).
fof(f4230,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3550]) ).
fof(f3550,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(nnf_transformation,[],[f1346]) ).
fof(f1346,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(rectify,[],[f486]) ).
fof(f486,axiom,
! [X30] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X30),X30),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X30,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__less__0) ).
fof(f16414,plain,
spl47_788,
inference(avatar_split_clause,[],[f4229,f16412]) ).
fof(f4229,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3550]) ).
fof(f16406,plain,
( ~ spl47_145
| ~ spl47_219 ),
inference(avatar_split_clause,[],[f3915,f7059,f6756]) ).
fof(f3915,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ~ sP0 ),
inference(cnf_transformation,[],[f3523]) ).
fof(f3523,plain,
( ( ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
| v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) )
| ~ sP0 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| sP0 ) ),
inference(flattening,[],[f3522]) ).
fof(f3522,plain,
( ( ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
| v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) )
| ~ sP0 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| sP0 ) ),
inference(nnf_transformation,[],[f3476]) ).
fof(f3476,plain,
( sP0
<~> ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ),
inference(definition_folding,[],[f2305,f3475]) ).
fof(f2305,plain,
( ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) )
<~> ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ),
inference(ennf_transformation,[],[f1208]) ).
fof(f1208,plain,
~ ( ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0)
=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) )
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ),
inference(rectify,[],[f1207]) ).
fof(f1207,negated_conjecture,
~ ( ! [X2] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X2) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X2) )
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ),
inference(negated_conjecture,[],[f1206]) ).
fof(f1206,conjecture,
( ! [X2] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X2) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X2) )
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f16405,plain,
( spl47_787
| spl47_145 ),
inference(avatar_split_clause,[],[f3911,f6756,f16402]) ).
fof(f3911,plain,
( sP0
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK27) ),
inference(cnf_transformation,[],[f3521]) ).
fof(f16398,plain,
( ~ spl47_145
| spl47_786 ),
inference(avatar_split_clause,[],[f3910,f16396,f6756]) ).
fof(f3910,plain,
! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)
| ~ sP0 ),
inference(cnf_transformation,[],[f3521]) ).
fof(f14779,plain,
spl47_785,
inference(avatar_split_clause,[],[f5939,f14777]) ).
fof(f14777,plain,
( spl47_785
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK37(X0,X1))) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_785])]) ).
fof(f5939,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK37(X0,X1))) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(forward_demodulation,[],[f5574,f4240]) ).
fof(f5574,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK37(X0,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f4524,f4118]) ).
fof(f4524,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK37(X0,X1))) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3614]) ).
fof(f3614,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ! [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X0 )
& ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK37(X0,X1))) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37])],[f3612,f3613]) ).
fof(f3613,plain,
! [X0,X1] :
( ? [X3] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) = X0
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK37(X0,X1))) = X0 ),
introduced(choice_axiom,[]) ).
fof(f3612,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ! [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X0 )
& ( ? [X3] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(rectify,[],[f3611]) ).
fof(f3611,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ! [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X0 )
& ( ? [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f1578]) ).
fof(f1578,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
<=> ? [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = X0 ),
inference(rectify,[],[f345]) ).
fof(f345,axiom,
! [X11,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X11)
<=> ? [X45] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X45)) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
fof(f14766,plain,
spl47_784,
inference(avatar_split_clause,[],[f5894,f14764]) ).
fof(f14764,plain,
( spl47_784
<=> ! [X0] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_784])]) ).
fof(f5894,plain,
! [X0] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(forward_demodulation,[],[f5519,f5515]) ).
fof(f5519,plain,
! [X0] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(definition_unfolding,[],[f4210,f4118]) ).
fof(f4210,plain,
! [X0] :
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(cnf_transformation,[],[f2386]) ).
fof(f2386,plain,
! [X0] :
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(ennf_transformation,[],[f1334]) ).
fof(f1334,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X0 ),
inference(rectify,[],[f873]) ).
fof(f873,axiom,
! [X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__1) ).
fof(f14762,plain,
spl47_783,
inference(avatar_split_clause,[],[f5827,f14760]) ).
fof(f14760,plain,
( spl47_783
<=> ! [X2,X0,X1] :
( sP16(c_Rings_Oinverse__class_Odivide(X2,X0,X1),X2,X1,X0)
| ~ sP17(X0,X1,X2,c_Rings_Oinverse__class_Odivide(X2,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_783])]) ).
fof(f5827,plain,
! [X2,X0,X1] :
( sP16(c_Rings_Oinverse__class_Odivide(X2,X0,X1),X2,X1,X0)
| ~ sP17(X0,X1,X2,c_Rings_Oinverse__class_Odivide(X2,X0,X1)) ),
inference(equality_resolution,[],[f5140]) ).
fof(f5140,plain,
! [X2,X3,X0,X1] :
( sP16(X3,X2,X1,X0)
| c_Rings_Oinverse__class_Odivide(X2,X0,X1) != X3
| ~ sP17(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3827]) ).
fof(f3827,plain,
! [X0,X1,X2,X3] :
( ( ( c_Rings_Oinverse__class_Odivide(X2,X0,X1) = X3
| ~ sP16(X3,X2,X1,X0) )
& ( sP16(X3,X2,X1,X0)
| c_Rings_Oinverse__class_Odivide(X2,X0,X1) != X3 ) )
| ~ sP17(X0,X1,X2,X3) ),
inference(rectify,[],[f3826]) ).
fof(f3826,plain,
! [X2,X1,X3,X0] :
( ( ( c_Rings_Oinverse__class_Odivide(X3,X2,X1) = X0
| ~ sP16(X0,X3,X1,X2) )
& ( sP16(X0,X3,X1,X2)
| c_Rings_Oinverse__class_Odivide(X3,X2,X1) != X0 ) )
| ~ sP17(X2,X1,X3,X0) ),
inference(nnf_transformation,[],[f3503]) ).
fof(f3503,plain,
! [X2,X1,X3,X0] :
( ( c_Rings_Oinverse__class_Odivide(X3,X2,X1) = X0
<=> sP16(X0,X3,X1,X2) )
| ~ sP17(X2,X1,X3,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
fof(f14758,plain,
spl47_782,
inference(avatar_split_clause,[],[f5819,f14756]) ).
fof(f14756,plain,
( spl47_782
<=> ! [X2,X0,X1] :
( sP14(c_Rings_Oinverse__class_Odivide(X2,X0,X1),X2,X1,X0)
| ~ sP15(X0,X1,X2,c_Rings_Oinverse__class_Odivide(X2,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_782])]) ).
fof(f5819,plain,
! [X2,X0,X1] :
( sP14(c_Rings_Oinverse__class_Odivide(X2,X0,X1),X2,X1,X0)
| ~ sP15(X0,X1,X2,c_Rings_Oinverse__class_Odivide(X2,X0,X1)) ),
inference(equality_resolution,[],[f5131]) ).
fof(f5131,plain,
! [X2,X3,X0,X1] :
( sP14(X3,X2,X1,X0)
| c_Rings_Oinverse__class_Odivide(X2,X0,X1) != X3
| ~ sP15(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3822]) ).
fof(f3822,plain,
! [X0,X1,X2,X3] :
( ( ( c_Rings_Oinverse__class_Odivide(X2,X0,X1) = X3
| ~ sP14(X3,X2,X1,X0) )
& ( sP14(X3,X2,X1,X0)
| c_Rings_Oinverse__class_Odivide(X2,X0,X1) != X3 ) )
| ~ sP15(X0,X1,X2,X3) ),
inference(rectify,[],[f3821]) ).
fof(f3821,plain,
! [X1,X0,X3,X2] :
( ( ( c_Rings_Oinverse__class_Odivide(X3,X1,X0) = X2
| ~ sP14(X2,X3,X0,X1) )
& ( sP14(X2,X3,X0,X1)
| c_Rings_Oinverse__class_Odivide(X3,X1,X0) != X2 ) )
| ~ sP15(X1,X0,X3,X2) ),
inference(nnf_transformation,[],[f3500]) ).
fof(f3500,plain,
! [X1,X0,X3,X2] :
( ( c_Rings_Oinverse__class_Odivide(X3,X1,X0) = X2
<=> sP14(X2,X3,X0,X1) )
| ~ sP15(X1,X0,X3,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f14754,plain,
spl47_781,
inference(avatar_split_clause,[],[f5639,f14752]) ).
fof(f14752,plain,
( spl47_781
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_781])]) ).
fof(f5639,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(definition_unfolding,[],[f5003,f4118]) ).
fof(f5003,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X2),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2984]) ).
fof(f2984,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X2),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(flattening,[],[f2983]) ).
fof(f2983,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X2),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1902]) ).
fof(f1902,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X2),X0) ) ),
inference(rectify,[],[f223]) ).
fof(f223,axiom,
! [X20,X33,X32] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32,X33)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,X20)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X32),X20) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
fof(f14750,plain,
spl47_780,
inference(avatar_split_clause,[],[f5592,f14748]) ).
fof(f14748,plain,
( spl47_780
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_780])]) ).
fof(f5592,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(definition_unfolding,[],[f4542,f4118,f4118]) ).
fof(f4542,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0)) ),
inference(cnf_transformation,[],[f3627]) ).
fof(f3627,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0)) ) ),
inference(nnf_transformation,[],[f1585]) ).
fof(f1585,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f97]) ).
fof(f97,axiom,
! [X14,X11] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X11),c_Nat_OSuc(X14))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
fof(f14746,plain,
spl47_779,
inference(avatar_split_clause,[],[f5562,f14744]) ).
fof(f14744,plain,
( spl47_779
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_779])]) ).
fof(f5562,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(definition_unfolding,[],[f4465,f4118,f4118]) ).
fof(f4465,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0)) ),
inference(cnf_transformation,[],[f2576]) ).
fof(f2576,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0)) ),
inference(ennf_transformation,[],[f1542]) ).
fof(f1542,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f220]) ).
fof(f220,axiom,
! [X7,X21] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X21),c_Nat_OSuc(X7))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
fof(f14742,plain,
spl47_778,
inference(avatar_split_clause,[],[f5555,f14740]) ).
fof(f14740,plain,
( spl47_778
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_778])]) ).
fof(f5555,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(definition_unfolding,[],[f4450,f4118]) ).
fof(f4450,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X0)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(cnf_transformation,[],[f2558]) ).
fof(f2558,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X0)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(ennf_transformation,[],[f1529]) ).
fof(f1529,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X0)),X1) ),
inference(rectify,[],[f856]) ).
fof(f856,axiom,
! [X32,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,c_Nat_OSuc(X32)),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__less) ).
fof(f14738,plain,
spl47_777,
inference(avatar_split_clause,[],[f5369,f14736]) ).
fof(f14736,plain,
( spl47_777
<=> ! [X2,X3,X0,X5,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X5),hAPP(X0,X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ~ class_Orderings_Oord(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_777])]) ).
fof(f5369,plain,
! [X2,X3,X0,X1,X5] :
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X5),hAPP(X0,X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ~ class_Orderings_Oord(X3) ),
inference(cnf_transformation,[],[f3874]) ).
fof(f14734,plain,
spl47_776,
inference(avatar_split_clause,[],[f5336,f14732]) ).
fof(f14732,plain,
( spl47_776
<=> ! [X0,X3,X2,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
| c_Polynomial_Osmult(X3,X2,X1) != c_Polynomial_OpCons(X3,X0,X1)
| ~ class_Rings_Ocomm__semiring__0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_776])]) ).
fof(f5336,plain,
! [X2,X3,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
| c_Polynomial_Osmult(X3,X2,X1) != c_Polynomial_OpCons(X3,X0,X1)
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f3281]) ).
fof(f3281,plain,
! [X0,X1,X2,X3] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
| c_Polynomial_Osmult(X3,X2,X1) != c_Polynomial_OpCons(X3,X0,X1)
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(flattening,[],[f3280]) ).
fof(f3280,plain,
! [X0,X1,X2,X3] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
| c_Polynomial_Osmult(X3,X2,X1) != c_Polynomial_OpCons(X3,X0,X1)
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f2132]) ).
fof(f2132,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> ( c_Polynomial_Osmult(X3,X2,X1) = c_Polynomial_OpCons(X3,X0,X1)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 ) ),
inference(rectify,[],[f88]) ).
fof(f88,axiom,
! [X4,X8,X16,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> ( c_Polynomial_OpCons(X5,X4,X8) = c_Polynomial_Osmult(X5,X16,X8)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__unique__lemma) ).
fof(f14730,plain,
spl47_775,
inference(avatar_split_clause,[],[f5312,f14728]) ).
fof(f14728,plain,
( spl47_775
<=> ! [X0,X3,X2,X1] :
( c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X0,X2)),X1)
| X1 = X2
| ~ class_Groups_Ozero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_775])]) ).
fof(f5312,plain,
! [X2,X3,X0,X1] :
( c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X0,X2)),X1)
| X1 = X2
| ~ class_Groups_Ozero(X3) ),
inference(cnf_transformation,[],[f3256]) ).
fof(f3256,plain,
! [X0,X1,X2,X3] :
( ( ( c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X0,X2)),X1)
| X1 = X2 )
& ( hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X0,X2)),X1) = X0
| X1 != X2 ) )
| ~ class_Groups_Ozero(X3) ),
inference(ennf_transformation,[],[f2109]) ).
fof(f2109,plain,
! [X0,X1,X2,X3] :
( class_Groups_Ozero(X3)
=> ( ( X1 != X2
=> c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X0,X2)),X1) )
& ( X1 = X2
=> hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X0,X2)),X1) = X0 ) ) ),
inference(rectify,[],[f757]) ).
fof(f757,axiom,
! [X4,X7,X21,X5] :
( class_Groups_Ozero(X5)
=> ( ( X7 != X21
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Polynomial_Ocoeff(X5,c_Polynomial_Omonom(X5,X4,X21)),X7) )
& ( X7 = X21
=> hAPP(c_Polynomial_Ocoeff(X5,c_Polynomial_Omonom(X5,X4,X21)),X7) = X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__monom) ).
fof(f14725,plain,
spl47_774,
inference(avatar_split_clause,[],[f5246,f14723]) ).
fof(f14723,plain,
( spl47_774
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_774])]) ).
fof(f5246,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(cnf_transformation,[],[f3860]) ).
fof(f3860,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0) )
& ( c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(nnf_transformation,[],[f3164]) ).
fof(f3164,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
<=> c_Orderings_Oord__class_Oless(X3,X1,X0) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(ennf_transformation,[],[f2053]) ).
fof(f2053,plain,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
<=> c_Orderings_Oord__class_Oless(X3,X1,X0) ) ),
inference(rectify,[],[f367]) ).
fof(f367,axiom,
! [X29,X12,X24,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X24,X12),c_Groups_Oplus__class_Oplus(X5,X24,X29))
<=> c_Orderings_Oord__class_Oless(X5,X12,X29) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
fof(f14721,plain,
spl47_773,
inference(avatar_split_clause,[],[f5244,f14719]) ).
fof(f14719,plain,
( spl47_773
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_773])]) ).
fof(f5244,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(cnf_transformation,[],[f3859]) ).
fof(f3859,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X0) )
& ( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(nnf_transformation,[],[f3163]) ).
fof(f3163,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
<=> c_Orderings_Oord__class_Oless(X3,X2,X0) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(ennf_transformation,[],[f2052]) ).
fof(f2052,plain,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
<=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ),
inference(rectify,[],[f366]) ).
fof(f366,axiom,
! [X29,X24,X12,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X12,X24),c_Groups_Oplus__class_Oplus(X5,X29,X24))
<=> c_Orderings_Oord__class_Oless(X5,X12,X29) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
fof(f14717,plain,
spl47_772,
inference(avatar_split_clause,[],[f5242,f14715]) ).
fof(f14715,plain,
( spl47_772
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_772])]) ).
fof(f5242,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(cnf_transformation,[],[f3858]) ).
fof(f3858,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(nnf_transformation,[],[f3162]) ).
fof(f3162,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(X3,X1,X0) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(ennf_transformation,[],[f2051]) ).
fof(f2051,plain,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(X3,X1,X0) ) ),
inference(rectify,[],[f360]) ).
fof(f360,axiom,
! [X29,X12,X24,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X24,X12),c_Groups_Oplus__class_Oplus(X5,X24,X29))
<=> c_Orderings_Oord__class_Oless__eq(X5,X12,X29) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
fof(f14713,plain,
spl47_771,
inference(avatar_split_clause,[],[f5240,f14711]) ).
fof(f14711,plain,
( spl47_771
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_771])]) ).
fof(f5240,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(cnf_transformation,[],[f3857]) ).
fof(f3857,plain,
! [X0,X1,X2,X3] :
( ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X0) )
& ( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(nnf_transformation,[],[f3161]) ).
fof(f3161,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
<=> c_Orderings_Oord__class_Oless__eq(X3,X2,X0) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(ennf_transformation,[],[f2050]) ).
fof(f2050,plain,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
<=> c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ) ),
inference(rectify,[],[f359]) ).
fof(f359,axiom,
! [X29,X24,X12,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X12,X24),c_Groups_Oplus__class_Oplus(X5,X29,X24))
<=> c_Orderings_Oord__class_Oless__eq(X5,X12,X29) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
fof(f14709,plain,
spl47_770,
inference(avatar_split_clause,[],[f5238,f14707]) ).
fof(f14707,plain,
( spl47_770
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_770])]) ).
fof(f5238,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(cnf_transformation,[],[f3160]) ).
fof(f3160,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(flattening,[],[f3159]) ).
fof(f3159,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(ennf_transformation,[],[f2049]) ).
fof(f2049,plain,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ),
inference(rectify,[],[f371]) ).
fof(f371,axiom,
! [X17,X16,X4,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X4,X16),c_Groups_Oplus__class_Oplus(X5,X17,X16))
=> c_Orderings_Oord__class_Oless(X5,X4,X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
fof(f14705,plain,
spl47_769,
inference(avatar_split_clause,[],[f5237,f14703]) ).
fof(f14703,plain,
( spl47_769
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_769])]) ).
fof(f5237,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(cnf_transformation,[],[f3158]) ).
fof(f3158,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(flattening,[],[f3157]) ).
fof(f3157,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(ennf_transformation,[],[f2048]) ).
fof(f2048,plain,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
=> c_Orderings_Oord__class_Oless(X3,X1,X0) ) ),
inference(rectify,[],[f372]) ).
fof(f372,axiom,
! [X17,X4,X16,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X16,X4),c_Groups_Oplus__class_Oplus(X5,X16,X17))
=> c_Orderings_Oord__class_Oless(X5,X4,X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
fof(f14701,plain,
spl47_768,
inference(avatar_split_clause,[],[f5236,f14699]) ).
fof(f14699,plain,
( spl47_768
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_768])]) ).
fof(f5236,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(cnf_transformation,[],[f3156]) ).
fof(f3156,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(flattening,[],[f3155]) ).
fof(f3155,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(ennf_transformation,[],[f2047]) ).
fof(f2047,plain,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X0,X1))
=> c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ) ),
inference(rectify,[],[f364]) ).
fof(f364,axiom,
! [X17,X16,X4,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X4,X16),c_Groups_Oplus__class_Oplus(X5,X17,X16))
=> c_Orderings_Oord__class_Oless__eq(X5,X4,X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
fof(f14697,plain,
spl47_767,
inference(avatar_split_clause,[],[f5235,f14695]) ).
fof(f14695,plain,
( spl47_767
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_767])]) ).
fof(f5235,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(cnf_transformation,[],[f3154]) ).
fof(f3154,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(flattening,[],[f3153]) ).
fof(f3153,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3) ),
inference(ennf_transformation,[],[f2046]) ).
fof(f2046,plain,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),c_Groups_Oplus__class_Oplus(X3,X2,X0))
=> c_Orderings_Oord__class_Oless__eq(X3,X1,X0) ) ),
inference(rectify,[],[f365]) ).
fof(f365,axiom,
! [X17,X4,X16,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X16,X4),c_Groups_Oplus__class_Oplus(X5,X16,X17))
=> c_Orderings_Oord__class_Oless__eq(X5,X4,X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
fof(f14693,plain,
spl47_766,
inference(avatar_split_clause,[],[f5233,f14691]) ).
fof(f14691,plain,
( spl47_766
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_766])]) ).
fof(f5233,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3) ),
inference(cnf_transformation,[],[f3150]) ).
fof(f3150,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3) ),
inference(flattening,[],[f3149]) ).
fof(f3149,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3) ),
inference(ennf_transformation,[],[f2044]) ).
fof(f2044,plain,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0)) ) ),
inference(rectify,[],[f368]) ).
fof(f368,axiom,
! [X16,X17,X4,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X17)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X4,X16),c_Groups_Oplus__class_Oplus(X5,X17,X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
fof(f14689,plain,
spl47_765,
inference(avatar_split_clause,[],[f5232,f14687]) ).
fof(f14687,plain,
( spl47_765
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_765])]) ).
fof(f5232,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3) ),
inference(cnf_transformation,[],[f3148]) ).
fof(f3148,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3) ),
inference(flattening,[],[f3147]) ).
fof(f3147,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3) ),
inference(ennf_transformation,[],[f2043]) ).
fof(f2043,plain,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1)) ) ),
inference(rectify,[],[f369]) ).
fof(f369,axiom,
! [X16,X17,X4,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,X17)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X16,X4),c_Groups_Oplus__class_Oplus(X5,X16,X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
fof(f14684,plain,
spl47_764,
inference(avatar_split_clause,[],[f5229,f14682]) ).
fof(f14682,plain,
( spl47_764
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Groups_Oordered__ab__semigroup__add(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_764])]) ).
fof(f5229,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Groups_Oordered__ab__semigroup__add(X3) ),
inference(cnf_transformation,[],[f3142]) ).
fof(f3142,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Groups_Oordered__ab__semigroup__add(X3) ),
inference(flattening,[],[f3141]) ).
fof(f3141,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Groups_Oordered__ab__semigroup__add(X3) ),
inference(ennf_transformation,[],[f2040]) ).
fof(f2040,plain,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X0,X2),c_Groups_Oplus__class_Oplus(X3,X0,X1)) ) ),
inference(rectify,[],[f362]) ).
fof(f362,axiom,
! [X16,X17,X4,X5] :
( class_Groups_Oordered__ab__semigroup__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X17)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X16,X4),c_Groups_Oplus__class_Oplus(X5,X16,X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__mono) ).
fof(f14680,plain,
spl47_763,
inference(avatar_split_clause,[],[f5228,f14678]) ).
fof(f14678,plain,
( spl47_763
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Groups_Oordered__ab__semigroup__add(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_763])]) ).
fof(f5228,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Groups_Oordered__ab__semigroup__add(X3) ),
inference(cnf_transformation,[],[f3140]) ).
fof(f3140,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Groups_Oordered__ab__semigroup__add(X3) ),
inference(flattening,[],[f3139]) ).
fof(f3139,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Groups_Oordered__ab__semigroup__add(X3) ),
inference(ennf_transformation,[],[f2039]) ).
fof(f2039,plain,
! [X0,X1,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X0),c_Groups_Oplus__class_Oplus(X3,X1,X0)) ) ),
inference(rectify,[],[f361]) ).
fof(f361,axiom,
! [X16,X17,X4,X5] :
( class_Groups_Oordered__ab__semigroup__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X17)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X4,X16),c_Groups_Oplus__class_Oplus(X5,X17,X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__mono) ).
fof(f14676,plain,
spl47_762,
inference(avatar_split_clause,[],[f5141,f14674]) ).
fof(f14674,plain,
( spl47_762
<=> ! [X0,X3,X2,X1] :
( c_Rings_Oinverse__class_Odivide(X2,X0,X1) = X3
| ~ sP16(X3,X2,X1,X0)
| ~ sP17(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_762])]) ).
fof(f5141,plain,
! [X2,X3,X0,X1] :
( c_Rings_Oinverse__class_Odivide(X2,X0,X1) = X3
| ~ sP16(X3,X2,X1,X0)
| ~ sP17(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3827]) ).
fof(f14672,plain,
spl47_761,
inference(avatar_split_clause,[],[f5132,f14670]) ).
fof(f14670,plain,
( spl47_761
<=> ! [X0,X3,X2,X1] :
( c_Rings_Oinverse__class_Odivide(X2,X0,X1) = X3
| ~ sP14(X3,X2,X1,X0)
| ~ sP15(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_761])]) ).
fof(f5132,plain,
! [X2,X3,X0,X1] :
( c_Rings_Oinverse__class_Odivide(X2,X0,X1) = X3
| ~ sP14(X3,X2,X1,X0)
| ~ sP15(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3822]) ).
fof(f14668,plain,
spl47_760,
inference(avatar_split_clause,[],[f5075,f14666]) ).
fof(f14666,plain,
( spl47_760
<=> ! [X2,X0,X1] :
( sP13(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK45(X0,X1,X2)))
| ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_760])]) ).
fof(f5075,plain,
! [X2,X0,X1] :
( sP13(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK45(X0,X1,X2)))
| ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(cnf_transformation,[],[f3793]) ).
fof(f14664,plain,
spl47_759,
inference(avatar_split_clause,[],[f5067,f14662]) ).
fof(f14662,plain,
( spl47_759
<=> ! [X2,X0,X1] :
( sP12(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK44(X0,X1,X2)))
| ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_759])]) ).
fof(f5067,plain,
! [X2,X0,X1] :
( sP12(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK44(X0,X1,X2)))
| ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(cnf_transformation,[],[f3787]) ).
fof(f14660,plain,
spl47_758,
inference(avatar_split_clause,[],[f4908,f14658]) ).
fof(f14658,plain,
( spl47_758
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osynthetic__div(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Odegree(X2,X1)
| ~ class_Rings_Ocomm__semiring__0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_758])]) ).
fof(f4908,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osynthetic__div(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Odegree(X2,X1)
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(cnf_transformation,[],[f3746]) ).
fof(f3746,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osynthetic__div(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Odegree(X2,X1) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X2,X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_Osynthetic__div(X2,X1,X0) ) )
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(nnf_transformation,[],[f2878]) ).
fof(f2878,plain,
! [X0,X1,X2] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osynthetic__div(X2,X1,X0)
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X2,X1) )
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(ennf_transformation,[],[f1826]) ).
fof(f1826,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__0(X2)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osynthetic__div(X2,X1,X0)
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X2,X1) ) ),
inference(rectify,[],[f36]) ).
fof(f36,axiom,
! [X24,X9,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_Osynthetic__div(X5,X9,X24)
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X5,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__eq__0__iff) ).
fof(f14656,plain,
spl47_757,
inference(avatar_split_clause,[],[f4907,f14654]) ).
fof(f14654,plain,
( spl47_757
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X2,X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_Osynthetic__div(X2,X1,X0)
| ~ class_Rings_Ocomm__semiring__0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_757])]) ).
fof(f4907,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X2,X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_Osynthetic__div(X2,X1,X0)
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(cnf_transformation,[],[f3746]) ).
fof(f14652,plain,
spl47_756,
inference(avatar_split_clause,[],[f4899,f14650]) ).
fof(f14650,plain,
( spl47_756
<=> ! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,c_Polynomial_Osynthetic__div(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_756])]) ).
fof(f4899,plain,
! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,c_Polynomial_Osynthetic__div(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(cnf_transformation,[],[f2871]) ).
fof(f2871,plain,
! [X0,X1,X2] :
( c_Polynomial_Odegree(X2,c_Polynomial_Osynthetic__div(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(ennf_transformation,[],[f1819]) ).
fof(f1819,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__0(X2)
=> c_Polynomial_Odegree(X2,c_Polynomial_Osynthetic__div(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rectify,[],[f871]) ).
fof(f871,axiom,
! [X16,X8,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Polynomial_Odegree(X5,c_Polynomial_Osynthetic__div(X5,X8,X16)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(X5,X8),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__synthetic__div) ).
fof(f14648,plain,
spl47_755,
inference(avatar_split_clause,[],[f4887,f14646]) ).
fof(f14646,plain,
( spl47_755
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Polynomial_Odegree(X2,X1))
| c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Ocoeff(X2,X1),X0)
| ~ class_Groups_Ozero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_755])]) ).
fof(f4887,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Polynomial_Odegree(X2,X1))
| c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Ocoeff(X2,X1),X0)
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f2864]) ).
fof(f2864,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Polynomial_Odegree(X2,X1))
| c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Ocoeff(X2,X1),X0)
| ~ class_Groups_Ozero(X2) ),
inference(flattening,[],[f2863]) ).
fof(f2863,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Polynomial_Odegree(X2,X1))
| c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Ocoeff(X2,X1),X0)
| ~ class_Groups_Ozero(X2) ),
inference(ennf_transformation,[],[f1812]) ).
fof(f1812,plain,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Ocoeff(X2,X1),X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Polynomial_Odegree(X2,X1)) ) ),
inference(rectify,[],[f862]) ).
fof(f862,axiom,
! [X7,X8,X5] :
( class_Groups_Ozero(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != hAPP(c_Polynomial_Ocoeff(X5,X8),X7)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Polynomial_Odegree(X5,X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__degree) ).
fof(f14643,plain,
spl47_754,
inference(avatar_split_clause,[],[f4886,f14641]) ).
fof(f14641,plain,
( spl47_754
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Ocoeff(X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
| ~ class_Groups_Ozero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_754])]) ).
fof(f4886,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Ocoeff(X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f2862]) ).
fof(f2862,plain,
! [X0,X1,X2] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Ocoeff(X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
| ~ class_Groups_Ozero(X2) ),
inference(flattening,[],[f2861]) ).
fof(f2861,plain,
! [X0,X1,X2] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Ocoeff(X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
| ~ class_Groups_Ozero(X2) ),
inference(ennf_transformation,[],[f1811]) ).
fof(f1811,plain,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X1),X0)
=> c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Ocoeff(X2,X1),X0) ) ),
inference(rectify,[],[f861]) ).
fof(f861,axiom,
! [X7,X8,X5] :
( class_Groups_Ozero(X5)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5,X8),X7)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Polynomial_Ocoeff(X5,X8),X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__eq__0) ).
fof(f14639,plain,
spl47_753,
inference(avatar_split_clause,[],[f4846,f14637]) ).
fof(f14637,plain,
( spl47_753
<=> ! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Omonom(X2,X1,X0)) = c_Polynomial_Omonom(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
| ~ class_Groups_Oab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_753])]) ).
fof(f4846,plain,
! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Omonom(X2,X1,X0)) = c_Polynomial_Omonom(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
| ~ class_Groups_Oab__group__add(X2) ),
inference(cnf_transformation,[],[f2806]) ).
fof(f2806,plain,
! [X0,X1,X2] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Omonom(X2,X1,X0)) = c_Polynomial_Omonom(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
| ~ class_Groups_Oab__group__add(X2) ),
inference(ennf_transformation,[],[f1775]) ).
fof(f1775,plain,
! [X0,X1,X2] :
( class_Groups_Oab__group__add(X2)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Omonom(X2,X1,X0)) = c_Polynomial_Omonom(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) ),
inference(rectify,[],[f405]) ).
fof(f405,axiom,
! [X7,X4,X5] :
( class_Groups_Oab__group__add(X5)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5),c_Polynomial_Omonom(X5,X4,X7)) = c_Polynomial_Omonom(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__monom) ).
fof(f14635,plain,
spl47_752,
inference(avatar_split_clause,[],[f4808,f14633]) ).
fof(f14633,plain,
( spl47_752
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(X2,X0,X1),c_Polynomial_Odegree(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Rings_Oidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_752])]) ).
fof(f4808,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(X2,X0,X1),c_Polynomial_Odegree(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f2779]) ).
fof(f2779,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(X2,X0,X1),c_Polynomial_Odegree(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Rings_Oidom(X2) ),
inference(flattening,[],[f2778]) ).
fof(f2778,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(X2,X0,X1),c_Polynomial_Odegree(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| ~ class_Rings_Oidom(X2) ),
inference(ennf_transformation,[],[f1754]) ).
fof(f1754,plain,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(X2,X0,X1),c_Polynomial_Odegree(X2,X1)) ) ),
inference(rectify,[],[f75]) ).
fof(f75,axiom,
! [X4,X8,X5] :
( class_Rings_Oidom(X5)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) != X8
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(X5,X4,X8),c_Polynomial_Odegree(X5,X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__degree) ).
fof(f14631,plain,
spl47_751,
inference(avatar_split_clause,[],[f4807,f14629]) ).
fof(f14629,plain,
( spl47_751
<=> ! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,X0) = c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0))
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Oidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_751])]) ).
fof(f4807,plain,
! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,X0) = c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0))
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f2777]) ).
fof(f2777,plain,
! [X0,X1,X2] :
( ( ( c_Polynomial_Odegree(X2,X0) = c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0))
| c_Groups_Ozero__class_Ozero(X2) = X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0))
| c_Groups_Ozero__class_Ozero(X2) != X1 ) )
| ~ class_Rings_Oidom(X2) ),
inference(ennf_transformation,[],[f1753]) ).
fof(f1753,plain,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( ( c_Groups_Ozero__class_Ozero(X2) != X1
=> c_Polynomial_Odegree(X2,X0) = c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)) )
& ( c_Groups_Ozero__class_Ozero(X2) = X1
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)) ) ) ),
inference(rectify,[],[f122]) ).
fof(f122,axiom,
! [X8,X4,X5] :
( class_Rings_Oidom(X5)
=> ( ( c_Groups_Ozero__class_Ozero(X5) != X4
=> c_Polynomial_Odegree(X5,X8) = c_Polynomial_Odegree(X5,c_Polynomial_Osmult(X5,X4,X8)) )
& ( c_Groups_Ozero__class_Ozero(X5) = X4
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X5,c_Polynomial_Osmult(X5,X4,X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__smult__eq) ).
fof(f14627,plain,
spl47_750,
inference(avatar_split_clause,[],[f4747,f14625]) ).
fof(f14625,plain,
( spl47_750
<=> ! [X2,X0,X1] :
( c_Polynomial_Osmult(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X0))
| ~ class_Rings_Ocomm__ring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_750])]) ).
fof(f4747,plain,
! [X2,X0,X1] :
( c_Polynomial_Osmult(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X0))
| ~ class_Rings_Ocomm__ring(X2) ),
inference(cnf_transformation,[],[f2704]) ).
fof(f2704,plain,
! [X0,X1,X2] :
( c_Polynomial_Osmult(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X0))
| ~ class_Rings_Ocomm__ring(X2) ),
inference(ennf_transformation,[],[f1707]) ).
fof(f1707,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__ring(X2)
=> c_Polynomial_Osmult(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X0)) ),
inference(rectify,[],[f401]) ).
fof(f401,axiom,
! [X8,X4,X5] :
( class_Rings_Ocomm__ring(X5)
=> c_Polynomial_Osmult(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),X8) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5),c_Polynomial_Osmult(X5,X4,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__minus__left) ).
fof(f14623,plain,
spl47_749,
inference(avatar_split_clause,[],[f4745,f14621]) ).
fof(f14621,plain,
( spl47_749
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| c_Groups_Ozero__class_Ozero(X2) != c_Divides_Odiv__class_Omod(X2,X0,X1)
| ~ class_Divides_Osemiring__div(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_749])]) ).
fof(f4745,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| c_Groups_Ozero__class_Ozero(X2) != c_Divides_Odiv__class_Omod(X2,X0,X1)
| ~ class_Divides_Osemiring__div(X2) ),
inference(cnf_transformation,[],[f3705]) ).
fof(f3705,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| c_Groups_Ozero__class_Ozero(X2) != c_Divides_Odiv__class_Omod(X2,X0,X1) )
& ( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0)) ) )
| ~ class_Divides_Osemiring__div(X2) ),
inference(nnf_transformation,[],[f2702]) ).
fof(f2702,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
<=> c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,X0,X1) )
| ~ class_Divides_Osemiring__div(X2) ),
inference(ennf_transformation,[],[f1705]) ).
fof(f1705,plain,
! [X0,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
<=> c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,X0,X1) ) ),
inference(rectify,[],[f993]) ).
fof(f993,axiom,
! [X29,X12,X5] :
( class_Divides_Osemiring__div(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X12),X29))
<=> c_Groups_Ozero__class_Ozero(X5) = c_Divides_Odiv__class_Omod(X5,X29,X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__eq__mod__eq__0) ).
fof(f14619,plain,
spl47_748,
inference(avatar_split_clause,[],[f4743,f14617]) ).
fof(f4743,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| ~ class_Divides_Osemiring__div(X2) ),
inference(cnf_transformation,[],[f2701]) ).
fof(f2701,plain,
! [X0,X1,X2] :
( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| ~ class_Divides_Osemiring__div(X2) ),
inference(flattening,[],[f2700]) ).
fof(f2700,plain,
! [X0,X1,X2] :
( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
| ~ class_Divides_Osemiring__div(X2) ),
inference(ennf_transformation,[],[f1704]) ).
fof(f1704,plain,
! [X0,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),X0))
=> c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,X0,X1) ) ),
inference(rectify,[],[f992]) ).
fof(f992,axiom,
! [X17,X4,X5] :
( class_Divides_Osemiring__div(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X4),X17))
=> c_Groups_Ozero__class_Ozero(X5) = c_Divides_Odiv__class_Omod(X5,X17,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__mod__0) ).
fof(f14615,plain,
spl47_747,
inference(avatar_split_clause,[],[f4724,f14613]) ).
fof(f14613,plain,
( spl47_747
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| c_Polynomial_Opos__poly(X2,X0)
| ~ c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
| ~ class_Rings_Olinordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_747])]) ).
fof(f4724,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| c_Polynomial_Opos__poly(X2,X0)
| ~ c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(cnf_transformation,[],[f3702]) ).
fof(f3702,plain,
! [X0,X1,X2] :
( ( ( c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
| ( ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0 )
& ~ c_Polynomial_Opos__poly(X2,X0) ) )
& ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0 )
| c_Polynomial_Opos__poly(X2,X0)
| ~ c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0)) ) )
| ~ class_Rings_Olinordered__idom(X2) ),
inference(flattening,[],[f3701]) ).
fof(f3701,plain,
! [X0,X1,X2] :
( ( ( c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
| ( ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0 )
& ~ c_Polynomial_Opos__poly(X2,X0) ) )
& ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0 )
| c_Polynomial_Opos__poly(X2,X0)
| ~ c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0)) ) )
| ~ class_Rings_Olinordered__idom(X2) ),
inference(nnf_transformation,[],[f2680]) ).
fof(f2680,plain,
! [X0,X1,X2] :
( ( c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0 )
| c_Polynomial_Opos__poly(X2,X0) ) )
| ~ class_Rings_Olinordered__idom(X2) ),
inference(ennf_transformation,[],[f1690]) ).
fof(f1690,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0 )
| c_Polynomial_Opos__poly(X2,X0) ) ) ),
inference(rectify,[],[f464]) ).
fof(f464,axiom,
! [X9,X12,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Polynomial_Opos__poly(X5,c_Polynomial_OpCons(X5,X12,X9))
<=> ( ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X12)
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X9 )
| c_Polynomial_Opos__poly(X5,X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__pCons) ).
fof(f14611,plain,
spl47_746,
inference(avatar_split_clause,[],[f4723,f14609]) ).
fof(f14609,plain,
( spl47_746
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Polynomial_Opos__poly(X2,X0)
| ~ c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
| ~ class_Rings_Olinordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_746])]) ).
fof(f4723,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Polynomial_Opos__poly(X2,X0)
| ~ c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(cnf_transformation,[],[f3702]) ).
fof(f14607,plain,
spl47_745,
inference(avatar_split_clause,[],[f4656,f14605]) ).
fof(f14605,plain,
( spl47_745
<=> ! [X2,X0,X1] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X1,X0) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0))
| ~ class_Fields_Ofield(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_745])]) ).
fof(f4656,plain,
! [X2,X0,X1] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X1,X0) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0))
| ~ class_Fields_Ofield(X2) ),
inference(cnf_transformation,[],[f2639]) ).
fof(f2639,plain,
! [X0,X1,X2] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X1,X0) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0))
| ~ class_Fields_Ofield(X2) ),
inference(ennf_transformation,[],[f1659]) ).
fof(f1659,plain,
! [X0,X1,X2] :
( class_Fields_Ofield(X2)
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X1,X0) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2),X0)) ),
inference(rectify,[],[f985]) ).
fof(f985,axiom,
! [X10,X6,X5] :
( class_Fields_Ofield(X5)
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X5),X6,X10) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X5),X6,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__mod__minus__right) ).
fof(f14577,plain,
spl47_744,
inference(avatar_split_clause,[],[f4650,f14575]) ).
fof(f14575,plain,
( spl47_744
<=> ! [X2,X0,X1] :
( X0 = X1
| c_Groups_Oone__class_Oone(X2) != c_Rings_Oinverse__class_Odivide(X2,X0,X1)
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Odivision__ring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_744])]) ).
fof(f4650,plain,
! [X2,X0,X1] :
( X0 = X1
| c_Groups_Oone__class_Oone(X2) != c_Rings_Oinverse__class_Odivide(X2,X0,X1)
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Odivision__ring(X2) ),
inference(cnf_transformation,[],[f3671]) ).
fof(f3671,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Oone__class_Oone(X2) = c_Rings_Oinverse__class_Odivide(X2,X0,X1)
| X0 != X1 )
& ( X0 = X1
| c_Groups_Oone__class_Oone(X2) != c_Rings_Oinverse__class_Odivide(X2,X0,X1) ) )
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Odivision__ring(X2) ),
inference(nnf_transformation,[],[f2634]) ).
fof(f2634,plain,
! [X0,X1,X2] :
( ( c_Groups_Oone__class_Oone(X2) = c_Rings_Oinverse__class_Odivide(X2,X0,X1)
<=> X0 = X1 )
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Odivision__ring(X2) ),
inference(flattening,[],[f2633]) ).
fof(f2633,plain,
! [X0,X1,X2] :
( ( c_Groups_Oone__class_Oone(X2) = c_Rings_Oinverse__class_Odivide(X2,X0,X1)
<=> X0 = X1 )
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Odivision__ring(X2) ),
inference(ennf_transformation,[],[f1654]) ).
fof(f1654,plain,
! [X0,X1,X2] :
( class_Rings_Odivision__ring(X2)
=> ( c_Groups_Ozero__class_Ozero(X2) != X1
=> ( c_Groups_Oone__class_Oone(X2) = c_Rings_Oinverse__class_Odivide(X2,X0,X1)
<=> X0 = X1 ) ) ),
inference(rectify,[],[f909]) ).
fof(f909,axiom,
! [X12,X29,X5] :
( class_Rings_Odivision__ring(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X29
=> ( c_Groups_Oone__class_Oone(X5) = c_Rings_Oinverse__class_Odivide(X5,X12,X29)
<=> X12 = X29 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__inverse__eq) ).
fof(f14573,plain,
spl47_743,
inference(avatar_split_clause,[],[f4554,f14571]) ).
fof(f14571,plain,
( spl47_743
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_743])]) ).
fof(f4554,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X0)) ),
inference(cnf_transformation,[],[f3633]) ).
fof(f3633,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X0)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ) ),
inference(nnf_transformation,[],[f1590]) ).
fof(f1590,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X0)) ),
inference(rectify,[],[f705]) ).
fof(f705,axiom,
! [X63,X52] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X52),X63))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X52)),X63)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I1_J) ).
fof(f14569,plain,
spl47_742,
inference(avatar_split_clause,[],[f4553,f14567]) ).
fof(f14567,plain,
( spl47_742
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_742])]) ).
fof(f4553,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ),
inference(cnf_transformation,[],[f3633]) ).
fof(f14565,plain,
spl47_741,
inference(avatar_split_clause,[],[f4552,f14563]) ).
fof(f14563,plain,
( spl47_741
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_741])]) ).
fof(f4552,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))) ),
inference(cnf_transformation,[],[f3632]) ).
fof(f3632,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ) ),
inference(nnf_transformation,[],[f1589]) ).
fof(f1589,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))) ),
inference(rectify,[],[f704]) ).
fof(f704,axiom,
! [X63,X52] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X52),X63))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X52),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X63))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I2_J) ).
fof(f14561,plain,
spl47_740,
inference(avatar_split_clause,[],[f4551,f14559]) ).
fof(f14559,plain,
( spl47_740
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_740])]) ).
fof(f4551,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ),
inference(cnf_transformation,[],[f3632]) ).
fof(f14557,plain,
spl47_739,
inference(avatar_split_clause,[],[f4480,f14555]) ).
fof(f14555,plain,
( spl47_739
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_739])]) ).
fof(f4480,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) != X1 ),
inference(cnf_transformation,[],[f2599]) ).
fof(f2599,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) != X1 ),
inference(flattening,[],[f2598]) ).
fof(f2598,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) != X1 ),
inference(ennf_transformation,[],[f1554]) ).
fof(f1554,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = X1
=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 ) ),
inference(rectify,[],[f689]) ).
fof(f689,axiom,
! [X7,X21] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X7) = X21
=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X21
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
fof(f14553,plain,
spl47_738,
inference(avatar_split_clause,[],[f4475,f14551]) ).
fof(f14551,plain,
( spl47_738
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_738])]) ).
fof(f4475,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f2592]) ).
fof(f2592,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) ),
inference(flattening,[],[f2591]) ).
fof(f2591,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0)) ),
inference(ennf_transformation,[],[f1550]) ).
fof(f1550,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(rectify,[],[f282]) ).
fof(f282,axiom,
! [X7,X20] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X20),X7))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__le) ).
fof(f14549,plain,
spl47_737,
inference(avatar_split_clause,[],[f4470,f14547]) ).
fof(f14547,plain,
( spl47_737
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_737])]) ).
fof(f4470,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ),
inference(cnf_transformation,[],[f2586]) ).
fof(f2586,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ),
inference(flattening,[],[f2585]) ).
fof(f2585,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ),
inference(ennf_transformation,[],[f1547]) ).
fof(f1547,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
inference(rectify,[],[f453]) ).
fof(f453,axiom,
! [X7,X26] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X26),X7))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X7)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X26,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__imp__le) ).
fof(f14545,plain,
spl47_736,
inference(avatar_split_clause,[],[f4451,f14543]) ).
fof(f14543,plain,
( spl47_736
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_736])]) ).
fof(f4451,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(cnf_transformation,[],[f2560]) ).
fof(f2560,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(flattening,[],[f2559]) ).
fof(f2559,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(ennf_transformation,[],[f1530]) ).
fof(f1530,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1)) ) ),
inference(rectify,[],[f258]) ).
fof(f258,axiom,
! [X7,X21] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X7)
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X7),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__not__less) ).
fof(f14541,plain,
spl47_735,
inference(avatar_split_clause,[],[f4446,f14539]) ).
fof(f14539,plain,
( spl47_735
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_735])]) ).
fof(f4446,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(cnf_transformation,[],[f2556]) ).
fof(f2556,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(flattening,[],[f2555]) ).
fof(f2555,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(ennf_transformation,[],[f1527]) ).
fof(f1527,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X0),X1)) ) ),
inference(rectify,[],[f454]) ).
fof(f454,axiom,
! [X7,X21] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X7)
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X7),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__not__zless) ).
fof(f14514,plain,
spl47_734,
inference(avatar_split_clause,[],[f4398,f14512]) ).
fof(f14512,plain,
( spl47_734
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_734])]) ).
fof(f4398,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2500]) ).
fof(f2500,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
& ( c_Groups_Oone__class_Oone(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1484]) ).
fof(f1484,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
=> c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
=> c_Groups_Oone__class_Oone(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0) ) ) ),
inference(rectify,[],[f880]) ).
fof(f880,axiom,
! [X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X7
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Polynomial_Ocoeff(X5,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X5))),X7) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X7
=> c_Groups_Oone__class_Oone(X5) = hAPP(c_Polynomial_Ocoeff(X5,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X5))),X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__1) ).
fof(f14510,plain,
spl47_733,
inference(avatar_split_clause,[],[f4317,f14508]) ).
fof(f14508,plain,
( spl47_733
<=> ! [X0,X1] :
( c_Polynomial_Opos__poly(X1,X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0)))
| ~ class_Rings_Olinordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_733])]) ).
fof(f4317,plain,
! [X0,X1] :
( c_Polynomial_Opos__poly(X1,X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(cnf_transformation,[],[f3566]) ).
fof(f3566,plain,
! [X0,X1] :
( ( ( c_Polynomial_Opos__poly(X1,X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0))) )
& ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0)))
| ~ c_Polynomial_Opos__poly(X1,X0) ) )
| ~ class_Rings_Olinordered__idom(X1) ),
inference(nnf_transformation,[],[f2430]) ).
fof(f2430,plain,
! [X0,X1] :
( ( c_Polynomial_Opos__poly(X1,X0)
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0))) )
| ~ class_Rings_Olinordered__idom(X1) ),
inference(ennf_transformation,[],[f1415]) ).
fof(f1415,plain,
! [X0,X1] :
( class_Rings_Olinordered__idom(X1)
=> ( c_Polynomial_Opos__poly(X1,X0)
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0))) ) ),
inference(rectify,[],[f881]) ).
fof(f881,axiom,
! [X9,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Polynomial_Opos__poly(X5,X9)
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(c_Polynomial_Ocoeff(X5,X9),c_Polynomial_Odegree(X5,X9))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__def) ).
fof(f14506,plain,
spl47_732,
inference(avatar_split_clause,[],[f4316,f14504]) ).
fof(f14504,plain,
( spl47_732
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0)))
| ~ c_Polynomial_Opos__poly(X1,X0)
| ~ class_Rings_Olinordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_732])]) ).
fof(f4316,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Polynomial_Ocoeff(X1,X0),c_Polynomial_Odegree(X1,X0)))
| ~ c_Polynomial_Opos__poly(X1,X0)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(cnf_transformation,[],[f3566]) ).
fof(f14502,plain,
spl47_731,
inference(avatar_split_clause,[],[f4315,f14500]) ).
fof(f14500,plain,
( spl47_731
<=> ! [X0,X1] :
( c_Polynomial_Opos__poly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0))
| c_Polynomial_Opos__poly(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
| ~ class_Rings_Olinordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_731])]) ).
fof(f4315,plain,
! [X0,X1] :
( c_Polynomial_Opos__poly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0))
| c_Polynomial_Opos__poly(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
| ~ class_Rings_Olinordered__idom(X1) ),
inference(cnf_transformation,[],[f2429]) ).
fof(f2429,plain,
! [X0,X1] :
( c_Polynomial_Opos__poly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0))
| c_Polynomial_Opos__poly(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
| ~ class_Rings_Olinordered__idom(X1) ),
inference(flattening,[],[f2428]) ).
fof(f2428,plain,
! [X0,X1] :
( c_Polynomial_Opos__poly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0))
| c_Polynomial_Opos__poly(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
| ~ class_Rings_Olinordered__idom(X1) ),
inference(ennf_transformation,[],[f1414]) ).
fof(f1414,plain,
! [X0,X1] :
( class_Rings_Olinordered__idom(X1)
=> ( c_Polynomial_Opos__poly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0))
| c_Polynomial_Opos__poly(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0 ) ),
inference(rectify,[],[f590]) ).
fof(f590,axiom,
! [X8,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Polynomial_Opos__poly(X5,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5),X8))
| c_Polynomial_Opos__poly(X5,X8)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__total) ).
fof(f13135,plain,
spl47_730,
inference(avatar_split_clause,[],[f6006,f13133]) ).
fof(f13133,plain,
( spl47_730
<=> ! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_730])]) ).
fof(f6006,plain,
! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
inference(forward_demodulation,[],[f4624,f4623]) ).
fof(f4624,plain,
! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1),
inference(cnf_transformation,[],[f1613]) ).
fof(f1613,plain,
! [X0,X1,X2] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1),
inference(rectify,[],[f777]) ).
fof(f777,axiom,
! [X20,X33,X32] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,X33),X20) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,X20),X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__commute) ).
fof(f13131,plain,
spl47_729,
inference(avatar_split_clause,[],[f6005,f13129]) ).
fof(f13129,plain,
( spl47_729
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_729])]) ).
fof(f6005,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) ),
inference(forward_demodulation,[],[f6004,f4114]) ).
fof(f6004,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) ),
inference(forward_demodulation,[],[f6003,f4240]) ).
fof(f6003,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(forward_demodulation,[],[f6002,f4114]) ).
fof(f6002,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(forward_demodulation,[],[f5617,f4240]) ).
fof(f5617,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(definition_unfolding,[],[f4615,f4118,f4118]) ).
fof(f4615,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f3668]) ).
fof(f13127,plain,
spl47_728,
inference(avatar_split_clause,[],[f6001,f13125]) ).
fof(f13125,plain,
( spl47_728
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_728])]) ).
fof(f6001,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(forward_demodulation,[],[f6000,f4114]) ).
fof(f6000,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(forward_demodulation,[],[f5999,f4240]) ).
fof(f5999,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(forward_demodulation,[],[f5998,f4114]) ).
fof(f5998,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(forward_demodulation,[],[f5616,f4240]) ).
fof(f5616,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(definition_unfolding,[],[f4616,f4118,f4118]) ).
fof(f4616,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f3668]) ).
fof(f13123,plain,
spl47_727,
inference(avatar_split_clause,[],[f5923,f13121]) ).
fof(f13121,plain,
( spl47_727
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_727])]) ).
fof(f5923,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ),
inference(forward_demodulation,[],[f5922,f4114]) ).
fof(f5922,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ),
inference(forward_demodulation,[],[f5921,f4240]) ).
fof(f5921,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(forward_demodulation,[],[f5920,f4114]) ).
fof(f5920,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(forward_demodulation,[],[f5561,f4240]) ).
fof(f5561,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(definition_unfolding,[],[f4464,f4118,f4118]) ).
fof(f4464,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(cnf_transformation,[],[f2575]) ).
fof(f2575,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(ennf_transformation,[],[f1541]) ).
fof(f1541,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ),
inference(rectify,[],[f77]) ).
fof(f77,axiom,
! [X7,X32] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X32),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__one__le__power) ).
fof(f13119,plain,
spl47_726,
inference(avatar_split_clause,[],[f5745,f13117]) ).
fof(f13117,plain,
( spl47_726
<=> ! [X2,X1] :
( c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_726])]) ).
fof(f5745,plain,
! [X2,X1] :
( c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(equality_resolution,[],[f4726]) ).
fof(f4726,plain,
! [X2,X0,X1] :
( c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
| ~ class_Rings_Olinordered__idom(X2) ),
inference(cnf_transformation,[],[f3702]) ).
fof(f13115,plain,
spl47_725,
inference(avatar_split_clause,[],[f5549,f13113]) ).
fof(f13113,plain,
( spl47_725
<=> ! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_725])]) ).
fof(f5549,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f4426,f4118]) ).
fof(f4426,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3578]) ).
fof(f3578,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
| X0 != X1 )
& ( X0 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(nnf_transformation,[],[f2533]) ).
fof(f2533,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
<=> X0 = X1 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1510]) ).
fof(f1510,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
<=> X0 = X1 ) ),
inference(rectify,[],[f265]) ).
fof(f265,axiom,
! [X11,X14] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X11)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,c_Nat_OSuc(X14))
<=> X11 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
fof(f13111,plain,
spl47_724,
inference(avatar_split_clause,[],[f5542,f13109]) ).
fof(f13109,plain,
( spl47_724
<=> ! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_724])]) ).
fof(f5542,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f4413,f4118]) ).
fof(f4413,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2518]) ).
fof(f2518,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(flattening,[],[f2517]) ).
fof(f2517,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1498]) ).
fof(f1498,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
=> X0 = X1 ) ),
inference(rectify,[],[f226]) ).
fof(f226,axiom,
! [X21,X7] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X21)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,c_Nat_OSuc(X21))
=> X7 = X21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__antisym) ).
fof(f13107,plain,
spl47_723,
inference(avatar_split_clause,[],[f5364,f13105]) ).
fof(f13105,plain,
( spl47_723
<=> ! [X0,X3,X2,X1] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,X3),X1),X0) = c_Groups_Ouminus__class_Ouminus(X3,hAPP(X1,X0))
| ~ class_Groups_Ouminus(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_723])]) ).
fof(f5364,plain,
! [X2,X3,X0,X1] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,X3),X1),X0) = c_Groups_Ouminus__class_Ouminus(X3,hAPP(X1,X0))
| ~ class_Groups_Ouminus(X3) ),
inference(cnf_transformation,[],[f3320]) ).
fof(f3320,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,X3),X1),X0) = c_Groups_Ouminus__class_Ouminus(X3,hAPP(X1,X0))
| ~ class_Groups_Ouminus(X3) ),
inference(ennf_transformation,[],[f2160]) ).
fof(f2160,plain,
! [X0,X1,X2,X3] :
( class_Groups_Ouminus(X3)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,X3),X1),X0) = c_Groups_Ouminus__class_Ouminus(X3,hAPP(X1,X0)) ),
inference(rectify,[],[f630]) ).
fof(f630,axiom,
! [X15,X58,X31,X5] :
( class_Groups_Ouminus(X5)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X31,X5),X58),X15) = c_Groups_Ouminus__class_Ouminus(X5,hAPP(X58,X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__apply) ).
fof(f13103,plain,
spl47_722,
inference(avatar_split_clause,[],[f5217,f13101]) ).
fof(f13101,plain,
( spl47_722
<=> ! [X2,X0,X1,X3] :
( c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ sP22(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_722])]) ).
fof(f5217,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ sP22(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3856]) ).
fof(f3856,plain,
! [X0,X1,X2,X3] :
( ( sP22(X0,X1,X2,X3)
| ( ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2)) )
& ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) ) ) )
& ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
& c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless(X2,X0,X1)
& c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) )
| ~ sP22(X0,X1,X2,X3) ) ),
inference(rectify,[],[f3855]) ).
fof(f3855,plain,
! [X2,X0,X3,X1] :
( ( sP22(X2,X0,X3,X1)
| ( ( ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
& ( ~ c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) ) )
& ( ( c_Orderings_Oord__class_Oless(X3,X0,X2)
& c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X2,X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) )
| ~ sP22(X2,X0,X3,X1) ) ),
inference(flattening,[],[f3854]) ).
fof(f3854,plain,
! [X2,X0,X3,X1] :
( ( sP22(X2,X0,X3,X1)
| ( ( ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
& ( ~ c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) ) )
& ( ( c_Orderings_Oord__class_Oless(X3,X0,X2)
& c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X2,X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) )
| ~ sP22(X2,X0,X3,X1) ) ),
inference(nnf_transformation,[],[f3511]) ).
fof(f3511,plain,
! [X2,X0,X3,X1] :
( sP22(X2,X0,X3,X1)
<=> ( ( c_Orderings_Oord__class_Oless(X3,X0,X2)
& c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X2,X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP22])]) ).
fof(f13099,plain,
spl47_721,
inference(avatar_split_clause,[],[f5208,f13097]) ).
fof(f13097,plain,
( spl47_721
<=> ! [X2,X0,X1,X3] :
( c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ sP20(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_721])]) ).
fof(f5208,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ sP20(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3851]) ).
fof(f3851,plain,
! [X0,X1,X2,X3] :
( ( sP20(X0,X1,X2,X3)
| ( ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2)) )
& ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) ) ) )
& ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
& c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless(X2,X0,X1)
& c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) )
| ~ sP20(X0,X1,X2,X3) ) ),
inference(rectify,[],[f3850]) ).
fof(f3850,plain,
! [X1,X0,X3,X2] :
( ( sP20(X1,X0,X3,X2)
| ( ( ~ c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
& ( ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) ) ) )
& ( ( c_Orderings_Oord__class_Oless(X3,X0,X1)
& c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X1,X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) )
| ~ sP20(X1,X0,X3,X2) ) ),
inference(flattening,[],[f3849]) ).
fof(f3849,plain,
! [X1,X0,X3,X2] :
( ( sP20(X1,X0,X3,X2)
| ( ( ~ c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
& ( ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) ) ) )
& ( ( c_Orderings_Oord__class_Oless(X3,X0,X1)
& c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X1,X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) )
| ~ sP20(X1,X0,X3,X2) ) ),
inference(nnf_transformation,[],[f3508]) ).
fof(f3508,plain,
! [X1,X0,X3,X2] :
( sP20(X1,X0,X3,X2)
<=> ( ( c_Orderings_Oord__class_Oless(X3,X0,X1)
& c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X1,X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP20])]) ).
fof(f13095,plain,
spl47_720,
inference(avatar_split_clause,[],[f5183,f13093]) ).
fof(f13093,plain,
( spl47_720
<=> ! [X0,X3,X2,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X0
| ~ c_Polynomial_Opdivmod__rel(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X2,X1,X0)
| ~ class_Fields_Ofield(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_720])]) ).
fof(f5183,plain,
! [X2,X3,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X0
| ~ c_Polynomial_Opdivmod__rel(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X2,X1,X0)
| ~ class_Fields_Ofield(X3) ),
inference(cnf_transformation,[],[f3837]) ).
fof(f3837,plain,
! [X0,X1,X2,X3] :
( ( ( c_Polynomial_Opdivmod__rel(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != X0
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X0
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 )
| ~ c_Polynomial_Opdivmod__rel(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X2,X1,X0) ) )
| ~ class_Fields_Ofield(X3) ),
inference(flattening,[],[f3836]) ).
fof(f3836,plain,
! [X0,X1,X2,X3] :
( ( ( c_Polynomial_Opdivmod__rel(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != X0
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X0
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 )
| ~ c_Polynomial_Opdivmod__rel(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X2,X1,X0) ) )
| ~ class_Fields_Ofield(X3) ),
inference(nnf_transformation,[],[f3111]) ).
fof(f3111,plain,
! [X0,X1,X2,X3] :
( ( c_Polynomial_Opdivmod__rel(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X2,X1,X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X0
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 ) )
| ~ class_Fields_Ofield(X3) ),
inference(ennf_transformation,[],[f2023]) ).
fof(f2023,plain,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( c_Polynomial_Opdivmod__rel(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X2,X1,X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X0
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 ) ) ),
inference(rectify,[],[f732]) ).
fof(f732,axiom,
! [X70,X18,X25,X5] :
( class_Fields_Ofield(X5)
=> ( c_Polynomial_Opdivmod__rel(X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X25,X18,X70)
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X70
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__0__iff) ).
fof(f13091,plain,
spl47_719,
inference(avatar_split_clause,[],[f5182,f13089]) ).
fof(f13089,plain,
( spl47_719
<=> ! [X0,X3,X2,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
| ~ c_Polynomial_Opdivmod__rel(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X2,X1,X0)
| ~ class_Fields_Ofield(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_719])]) ).
fof(f5182,plain,
! [X2,X3,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
| ~ c_Polynomial_Opdivmod__rel(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X2,X1,X0)
| ~ class_Fields_Ofield(X3) ),
inference(cnf_transformation,[],[f3837]) ).
fof(f13087,plain,
spl47_718,
inference(avatar_split_clause,[],[f5179,f13085]) ).
fof(f13085,plain,
( spl47_718
<=> ! [X0,X3,X2,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
| ~ c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0)
| ~ class_Fields_Ofield(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_718])]) ).
fof(f5179,plain,
! [X2,X3,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
| ~ c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0)
| ~ class_Fields_Ofield(X3) ),
inference(cnf_transformation,[],[f3835]) ).
fof(f3835,plain,
! [X0,X1,X2,X3] :
( ( ( c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0)
| X0 != X2
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != X1 )
& ( ( X0 = X2
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 )
| ~ c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0) ) )
| ~ class_Fields_Ofield(X3) ),
inference(flattening,[],[f3834]) ).
fof(f3834,plain,
! [X0,X1,X2,X3] :
( ( ( c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0)
| X0 != X2
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != X1 )
& ( ( X0 = X2
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 )
| ~ c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0) ) )
| ~ class_Fields_Ofield(X3) ),
inference(nnf_transformation,[],[f3110]) ).
fof(f3110,plain,
! [X0,X1,X2,X3] :
( ( c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0)
<=> ( X0 = X2
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 ) )
| ~ class_Fields_Ofield(X3) ),
inference(ennf_transformation,[],[f2022]) ).
fof(f2022,plain,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0)
<=> ( X0 = X2
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 ) ) ),
inference(rectify,[],[f733]) ).
fof(f733,axiom,
! [X70,X18,X15,X5] :
( class_Fields_Ofield(X5)
=> ( c_Polynomial_Opdivmod__rel(X5,X15,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X18,X70)
<=> ( X15 = X70
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__by__0__iff) ).
fof(f13083,plain,
spl47_717,
inference(avatar_split_clause,[],[f5074,f13081]) ).
fof(f13081,plain,
( spl47_717
<=> ! [X2,X0,X1] :
( sP13(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK45(X0,X1,X2)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_717])]) ).
fof(f5074,plain,
! [X2,X0,X1] :
( sP13(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK45(X0,X1,X2)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(cnf_transformation,[],[f3793]) ).
fof(f13079,plain,
spl47_716,
inference(avatar_split_clause,[],[f5066,f13077]) ).
fof(f13077,plain,
( spl47_716
<=> ! [X2,X0,X1] :
( sP12(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK44(X0,X1,X2)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_716])]) ).
fof(f5066,plain,
! [X2,X0,X1] :
( sP12(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK44(X0,X1,X2)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(cnf_transformation,[],[f3787]) ).
fof(f13075,plain,
( spl47_715
| ~ spl47_91
| ~ spl47_454
| ~ spl47_506
| ~ spl47_516 ),
inference(avatar_split_clause,[],[f10013,f9797,f9197,f8970,f6486,f13073]) ).
fof(f13073,plain,
( spl47_715
<=> ! [X0] : sP14(c_Groups_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_715])]) ).
fof(f6486,plain,
( spl47_91
<=> class_Rings_Omult__zero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_91])]) ).
fof(f8970,plain,
( spl47_454
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Omult__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_454])]) ).
fof(f9197,plain,
( spl47_506
<=> ! [X2,X1] : sP14(c_Groups_Ozero__class_Ozero(X1),X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_506])]) ).
fof(f9797,plain,
( spl47_516
<=> ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_516])]) ).
fof(f10013,plain,
( ! [X0] : sP14(c_Groups_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ spl47_91
| ~ spl47_454
| ~ spl47_506
| ~ spl47_516 ),
inference(forward_demodulation,[],[f9994,f9257]) ).
fof(f9257,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ spl47_91
| ~ spl47_454 ),
inference(resolution,[],[f8971,f6488]) ).
fof(f6488,plain,
( class_Rings_Omult__zero(tc_Int_Oint)
| ~ spl47_91 ),
inference(avatar_component_clause,[],[f6486]) ).
fof(f8971,plain,
( ! [X0,X1] :
( ~ class_Rings_Omult__zero(X1)
| c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) )
| ~ spl47_454 ),
inference(avatar_component_clause,[],[f8970]) ).
fof(f9994,plain,
( ! [X0] : sP14(c_Groups_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ spl47_506
| ~ spl47_516 ),
inference(superposition,[],[f9198,f9798]) ).
fof(f9798,plain,
( ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1)
| ~ spl47_516 ),
inference(avatar_component_clause,[],[f9797]) ).
fof(f9198,plain,
( ! [X2,X1] : sP14(c_Groups_Ozero__class_Ozero(X1),X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ spl47_506 ),
inference(avatar_component_clause,[],[f9197]) ).
fof(f13071,plain,
spl47_714,
inference(avatar_split_clause,[],[f4912,f13069]) ).
fof(f13069,plain,
( spl47_714
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_714])]) ).
fof(f4912,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(cnf_transformation,[],[f2882]) ).
fof(f2882,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f1830]) ).
fof(f1830,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1) ),
inference(rectify,[],[f510]) ).
fof(f510,axiom,
! [X17,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(f13067,plain,
spl47_713,
inference(avatar_split_clause,[],[f4905,f13065]) ).
fof(f13065,plain,
( spl47_713
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0)
| ~ class_Rings_Ocomm__semiring__0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_713])]) ).
fof(f4905,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0)
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(cnf_transformation,[],[f3745]) ).
fof(f3745,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0) ) )
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(nnf_transformation,[],[f2877]) ).
fof(f2877,plain,
! [X0,X1,X2] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0)
<=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1 )
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(ennf_transformation,[],[f1825]) ).
fof(f1825,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__0(X2)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0)
<=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1 ) ),
inference(rectify,[],[f273]) ).
fof(f273,axiom,
! [X42,X9,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5,X9,X42)
<=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__eq__0__iff) ).
fof(f13063,plain,
spl47_712,
inference(avatar_split_clause,[],[f4895,f13061]) ).
fof(f13061,plain,
( spl47_712
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Polynomial_OpCons(X2,X1,X0) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Groups_Ozero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_712])]) ).
fof(f4895,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Polynomial_OpCons(X2,X1,X0) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f3744]) ).
fof(f3744,plain,
! [X0,X1,X2] :
( ( ( c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 )
| c_Polynomial_OpCons(X2,X1,X0) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) )
| ~ class_Groups_Ozero(X2) ),
inference(flattening,[],[f3743]) ).
fof(f3743,plain,
! [X0,X1,X2] :
( ( ( c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 )
| c_Polynomial_OpCons(X2,X1,X0) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) )
| ~ class_Groups_Ozero(X2) ),
inference(nnf_transformation,[],[f2868]) ).
fof(f2868,plain,
! [X0,X1,X2] :
( ( c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 ) )
| ~ class_Groups_Ozero(X2) ),
inference(ennf_transformation,[],[f1816]) ).
fof(f1816,plain,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( c_Polynomial_OpCons(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 ) ) ),
inference(rectify,[],[f105]) ).
fof(f105,axiom,
! [X9,X12,X5] :
( class_Groups_Ozero(X5)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_OpCons(X5,X12,X9)
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X9
& c_Groups_Ozero__class_Ozero(X5) = X12 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).
fof(f13059,plain,
spl47_711,
inference(avatar_split_clause,[],[f4731,f13057]) ).
fof(f13057,plain,
( spl47_711
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_711])]) ).
fof(f4731,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(cnf_transformation,[],[f2684]) ).
fof(f2684,plain,
! [X0,X1,X2] :
( c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(flattening,[],[f2683]) ).
fof(f2683,plain,
! [X0,X1,X2] :
( c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0)
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(ennf_transformation,[],[f1693]) ).
fof(f1693,plain,
! [X0,X1,X2] :
( class_Rings_Oring__1__no__zero__divisors(X2)
=> ( c_Groups_Ozero__class_Ozero(X2) != X1
=> c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X0) ) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X7,X4,X5] :
( class_Rings_Oring__1__no__zero__divisors(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X4
=> c_Groups_Ozero__class_Ozero(X5) != hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
fof(f13055,plain,
spl47_710,
inference(avatar_split_clause,[],[f4714,f13053]) ).
fof(f13053,plain,
( spl47_710
<=> ! [X2,X0,X1] :
( c_Polynomial_Opos__poly(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0))
| ~ c_Polynomial_Opos__poly(X2,X0)
| ~ c_Polynomial_Opos__poly(X2,X1)
| ~ class_Rings_Olinordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_710])]) ).
fof(f4714,plain,
! [X2,X0,X1] :
( c_Polynomial_Opos__poly(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0))
| ~ c_Polynomial_Opos__poly(X2,X0)
| ~ c_Polynomial_Opos__poly(X2,X1)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(cnf_transformation,[],[f2671]) ).
fof(f2671,plain,
! [X0,X1,X2] :
( c_Polynomial_Opos__poly(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0))
| ~ c_Polynomial_Opos__poly(X2,X0)
| ~ c_Polynomial_Opos__poly(X2,X1)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(flattening,[],[f2670]) ).
fof(f2670,plain,
! [X0,X1,X2] :
( c_Polynomial_Opos__poly(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0))
| ~ c_Polynomial_Opos__poly(X2,X0)
| ~ c_Polynomial_Opos__poly(X2,X1)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(ennf_transformation,[],[f1684]) ).
fof(f1684,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Polynomial_Opos__poly(X2,X1)
=> ( c_Polynomial_Opos__poly(X2,X0)
=> c_Polynomial_Opos__poly(X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X1,X0)) ) ) ),
inference(rectify,[],[f601]) ).
fof(f601,axiom,
! [X13,X8,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Polynomial_Opos__poly(X5,X8)
=> ( c_Polynomial_Opos__poly(X5,X13)
=> c_Polynomial_Opos__poly(X5,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),X8,X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__add) ).
fof(f13051,plain,
spl47_709,
inference(avatar_split_clause,[],[f4647,f13049]) ).
fof(f13049,plain,
( spl47_709
<=> ! [X2,X0,X1] :
( c_Rings_Oinverse__class_Odivide(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) = c_Groups_Ouminus__class_Ouminus(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X0))
| ~ class_Rings_Odivision__ring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_709])]) ).
fof(f4647,plain,
! [X2,X0,X1] :
( c_Rings_Oinverse__class_Odivide(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) = c_Groups_Ouminus__class_Ouminus(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X0))
| ~ class_Rings_Odivision__ring(X2) ),
inference(cnf_transformation,[],[f2628]) ).
fof(f2628,plain,
! [X0,X1,X2] :
( c_Rings_Oinverse__class_Odivide(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) = c_Groups_Ouminus__class_Ouminus(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X0))
| ~ class_Rings_Odivision__ring(X2) ),
inference(ennf_transformation,[],[f1651]) ).
fof(f1651,plain,
! [X0,X1,X2] :
( class_Rings_Odivision__ring(X2)
=> c_Rings_Oinverse__class_Odivide(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) = c_Groups_Ouminus__class_Ouminus(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X0)) ),
inference(rectify,[],[f904]) ).
fof(f904,axiom,
! [X17,X4,X5] :
( class_Rings_Odivision__ring(X5)
=> c_Groups_Ouminus__class_Ouminus(X5,c_Rings_Oinverse__class_Odivide(X5,X4,X17)) = c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__left) ).
fof(f13047,plain,
spl47_708,
inference(avatar_split_clause,[],[f4645,f13045]) ).
fof(f13045,plain,
( spl47_708
<=> ! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X0)) = c_Rings_Oinverse__class_Odivide(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Fields_Ofield__inverse__zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_708])]) ).
fof(f4645,plain,
! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X0)) = c_Rings_Oinverse__class_Odivide(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(cnf_transformation,[],[f2626]) ).
fof(f2626,plain,
! [X0,X1,X2] :
( c_Groups_Ouminus__class_Ouminus(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X0)) = c_Rings_Oinverse__class_Odivide(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(ennf_transformation,[],[f1649]) ).
fof(f1649,plain,
! [X0,X1,X2] :
( class_Fields_Ofield__inverse__zero(X2)
=> c_Groups_Ouminus__class_Ouminus(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X0)) = c_Rings_Oinverse__class_Odivide(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(rectify,[],[f929]) ).
fof(f929,axiom,
! [X17,X4,X5] :
( class_Fields_Ofield__inverse__zero(X5)
=> c_Groups_Ouminus__class_Ouminus(X5,c_Rings_Oinverse__class_Odivide(X5,X4,X17)) = c_Rings_Oinverse__class_Odivide(X5,X4,c_Groups_Ouminus__class_Ouminus(X5,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__right) ).
fof(f13043,plain,
spl47_707,
inference(avatar_split_clause,[],[f4644,f13041]) ).
fof(f13041,plain,
( spl47_707
<=> ! [X2,X0,X1] :
( c_Rings_Oinverse__class_Odivide(X2,X1,X0) = c_Rings_Oinverse__class_Odivide(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Fields_Ofield__inverse__zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_707])]) ).
fof(f4644,plain,
! [X2,X0,X1] :
( c_Rings_Oinverse__class_Odivide(X2,X1,X0) = c_Rings_Oinverse__class_Odivide(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(cnf_transformation,[],[f2625]) ).
fof(f2625,plain,
! [X0,X1,X2] :
( c_Rings_Oinverse__class_Odivide(X2,X1,X0) = c_Rings_Oinverse__class_Odivide(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(ennf_transformation,[],[f1648]) ).
fof(f1648,plain,
! [X0,X1,X2] :
( class_Fields_Ofield__inverse__zero(X2)
=> c_Rings_Oinverse__class_Odivide(X2,X1,X0) = c_Rings_Oinverse__class_Odivide(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(rectify,[],[f930]) ).
fof(f930,axiom,
! [X17,X4,X5] :
( class_Fields_Ofield__inverse__zero(X5)
=> c_Rings_Oinverse__class_Odivide(X5,X4,X17) = c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),c_Groups_Ouminus__class_Ouminus(X5,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__divide) ).
fof(f13039,plain,
spl47_706,
inference(avatar_split_clause,[],[f4643,f13037]) ).
fof(f13037,plain,
( spl47_706
<=> ! [X2,X0,X1] :
( c_Rings_Oinverse__class_Odivide(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) = c_Groups_Ouminus__class_Ouminus(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X0))
| ~ class_RealVector_Oreal__normed__field(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_706])]) ).
fof(f4643,plain,
! [X2,X0,X1] :
( c_Rings_Oinverse__class_Odivide(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) = c_Groups_Ouminus__class_Ouminus(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X0))
| ~ class_RealVector_Oreal__normed__field(X2) ),
inference(cnf_transformation,[],[f2624]) ).
fof(f2624,plain,
! [X0,X1,X2] :
( c_Rings_Oinverse__class_Odivide(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) = c_Groups_Ouminus__class_Ouminus(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X0))
| ~ class_RealVector_Oreal__normed__field(X2) ),
inference(ennf_transformation,[],[f1647]) ).
fof(f1647,plain,
! [X0,X1,X2] :
( class_RealVector_Oreal__normed__field(X2)
=> c_Rings_Oinverse__class_Odivide(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) = c_Groups_Ouminus__class_Ouminus(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X0)) ),
inference(rectify,[],[f924]) ).
fof(f924,axiom,
! [X10,X6,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ouminus__class_Ouminus(X5,X6),X10) = c_Groups_Ouminus__class_Ouminus(X5,c_Rings_Oinverse__class_Odivide(X5,X6,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Ominus) ).
fof(f13035,plain,
spl47_705,
inference(avatar_split_clause,[],[f4629,f13033]) ).
fof(f13033,plain,
( spl47_705
<=> ! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_705])]) ).
fof(f4629,plain,
! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
inference(cnf_transformation,[],[f1618]) ).
fof(f1618,plain,
! [X0,X1,X2] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
inference(rectify,[],[f762]) ).
fof(f762,axiom,
! [X7,X20,X21] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X20),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X20)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel2) ).
fof(f13031,plain,
( spl47_704
| ~ spl47_91
| ~ spl47_454
| ~ spl47_507
| ~ spl47_516 ),
inference(avatar_split_clause,[],[f10012,f9797,f9201,f8970,f6486,f13029]) ).
fof(f13029,plain,
( spl47_704
<=> ! [X0] : sP16(c_Groups_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_704])]) ).
fof(f9201,plain,
( spl47_507
<=> ! [X2,X1] : sP16(c_Groups_Ozero__class_Ozero(X1),X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_507])]) ).
fof(f10012,plain,
( ! [X0] : sP16(c_Groups_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ spl47_91
| ~ spl47_454
| ~ spl47_507
| ~ spl47_516 ),
inference(forward_demodulation,[],[f9993,f9257]) ).
fof(f9993,plain,
( ! [X0] : sP16(c_Groups_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ spl47_507
| ~ spl47_516 ),
inference(superposition,[],[f9202,f9798]) ).
fof(f9202,plain,
( ! [X2,X1] : sP16(c_Groups_Ozero__class_Ozero(X1),X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ spl47_507 ),
inference(avatar_component_clause,[],[f9201]) ).
fof(f13027,plain,
spl47_703,
inference(avatar_split_clause,[],[f4628,f13025]) ).
fof(f13025,plain,
( spl47_703
<=> ! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_703])]) ).
fof(f4628,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0),
inference(cnf_transformation,[],[f1617]) ).
fof(f1617,plain,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0),
inference(rectify,[],[f394]) ).
fof(f394,axiom,
! [X20,X7,X21] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X7),X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(f13023,plain,
spl47_702,
inference(avatar_split_clause,[],[f4627,f13021]) ).
fof(f13021,plain,
( spl47_702
<=> ! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_702])]) ).
fof(f4627,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)),
inference(cnf_transformation,[],[f1616]) ).
fof(f1616,plain,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)),
inference(rectify,[],[f393]) ).
fof(f393,axiom,
! [X26,X10,X6] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X26)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X26)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
fof(f13019,plain,
spl47_701,
inference(avatar_split_clause,[],[f4626,f13017]) ).
fof(f13017,plain,
( spl47_701
<=> ! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_701])]) ).
fof(f13015,plain,
spl47_700,
inference(avatar_split_clause,[],[f4625,f13013]) ).
fof(f13013,plain,
( spl47_700
<=> ! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_700])]) ).
fof(f4625,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0)),
inference(cnf_transformation,[],[f1614]) ).
fof(f1614,plain,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0)),
inference(rectify,[],[f673]) ).
fof(f673,axiom,
! [X26,X10,X6] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X6,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,X26)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X6,X26)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
fof(f13011,plain,
spl47_699,
inference(avatar_split_clause,[],[f4623,f13009]) ).
fof(f13009,plain,
( spl47_699
<=> ! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_699])]) ).
fof(f13007,plain,
spl47_698,
inference(avatar_split_clause,[],[f4622,f13005]) ).
fof(f13005,plain,
( spl47_698
<=> ! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_698])]) ).
fof(f4622,plain,
! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)),
inference(cnf_transformation,[],[f1611]) ).
fof(f1611,plain,
! [X0,X1,X2] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)),
inference(rectify,[],[f763]) ).
fof(f763,axiom,
! [X7,X21,X20] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X7) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X21),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel) ).
fof(f13003,plain,
spl47_697,
inference(avatar_split_clause,[],[f4613,f13001]) ).
fof(f13001,plain,
( spl47_697
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_697])]) ).
fof(f4613,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f3666]) ).
fof(f12999,plain,
spl47_696,
inference(avatar_split_clause,[],[f4612,f12997]) ).
fof(f12997,plain,
( spl47_696
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_696])]) ).
fof(f4612,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f3666]) ).
fof(f12995,plain,
spl47_695,
inference(avatar_split_clause,[],[f4608,f12993]) ).
fof(f12993,plain,
( spl47_695
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_695])]) ).
fof(f4608,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(cnf_transformation,[],[f3662]) ).
fof(f12991,plain,
spl47_694,
inference(avatar_split_clause,[],[f4581,f12989]) ).
fof(f12989,plain,
( spl47_694
<=> ! [X0,X1] :
( X0 = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_694])]) ).
fof(f4581,plain,
! [X0,X1] :
( X0 = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f3646]) ).
fof(f3646,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ( X0 != X1
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) )
& ( X0 = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(flattening,[],[f3645]) ).
fof(f3645,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ( X0 != X1
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) )
& ( X0 = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(nnf_transformation,[],[f1597]) ).
fof(f1597,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> ( X0 = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
inference(rectify,[],[f493]) ).
fof(f493,axiom,
! [X30,X49] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X30,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> ( X30 = X49
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,X30) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
fof(f12987,plain,
spl47_693,
inference(avatar_split_clause,[],[f4442,f12985]) ).
fof(f12985,plain,
( spl47_693
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_693])]) ).
fof(f4442,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(cnf_transformation,[],[f2548]) ).
fof(f2548,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(ennf_transformation,[],[f1523]) ).
fof(f1523,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0)) ),
inference(rectify,[],[f639]) ).
fof(f639,axiom,
! [X7,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(f12983,plain,
spl47_692,
inference(avatar_split_clause,[],[f4438,f12981]) ).
fof(f12981,plain,
( spl47_692
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK33(X0,X1),X0)
| ~ hBOOL(hAPP(X1,X0))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_692])]) ).
fof(f4438,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK33(X0,X1),X0)
| ~ hBOOL(hAPP(X1,X0))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(cnf_transformation,[],[f3580]) ).
fof(f12979,plain,
spl47_691,
inference(avatar_split_clause,[],[f4382,f12977]) ).
fof(f12977,plain,
( spl47_691
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0)
| ~ class_Rings_Ocomm__semiring__0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_691])]) ).
fof(f4382,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(cnf_transformation,[],[f2485]) ).
fof(f2485,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(ennf_transformation,[],[f1469]) ).
fof(f1469,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) ),
inference(rectify,[],[f542]) ).
fof(f542,axiom,
! [X13,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__left) ).
fof(f12975,plain,
spl47_690,
inference(avatar_split_clause,[],[f4381,f12973]) ).
fof(f12973,plain,
( spl47_690
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Rings_Ocomm__semiring__0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_690])]) ).
fof(f4381,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(cnf_transformation,[],[f2484]) ).
fof(f2484,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(ennf_transformation,[],[f1468]) ).
fof(f1468,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(rectify,[],[f541]) ).
fof(f541,axiom,
! [X8,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__right) ).
fof(f12971,plain,
spl47_689,
inference(avatar_split_clause,[],[f4329,f12969]) ).
fof(f12969,plain,
( spl47_689
<=> ! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X0)
| ~ class_Rings_Ocomm__ring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_689])]) ).
fof(f4329,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X0)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(cnf_transformation,[],[f2438]) ).
fof(f2438,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X0)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(ennf_transformation,[],[f1423]) ).
fof(f1423,plain,
! [X0,X1] :
( class_Rings_Ocomm__ring__1(X1)
=> c_Groups_Ouminus__class_Ouminus(X1,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X0) ),
inference(rectify,[],[f592]) ).
fof(f592,axiom,
! [X6,X5] :
( class_Rings_Ocomm__ring__1(X5)
=> c_Groups_Ouminus__class_Ouminus(X5,X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Oone__class_Oone(X5))),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
fof(f12967,plain,
spl47_688,
inference(avatar_split_clause,[],[f4321,f12965]) ).
fof(f12965,plain,
( spl47_688
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_688])]) ).
fof(f4321,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(cnf_transformation,[],[f3568]) ).
fof(f3568,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
& ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1)) ) )
| ~ class_Rings_Olinordered__idom(X1) ),
inference(nnf_transformation,[],[f2432]) ).
fof(f2432,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
| ~ class_Rings_Olinordered__idom(X1) ),
inference(ennf_transformation,[],[f1417]) ).
fof(f1417,plain,
! [X0,X1] :
( class_Rings_Olinordered__idom(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
inference(rectify,[],[f387]) ).
fof(f387,axiom,
! [X12,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X12,X12),c_Groups_Ozero__class_Ozero(X5))
<=> c_Orderings_Oord__class_Oless(X5,X12,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
fof(f12963,plain,
spl47_687,
inference(avatar_split_clause,[],[f4320,f12961]) ).
fof(f12961,plain,
( spl47_687
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_687])]) ).
fof(f4320,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(cnf_transformation,[],[f3568]) ).
fof(f12959,plain,
spl47_686,
inference(avatar_split_clause,[],[f4306,f12957]) ).
fof(f12957,plain,
( spl47_686
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_686])]) ).
fof(f4306,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3561]) ).
fof(f3561,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
& ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1)) ) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f2423]) ).
fof(f2423,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f1409]) ).
fof(f1409,plain,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
inference(rectify,[],[f382]) ).
fof(f382,axiom,
! [X12,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X12,X12),c_Groups_Ozero__class_Ozero(X5))
<=> c_Orderings_Oord__class_Oless(X5,X12,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(f12955,plain,
spl47_685,
inference(avatar_split_clause,[],[f4305,f12953]) ).
fof(f12953,plain,
( spl47_685
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_685])]) ).
fof(f4305,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3561]) ).
fof(f12951,plain,
spl47_684,
inference(avatar_split_clause,[],[f4304,f12949]) ).
fof(f12949,plain,
( spl47_684
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_684])]) ).
fof(f4304,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3560]) ).
fof(f3560,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
& ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0)) ) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f2422]) ).
fof(f2422,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f1408]) ).
fof(f1408,plain,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
inference(rectify,[],[f383]) ).
fof(f383,axiom,
! [X12,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,X12,X12))
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(f12947,plain,
spl47_683,
inference(avatar_split_clause,[],[f4303,f12945]) ).
fof(f12945,plain,
( spl47_683
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_683])]) ).
fof(f4303,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3560]) ).
fof(f12943,plain,
spl47_682,
inference(avatar_split_clause,[],[f4302,f12941]) ).
fof(f12941,plain,
( spl47_682
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_682])]) ).
fof(f4302,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3559]) ).
fof(f3559,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
& ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1)) ) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f2421]) ).
fof(f2421,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f1407]) ).
fof(f1407,plain,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
inference(rectify,[],[f378]) ).
fof(f378,axiom,
! [X12,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X12,X12),c_Groups_Ozero__class_Ozero(X5))
<=> c_Orderings_Oord__class_Oless__eq(X5,X12,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(f12939,plain,
spl47_681,
inference(avatar_split_clause,[],[f4301,f12937]) ).
fof(f12937,plain,
( spl47_681
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_681])]) ).
fof(f4301,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X0,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3559]) ).
fof(f12935,plain,
spl47_680,
inference(avatar_split_clause,[],[f4300,f12933]) ).
fof(f12933,plain,
( spl47_680
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_680])]) ).
fof(f4300,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3558]) ).
fof(f3558,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
& ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0)) ) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f2420]) ).
fof(f2420,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f1406]) ).
fof(f1406,plain,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
inference(rectify,[],[f379]) ).
fof(f379,axiom,
! [X12,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,X12,X12))
<=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(f12931,plain,
spl47_679,
inference(avatar_split_clause,[],[f4299,f12929]) ).
fof(f12929,plain,
( spl47_679
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_679])]) ).
fof(f4299,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X0,X0))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3558]) ).
fof(f12927,plain,
spl47_678,
inference(avatar_split_clause,[],[f4253,f12925]) ).
fof(f12925,plain,
( spl47_678
<=> ! [X0,X1] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_678])]) ).
fof(f4253,plain,
! [X0,X1] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),
inference(cnf_transformation,[],[f1369]) ).
fof(f1369,plain,
! [X0,X1] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),
inference(rectify,[],[f646]) ).
fof(f646,axiom,
! [X48,X26] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,X48)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X26),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X48)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).
fof(f12533,plain,
( spl47_677
| ~ spl47_332
| ~ spl47_507 ),
inference(avatar_split_clause,[],[f9782,f9201,f7725,f12531]) ).
fof(f12531,plain,
( spl47_677
<=> ! [X0] : sP16(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_677])]) ).
fof(f7725,plain,
( spl47_332
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_332])]) ).
fof(f9782,plain,
( ! [X0] : sP16(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl47_332
| ~ spl47_507 ),
inference(superposition,[],[f9202,f7726]) ).
fof(f7726,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ spl47_332 ),
inference(avatar_component_clause,[],[f7725]) ).
fof(f12361,plain,
( spl47_676
| ~ spl47_332
| ~ spl47_506 ),
inference(avatar_split_clause,[],[f9772,f9197,f7725,f12359]) ).
fof(f12359,plain,
( spl47_676
<=> ! [X0] : sP14(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_676])]) ).
fof(f9772,plain,
( ! [X0] : sP14(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl47_332
| ~ spl47_506 ),
inference(superposition,[],[f9198,f7726]) ).
fof(f11488,plain,
( ~ spl47_674
| spl47_675
| ~ spl47_155
| ~ spl47_601 ),
inference(avatar_split_clause,[],[f11465,f10774,f6799,f11486,f11482]) ).
fof(f11482,plain,
( spl47_674
<=> class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_674])]) ).
fof(f11486,plain,
( spl47_675
<=> ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_675])]) ).
fof(f6799,plain,
( spl47_155
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_155])]) ).
fof(f10774,plain,
( spl47_601
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Groups_Oordered__ab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_601])]) ).
fof(f11465,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) )
| ~ spl47_155
| ~ spl47_601 ),
inference(resolution,[],[f10775,f6800]) ).
fof(f6800,plain,
( ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl47_155 ),
inference(avatar_component_clause,[],[f6799]) ).
fof(f10775,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Groups_Oordered__ab__group__add(X2) )
| ~ spl47_601 ),
inference(avatar_component_clause,[],[f10774]) ).
fof(f11343,plain,
( spl47_673
| ~ spl47_148
| ~ spl47_416 ),
inference(avatar_split_clause,[],[f8698,f8258,f6769,f11341]) ).
fof(f11341,plain,
( spl47_673
<=> ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_673])]) ).
fof(f6769,plain,
( spl47_148
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_148])]) ).
fof(f8258,plain,
( spl47_416
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_416])]) ).
fof(f8698,plain,
( ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))
| ~ spl47_148
| ~ spl47_416 ),
inference(resolution,[],[f8259,f6770]) ).
fof(f6770,plain,
( ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0)
| ~ spl47_148 ),
inference(avatar_component_clause,[],[f6769]) ).
fof(f8259,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
| ~ spl47_416 ),
inference(avatar_component_clause,[],[f8258]) ).
fof(f11229,plain,
( spl47_672
| ~ spl47_319
| ~ spl47_356 ),
inference(avatar_split_clause,[],[f8027,f7822,f7506,f11227]) ).
fof(f11227,plain,
( spl47_672
<=> ! [X0,X1] :
( ~ sP11(X0,X0,c_Rings_Odvd__class_Odvd(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_672])]) ).
fof(f7506,plain,
( spl47_319
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_319])]) ).
fof(f8027,plain,
( ! [X0,X1] :
( ~ sP11(X0,X0,c_Rings_Odvd__class_Odvd(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) )
| ~ spl47_319
| ~ spl47_356 ),
inference(resolution,[],[f7823,f7507]) ).
fof(f7507,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) )
| ~ spl47_319 ),
inference(avatar_component_clause,[],[f7506]) ).
fof(f11085,plain,
( spl47_671
| ~ spl47_320
| ~ spl47_322 ),
inference(avatar_split_clause,[],[f7701,f7520,f7510,f11082]) ).
fof(f11082,plain,
( spl47_671
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_671])]) ).
fof(f7510,plain,
( spl47_320
<=> c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_320])]) ).
fof(f7520,plain,
( spl47_322
<=> ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_322])]) ).
fof(f7701,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))
| ~ spl47_320
| ~ spl47_322 ),
inference(superposition,[],[f7521,f7512]) ).
fof(f7512,plain,
( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_n____,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl47_320 ),
inference(avatar_component_clause,[],[f7510]) ).
fof(f7521,plain,
( ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ spl47_322 ),
inference(avatar_component_clause,[],[f7520]) ).
fof(f11057,plain,
spl47_670,
inference(avatar_split_clause,[],[f5872,f11055]) ).
fof(f11055,plain,
( spl47_670
<=> ! [X4,X3,X2,X1] :
( X2 = X3
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X1)
| ~ class_Groups_Oab__group__add(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_670])]) ).
fof(f5872,plain,
! [X2,X3,X1,X4] :
( X2 = X3
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X1)
| ~ class_Groups_Oab__group__add(X4) ),
inference(equality_resolution,[],[f5431]) ).
fof(f5431,plain,
! [X2,X3,X0,X1,X4] :
( X2 = X3
| X0 != X1
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ~ class_Groups_Oab__group__add(X4) ),
inference(cnf_transformation,[],[f3890]) ).
fof(f3890,plain,
! [X0,X1,X2,X3,X4] :
( ( ( X2 = X3
| X0 != X1 )
& ( X0 = X1
| X2 != X3 ) )
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ~ class_Groups_Oab__group__add(X4) ),
inference(nnf_transformation,[],[f3406]) ).
fof(f3406,plain,
! [X0,X1,X2,X3,X4] :
( ( X2 = X3
<=> X0 = X1 )
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ~ class_Groups_Oab__group__add(X4) ),
inference(flattening,[],[f3405]) ).
fof(f3405,plain,
! [X0,X1,X2,X3,X4] :
( ( X2 = X3
<=> X0 = X1 )
| c_Groups_Ominus__class_Ominus(X4,X3,X2) != c_Groups_Ominus__class_Ominus(X4,X1,X0)
| ~ class_Groups_Oab__group__add(X4) ),
inference(ennf_transformation,[],[f2211]) ).
fof(f2211,plain,
! [X0,X1,X2,X3,X4] :
( class_Groups_Oab__group__add(X4)
=> ( c_Groups_Ominus__class_Ominus(X4,X3,X2) = c_Groups_Ominus__class_Ominus(X4,X1,X0)
=> ( X2 = X3
<=> X0 = X1 ) ) ),
inference(rectify,[],[f781]) ).
fof(f781,axiom,
! [X52,X24,X29,X12,X5] :
( class_Groups_Oab__group__add(X5)
=> ( c_Groups_Ominus__class_Ominus(X5,X12,X29) = c_Groups_Ominus__class_Ominus(X5,X24,X52)
=> ( X12 = X29
<=> X24 = X52 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).
fof(f11053,plain,
spl47_669,
inference(avatar_split_clause,[],[f5853,f11051]) ).
fof(f11051,plain,
( spl47_669
<=> ! [X0,X1,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)))
| ~ class_Rings_Odvd(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_669])]) ).
fof(f5853,plain,
! [X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)))
| ~ class_Rings_Odvd(X3) ),
inference(equality_resolution,[],[f5296]) ).
fof(f5296,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X2))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0) != X2
| ~ class_Rings_Odvd(X3) ),
inference(cnf_transformation,[],[f3238]) ).
fof(f3238,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X2))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0) != X2
| ~ class_Rings_Odvd(X3) ),
inference(flattening,[],[f3237]) ).
fof(f3237,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X2))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0) != X2
| ~ class_Rings_Odvd(X3) ),
inference(ennf_transformation,[],[f2096]) ).
fof(f2096,plain,
! [X0,X1,X2,X3] :
( class_Rings_Odvd(X3)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0) = X2
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X2)) ) ),
inference(rectify,[],[f530]) ).
fof(f530,axiom,
! [X20,X17,X4,X5] :
( class_Rings_Odvd(X5)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X20) = X4
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X17),X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvdI) ).
fof(f11049,plain,
spl47_668,
inference(avatar_split_clause,[],[f5832,f11047]) ).
fof(f11047,plain,
( spl47_668
<=> ! [X2,X0,X1] :
( sP16(X0,X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2))
| c_Groups_Ozero__class_Ozero(X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_668])]) ).
fof(f5832,plain,
! [X2,X0,X1] :
( sP16(X0,X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2))
| c_Groups_Ozero__class_Ozero(X1) = X2 ),
inference(equality_resolution,[],[f5145]) ).
fof(f5145,plain,
! [X2,X3,X0,X1] :
( sP16(X0,X1,X2,X3)
| c_Groups_Ozero__class_Ozero(X1) = X2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2) != X3 ),
inference(cnf_transformation,[],[f3830]) ).
fof(f11045,plain,
spl47_667,
inference(avatar_split_clause,[],[f5824,f11043]) ).
fof(f11043,plain,
( spl47_667
<=> ! [X2,X0,X1] :
( sP14(X0,X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2))
| c_Groups_Ozero__class_Ozero(X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_667])]) ).
fof(f5824,plain,
! [X2,X0,X1] :
( sP14(X0,X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2))
| c_Groups_Ozero__class_Ozero(X1) = X2 ),
inference(equality_resolution,[],[f5136]) ).
fof(f5136,plain,
! [X2,X3,X0,X1] :
( sP14(X0,X1,X2,X3)
| c_Groups_Ozero__class_Ozero(X1) = X2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2) != X3 ),
inference(cnf_transformation,[],[f3825]) ).
fof(f11041,plain,
spl47_666,
inference(avatar_split_clause,[],[f5441,f11039]) ).
fof(f11039,plain,
( spl47_666
<=> ! [X4,X0,X3,X2,X1] :
( X0 = X2
| c_Polynomial_OpCons(X4,X3,X2) != c_Polynomial_OpCons(X4,X1,X0)
| ~ class_Groups_Ozero(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_666])]) ).
fof(f5441,plain,
! [X2,X3,X0,X1,X4] :
( X0 = X2
| c_Polynomial_OpCons(X4,X3,X2) != c_Polynomial_OpCons(X4,X1,X0)
| ~ class_Groups_Ozero(X4) ),
inference(cnf_transformation,[],[f3896]) ).
fof(f3896,plain,
! [X0,X1,X2,X3,X4] :
( ( ( c_Polynomial_OpCons(X4,X3,X2) = c_Polynomial_OpCons(X4,X1,X0)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Polynomial_OpCons(X4,X3,X2) != c_Polynomial_OpCons(X4,X1,X0) ) )
| ~ class_Groups_Ozero(X4) ),
inference(flattening,[],[f3895]) ).
fof(f3895,plain,
! [X0,X1,X2,X3,X4] :
( ( ( c_Polynomial_OpCons(X4,X3,X2) = c_Polynomial_OpCons(X4,X1,X0)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Polynomial_OpCons(X4,X3,X2) != c_Polynomial_OpCons(X4,X1,X0) ) )
| ~ class_Groups_Ozero(X4) ),
inference(nnf_transformation,[],[f3411]) ).
fof(f3411,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Polynomial_OpCons(X4,X3,X2) = c_Polynomial_OpCons(X4,X1,X0)
<=> ( X0 = X2
& X1 = X3 ) )
| ~ class_Groups_Ozero(X4) ),
inference(ennf_transformation,[],[f2216]) ).
fof(f2216,plain,
! [X0,X1,X2,X3,X4] :
( class_Groups_Ozero(X4)
=> ( c_Polynomial_OpCons(X4,X3,X2) = c_Polynomial_OpCons(X4,X1,X0)
<=> ( X0 = X2
& X1 = X3 ) ) ),
inference(rectify,[],[f87]) ).
fof(f87,axiom,
! [X18,X29,X9,X12,X5] :
( class_Groups_Ozero(X5)
=> ( c_Polynomial_OpCons(X5,X12,X9) = c_Polynomial_OpCons(X5,X29,X18)
<=> ( X9 = X18
& X12 = X29 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__iff) ).
fof(f11037,plain,
spl47_665,
inference(avatar_split_clause,[],[f5440,f11035]) ).
fof(f11035,plain,
( spl47_665
<=> ! [X2,X4,X0,X3,X1] :
( X1 = X3
| c_Polynomial_OpCons(X4,X3,X2) != c_Polynomial_OpCons(X4,X1,X0)
| ~ class_Groups_Ozero(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_665])]) ).
fof(f5440,plain,
! [X2,X3,X0,X1,X4] :
( X1 = X3
| c_Polynomial_OpCons(X4,X3,X2) != c_Polynomial_OpCons(X4,X1,X0)
| ~ class_Groups_Ozero(X4) ),
inference(cnf_transformation,[],[f3896]) ).
fof(f11033,plain,
spl47_664,
inference(avatar_split_clause,[],[f5385,f11031]) ).
fof(f11031,plain,
( spl47_664
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_664])]) ).
fof(f5385,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(cnf_transformation,[],[f3354]) ).
fof(f3354,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(flattening,[],[f3353]) ).
fof(f3353,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(ennf_transformation,[],[f2178]) ).
fof(f2178,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,X0,X2)
=> c_Orderings_Oord__class_Oless(X3,X0,X1) ) ) ),
inference(rectify,[],[f151]) ).
fof(f151,axiom,
! [X26,X6,X10,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X10,X6)
=> ( c_Orderings_Oord__class_Oless(X5,X26,X10)
=> c_Orderings_Oord__class_Oless(X5,X26,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(f11029,plain,
spl47_663,
inference(avatar_split_clause,[],[f5384,f11027]) ).
fof(f11027,plain,
( spl47_663
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_663])]) ).
fof(f5384,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(cnf_transformation,[],[f3352]) ).
fof(f3352,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(flattening,[],[f3351]) ).
fof(f3351,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(ennf_transformation,[],[f2177]) ).
fof(f2177,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
=> c_Orderings_Oord__class_Oless(X3,X0,X1) ) ) ),
inference(rectify,[],[f185]) ).
fof(f185,axiom,
! [X26,X6,X10,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X10,X6)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X26,X10)
=> c_Orderings_Oord__class_Oless(X5,X26,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(f11025,plain,
( spl47_662
| ~ spl47_253
| ~ spl47_320 ),
inference(avatar_split_clause,[],[f7684,f7510,f7201,f11022]) ).
fof(f11022,plain,
( spl47_662
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_662])]) ).
fof(f7684,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))
| ~ spl47_253
| ~ spl47_320 ),
inference(superposition,[],[f7202,f7512]) ).
fof(f11020,plain,
spl47_661,
inference(avatar_split_clause,[],[f5382,f11018]) ).
fof(f11018,plain,
( spl47_661
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_661])]) ).
fof(f5382,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(cnf_transformation,[],[f3348]) ).
fof(f3348,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(flattening,[],[f3347]) ).
fof(f3347,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(ennf_transformation,[],[f2175]) ).
fof(f2175,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,X0,X2)
=> c_Orderings_Oord__class_Oless(X3,X0,X1) ) ) ),
inference(rectify,[],[f183]) ).
fof(f183,axiom,
! [X26,X6,X10,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X10,X6)
=> ( c_Orderings_Oord__class_Oless(X5,X26,X10)
=> c_Orderings_Oord__class_Oless(X5,X26,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(f11016,plain,
spl47_660,
inference(avatar_split_clause,[],[f5381,f11014]) ).
fof(f11014,plain,
( spl47_660
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_660])]) ).
fof(f5381,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(cnf_transformation,[],[f3346]) ).
fof(f3346,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(flattening,[],[f3345]) ).
fof(f3345,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(ennf_transformation,[],[f2174]) ).
fof(f2174,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
=> c_Orderings_Oord__class_Oless__eq(X3,X0,X1) ) ) ),
inference(rectify,[],[f285]) ).
fof(f285,axiom,
! [X26,X6,X10,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X10,X6)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X26,X10)
=> c_Orderings_Oord__class_Oless__eq(X5,X26,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(f11012,plain,
spl47_659,
inference(avatar_split_clause,[],[f5377,f11010]) ).
fof(f11010,plain,
( spl47_659
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_659])]) ).
fof(f5377,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(cnf_transformation,[],[f3338]) ).
fof(f3338,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(flattening,[],[f3337]) ).
fof(f3337,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(ennf_transformation,[],[f2170]) ).
fof(f2170,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Opreorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,X1,X0)
=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ) ),
inference(rectify,[],[f152]) ).
fof(f152,axiom,
! [X26,X10,X6,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X6,X10)
=> ( c_Orderings_Oord__class_Oless(X5,X10,X26)
=> c_Orderings_Oord__class_Oless(X5,X6,X26) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(f11008,plain,
spl47_658,
inference(avatar_split_clause,[],[f5376,f11006]) ).
fof(f11006,plain,
( spl47_658
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_658])]) ).
fof(f5376,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(cnf_transformation,[],[f3336]) ).
fof(f3336,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(flattening,[],[f3335]) ).
fof(f3335,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(ennf_transformation,[],[f2169]) ).
fof(f2169,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Opreorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ) ),
inference(rectify,[],[f186]) ).
fof(f186,axiom,
! [X26,X10,X6,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X6,X10)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X10,X26)
=> c_Orderings_Oord__class_Oless(X5,X6,X26) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
fof(f11004,plain,
spl47_657,
inference(avatar_split_clause,[],[f5375,f11002]) ).
fof(f11002,plain,
( spl47_657
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_657])]) ).
fof(f5375,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(cnf_transformation,[],[f3334]) ).
fof(f3334,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(flattening,[],[f3333]) ).
fof(f3333,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(ennf_transformation,[],[f2168]) ).
fof(f2168,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Opreorder(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,X1,X0)
=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ) ),
inference(rectify,[],[f184]) ).
fof(f184,axiom,
! [X26,X10,X6,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X6,X10)
=> ( c_Orderings_Oord__class_Oless(X5,X10,X26)
=> c_Orderings_Oord__class_Oless(X5,X6,X26) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
fof(f11000,plain,
spl47_656,
inference(avatar_split_clause,[],[f5374,f10998]) ).
fof(f10998,plain,
( spl47_656
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_656])]) ).
fof(f5374,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(cnf_transformation,[],[f3332]) ).
fof(f3332,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(flattening,[],[f3331]) ).
fof(f3331,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(ennf_transformation,[],[f2167]) ).
fof(f2167,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Opreorder(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ) ) ),
inference(rectify,[],[f287]) ).
fof(f287,axiom,
! [X26,X10,X6,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X6,X10)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X10,X26)
=> c_Orderings_Oord__class_Oless__eq(X5,X6,X26) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).
fof(f10996,plain,
spl47_655,
inference(avatar_split_clause,[],[f5372,f10994]) ).
fof(f10994,plain,
( spl47_655
<=> ! [X0,X3,X2,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
| ~ class_Orderings_Oord(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_655])]) ).
fof(f5372,plain,
! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
| ~ class_Orderings_Oord(X3) ),
inference(cnf_transformation,[],[f3876]) ).
fof(f10992,plain,
spl47_654,
inference(avatar_split_clause,[],[f5371,f10990]) ).
fof(f10990,plain,
( spl47_654
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
| ~ class_Orderings_Oord(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_654])]) ).
fof(f5371,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X3),X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X2,X3),X1,X0)
| ~ class_Orderings_Oord(X3) ),
inference(cnf_transformation,[],[f3876]) ).
fof(f10988,plain,
spl47_653,
inference(avatar_split_clause,[],[f5314,f10986]) ).
fof(f10986,plain,
( spl47_653
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| c_Polynomial_Omonom(X3,X2,X1) != c_Polynomial_Omonom(X3,X0,X1)
| ~ class_Groups_Ozero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_653])]) ).
fof(f5314,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| c_Polynomial_Omonom(X3,X2,X1) != c_Polynomial_Omonom(X3,X0,X1)
| ~ class_Groups_Ozero(X3) ),
inference(cnf_transformation,[],[f3870]) ).
fof(f3870,plain,
! [X0,X1,X2,X3] :
( ( ( c_Polynomial_Omonom(X3,X2,X1) = c_Polynomial_Omonom(X3,X0,X1)
| X0 != X2 )
& ( X0 = X2
| c_Polynomial_Omonom(X3,X2,X1) != c_Polynomial_Omonom(X3,X0,X1) ) )
| ~ class_Groups_Ozero(X3) ),
inference(nnf_transformation,[],[f3259]) ).
fof(f3259,plain,
! [X0,X1,X2,X3] :
( ( c_Polynomial_Omonom(X3,X2,X1) = c_Polynomial_Omonom(X3,X0,X1)
<=> X0 = X2 )
| ~ class_Groups_Ozero(X3) ),
inference(ennf_transformation,[],[f2111]) ).
fof(f2111,plain,
! [X0,X1,X2,X3] :
( class_Groups_Ozero(X3)
=> ( c_Polynomial_Omonom(X3,X2,X1) = c_Polynomial_Omonom(X3,X0,X1)
<=> X0 = X2 ) ),
inference(rectify,[],[f146]) ).
fof(f146,axiom,
! [X29,X11,X12,X5] :
( class_Groups_Ozero(X5)
=> ( c_Polynomial_Omonom(X5,X12,X11) = c_Polynomial_Omonom(X5,X29,X11)
<=> X12 = X29 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__iff) ).
fof(f10984,plain,
spl47_652,
inference(avatar_split_clause,[],[f5298,f10982]) ).
fof(f10982,plain,
( spl47_652
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X0,X1)
| ~ class_Groups_Ocancel__semigroup__add(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_652])]) ).
fof(f5298,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X0,X1)
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
inference(cnf_transformation,[],[f3242]) ).
fof(f3242,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X0,X1)
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
inference(flattening,[],[f3241]) ).
fof(f3241,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X0,X1)
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
inference(ennf_transformation,[],[f2098]) ).
fof(f2098,plain,
! [X0,X1,X2,X3] :
( class_Groups_Ocancel__semigroup__add(X3)
=> ( c_Groups_Oplus__class_Oplus(X3,X2,X1) = c_Groups_Oplus__class_Oplus(X3,X0,X1)
=> X0 = X2 ) ),
inference(rectify,[],[f352]) ).
fof(f352,axiom,
! [X16,X4,X17,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,X17,X4) = c_Groups_Oplus__class_Oplus(X5,X16,X4)
=> X16 = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
fof(f10980,plain,
( ~ spl47_651
| ~ spl47_251
| ~ spl47_320 ),
inference(avatar_split_clause,[],[f7682,f7510,f7193,f10977]) ).
fof(f10977,plain,
( spl47_651
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_651])]) ).
fof(f7682,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl47_251
| ~ spl47_320 ),
inference(superposition,[],[f7194,f7512]) ).
fof(f10975,plain,
spl47_650,
inference(avatar_split_clause,[],[f5297,f10973]) ).
fof(f10973,plain,
( spl47_650
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X2,X0)
| ~ class_Groups_Ocancel__semigroup__add(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_650])]) ).
fof(f5297,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X2,X0)
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
inference(cnf_transformation,[],[f3240]) ).
fof(f3240,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X2,X0)
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
inference(flattening,[],[f3239]) ).
fof(f3239,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X2,X0)
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
inference(ennf_transformation,[],[f2097]) ).
fof(f2097,plain,
! [X0,X1,X2,X3] :
( class_Groups_Ocancel__semigroup__add(X3)
=> ( c_Groups_Oplus__class_Oplus(X3,X2,X1) = c_Groups_Oplus__class_Oplus(X3,X2,X0)
=> X0 = X1 ) ),
inference(rectify,[],[f350]) ).
fof(f350,axiom,
! [X16,X17,X4,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,X4,X16) = c_Groups_Oplus__class_Oplus(X5,X4,X17)
=> X16 = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
fof(f10971,plain,
spl47_649,
inference(avatar_split_clause,[],[f5294,f10969]) ).
fof(f10969,plain,
( spl47_649
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X2,X0)
| ~ class_Groups_Ocancel__ab__semigroup__add(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_649])]) ).
fof(f5294,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X2,X0)
| ~ class_Groups_Ocancel__ab__semigroup__add(X3) ),
inference(cnf_transformation,[],[f3235]) ).
fof(f3235,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X2,X0)
| ~ class_Groups_Ocancel__ab__semigroup__add(X3) ),
inference(flattening,[],[f3234]) ).
fof(f3234,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| c_Groups_Oplus__class_Oplus(X3,X2,X1) != c_Groups_Oplus__class_Oplus(X3,X2,X0)
| ~ class_Groups_Ocancel__ab__semigroup__add(X3) ),
inference(ennf_transformation,[],[f2094]) ).
fof(f2094,plain,
! [X0,X1,X2,X3] :
( class_Groups_Ocancel__ab__semigroup__add(X3)
=> ( c_Groups_Oplus__class_Oplus(X3,X2,X1) = c_Groups_Oplus__class_Oplus(X3,X2,X0)
=> X0 = X1 ) ),
inference(rectify,[],[f351]) ).
fof(f351,axiom,
! [X16,X17,X4,X5] :
( class_Groups_Ocancel__ab__semigroup__add(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,X4,X16) = c_Groups_Oplus__class_Oplus(X5,X4,X17)
=> X16 = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).
fof(f10967,plain,
spl47_648,
inference(avatar_split_clause,[],[f5222,f10965]) ).
fof(f10965,plain,
( spl47_648
<=> ! [X0,X3,X2,X1] :
( sP22(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_648])]) ).
fof(f5222,plain,
! [X2,X3,X0,X1] :
( sP22(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2)) ),
inference(cnf_transformation,[],[f3856]) ).
fof(f10963,plain,
spl47_647,
inference(avatar_split_clause,[],[f5221,f10961]) ).
fof(f10961,plain,
( spl47_647
<=> ! [X0,X3,X2,X1] :
( sP22(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_647])]) ).
fof(f5221,plain,
! [X2,X3,X0,X1] :
( sP22(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) ),
inference(cnf_transformation,[],[f3856]) ).
fof(f10959,plain,
spl47_646,
inference(avatar_split_clause,[],[f5219,f10957]) ).
fof(f10957,plain,
( spl47_646
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ sP22(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_646])]) ).
fof(f5219,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ sP22(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3856]) ).
fof(f10955,plain,
spl47_645,
inference(avatar_split_clause,[],[f5218,f10953]) ).
fof(f10953,plain,
( spl47_645
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ sP22(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_645])]) ).
fof(f5218,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ sP22(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3856]) ).
fof(f10951,plain,
spl47_644,
inference(avatar_split_clause,[],[f5213,f10949]) ).
fof(f10949,plain,
( spl47_644
<=> ! [X0,X3,X2,X1] :
( sP20(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_644])]) ).
fof(f5213,plain,
! [X2,X3,X0,X1] :
( sP20(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2)) ),
inference(cnf_transformation,[],[f3851]) ).
fof(f10947,plain,
spl47_643,
inference(avatar_split_clause,[],[f5212,f10945]) ).
fof(f10945,plain,
( spl47_643
<=> ! [X0,X3,X2,X1] :
( sP20(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_643])]) ).
fof(f5212,plain,
! [X2,X3,X0,X1] :
( sP20(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) ),
inference(cnf_transformation,[],[f3851]) ).
fof(f10943,plain,
spl47_642,
inference(avatar_split_clause,[],[f5210,f10941]) ).
fof(f10941,plain,
( spl47_642
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ sP20(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_642])]) ).
fof(f5210,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ sP20(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3851]) ).
fof(f10939,plain,
spl47_641,
inference(avatar_split_clause,[],[f5209,f10937]) ).
fof(f10937,plain,
( spl47_641
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ sP20(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_641])]) ).
fof(f5209,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ sP20(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3851]) ).
fof(f10935,plain,
( spl47_640
| ~ spl47_127
| ~ spl47_316 ),
inference(avatar_split_clause,[],[f7668,f7494,f6666,f10933]) ).
fof(f10933,plain,
( spl47_640
<=> ! [X0] : c_Polynomial_Osmult(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_640])]) ).
fof(f7668,plain,
( ! [X0] : c_Polynomial_Osmult(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) = X0
| ~ spl47_127
| ~ spl47_316 ),
inference(resolution,[],[f7495,f6668]) ).
fof(f10931,plain,
spl47_639,
inference(avatar_split_clause,[],[f5089,f10929]) ).
fof(f10929,plain,
( spl47_639
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_639])]) ).
fof(f5089,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3800]) ).
fof(f3800,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ) ),
inference(nnf_transformation,[],[f1947]) ).
fof(f1947,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f325]) ).
fof(f325,axiom,
! [X11,X14,X44] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X44,X14),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X44,X11))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(f10927,plain,
spl47_638,
inference(avatar_split_clause,[],[f5088,f10925]) ).
fof(f10925,plain,
( spl47_638
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_638])]) ).
fof(f5088,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
inference(cnf_transformation,[],[f3800]) ).
fof(f10923,plain,
spl47_637,
inference(avatar_split_clause,[],[f5087,f10921]) ).
fof(f10921,plain,
( spl47_637
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_637])]) ).
fof(f5087,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3799]) ).
fof(f3799,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ) ),
inference(nnf_transformation,[],[f1946]) ).
fof(f1946,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f336]) ).
fof(f336,axiom,
! [X11,X14,X44] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X44,X14),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X44,X11))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(f10919,plain,
spl47_636,
inference(avatar_split_clause,[],[f5086,f10917]) ).
fof(f10917,plain,
( spl47_636
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_636])]) ).
fof(f5086,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
inference(cnf_transformation,[],[f3799]) ).
fof(f10915,plain,
spl47_635,
inference(avatar_split_clause,[],[f5081,f10913]) ).
fof(f10913,plain,
( spl47_635
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_635])]) ).
fof(f5081,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1) ),
inference(cnf_transformation,[],[f3796]) ).
fof(f3796,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ) ),
inference(nnf_transformation,[],[f1943]) ).
fof(f1943,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1) ),
inference(rectify,[],[f823]) ).
fof(f823,axiom,
! [X44,X81,X80] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X80,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X81,X44))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X80,X44),X81) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__conv) ).
fof(f10911,plain,
spl47_634,
inference(avatar_split_clause,[],[f5080,f10909]) ).
fof(f10909,plain,
( spl47_634
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_634])]) ).
fof(f5080,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ),
inference(cnf_transformation,[],[f3796]) ).
fof(f10907,plain,
spl47_633,
inference(avatar_split_clause,[],[f5079,f10905]) ).
fof(f10905,plain,
( spl47_633
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_633])]) ).
fof(f5079,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(cnf_transformation,[],[f3795]) ).
fof(f3795,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) ) ),
inference(nnf_transformation,[],[f1942]) ).
fof(f1942,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(rectify,[],[f808]) ).
fof(f808,axiom,
! [X80,X44,X81] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X81,X44),X80)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X81,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X80,X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv) ).
fof(f10903,plain,
spl47_632,
inference(avatar_split_clause,[],[f5078,f10901]) ).
fof(f10901,plain,
( spl47_632
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_632])]) ).
fof(f5078,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) ),
inference(cnf_transformation,[],[f3795]) ).
fof(f10899,plain,
spl47_631,
inference(avatar_split_clause,[],[f5040,f10897]) ).
fof(f10897,plain,
( spl47_631
<=> ! [X2,X0,X1] :
( X0 = X1
| c_Polynomial_Opoly(X2,X1) != c_Polynomial_Opoly(X2,X0)
| ~ class_Rings_Oidom(X2)
| ~ class_Int_Oring__char__0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_631])]) ).
fof(f5040,plain,
! [X2,X0,X1] :
( X0 = X1
| c_Polynomial_Opoly(X2,X1) != c_Polynomial_Opoly(X2,X0)
| ~ class_Rings_Oidom(X2)
| ~ class_Int_Oring__char__0(X2) ),
inference(cnf_transformation,[],[f3771]) ).
fof(f3771,plain,
! [X0,X1,X2] :
( ( ( c_Polynomial_Opoly(X2,X1) = c_Polynomial_Opoly(X2,X0)
| X0 != X1 )
& ( X0 = X1
| c_Polynomial_Opoly(X2,X1) != c_Polynomial_Opoly(X2,X0) ) )
| ~ class_Rings_Oidom(X2)
| ~ class_Int_Oring__char__0(X2) ),
inference(nnf_transformation,[],[f3036]) ).
fof(f3036,plain,
! [X0,X1,X2] :
( ( c_Polynomial_Opoly(X2,X1) = c_Polynomial_Opoly(X2,X0)
<=> X0 = X1 )
| ~ class_Rings_Oidom(X2)
| ~ class_Int_Oring__char__0(X2) ),
inference(flattening,[],[f3035]) ).
fof(f3035,plain,
! [X0,X1,X2] :
( ( c_Polynomial_Opoly(X2,X1) = c_Polynomial_Opoly(X2,X0)
<=> X0 = X1 )
| ~ class_Rings_Oidom(X2)
| ~ class_Int_Oring__char__0(X2) ),
inference(ennf_transformation,[],[f1932]) ).
fof(f1932,plain,
! [X0,X1,X2] :
( ( class_Rings_Oidom(X2)
& class_Int_Oring__char__0(X2) )
=> ( c_Polynomial_Opoly(X2,X1) = c_Polynomial_Opoly(X2,X0)
<=> X0 = X1 ) ),
inference(rectify,[],[f25]) ).
fof(f25,axiom,
! [X18,X9,X5] :
( ( class_Rings_Oidom(X5)
& class_Int_Oring__char__0(X5) )
=> ( c_Polynomial_Opoly(X5,X9) = c_Polynomial_Opoly(X5,X18)
<=> X9 = X18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__iff) ).
fof(f10895,plain,
spl47_630,
inference(avatar_split_clause,[],[f5001,f10893]) ).
fof(f10893,plain,
( spl47_630
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_630])]) ).
fof(f5001,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2980]) ).
fof(f2980,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1900]) ).
fof(f1900,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(rectify,[],[f322]) ).
fof(f322,axiom,
! [X20,X33,X32] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32,X33)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X20),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).
fof(f10891,plain,
( spl47_629
| ~ spl47_128
| ~ spl47_316 ),
inference(avatar_split_clause,[],[f7667,f7494,f6671,f10889]) ).
fof(f10889,plain,
( spl47_629
<=> ! [X0] : c_Polynomial_Osmult(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_629])]) ).
fof(f7667,plain,
( ! [X0] : c_Polynomial_Osmult(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) = X0
| ~ spl47_128
| ~ spl47_316 ),
inference(resolution,[],[f7495,f6673]) ).
fof(f10887,plain,
spl47_628,
inference(avatar_split_clause,[],[f4994,f10885]) ).
fof(f10885,plain,
( spl47_628
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_628])]) ).
fof(f4994,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
inference(cnf_transformation,[],[f2972]) ).
fof(f2972,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
inference(ennf_transformation,[],[f1893]) ).
fof(f1893,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) ),
inference(rectify,[],[f487]) ).
fof(f487,axiom,
! [X20,X33,X32] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X32,X33)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X32,X20),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X33,X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
fof(f10883,plain,
spl47_627,
inference(avatar_split_clause,[],[f4972,f10881]) ).
fof(f10881,plain,
( spl47_627
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_627])]) ).
fof(f4972,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2950]) ).
fof(f2950,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1876]) ).
fof(f1876,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(rectify,[],[f333]) ).
fof(f333,axiom,
! [X20,X33,X32] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32,X33)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X20),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).
fof(f10879,plain,
spl47_626,
inference(avatar_split_clause,[],[f4971,f10877]) ).
fof(f10877,plain,
( spl47_626
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_626])]) ).
fof(f4971,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2949]) ).
fof(f2949,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1875]) ).
fof(f1875,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ),
inference(rectify,[],[f787]) ).
fof(f787,axiom,
! [X43,X7,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X43),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono) ).
fof(f10875,plain,
spl47_625,
inference(avatar_split_clause,[],[f4970,f10873]) ).
fof(f10873,plain,
( spl47_625
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_625])]) ).
fof(f4970,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2948]) ).
fof(f2948,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1874]) ).
fof(f1874,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) ),
inference(rectify,[],[f788]) ).
fof(f788,axiom,
! [X43,X7,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X43,X7),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X43,X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
fof(f10871,plain,
spl47_624,
inference(avatar_split_clause,[],[f4969,f10869]) ).
fof(f10869,plain,
( spl47_624
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_624])]) ).
fof(f4969,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2947]) ).
fof(f2947,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1873]) ).
fof(f1873,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2)) ),
inference(rectify,[],[f809]) ).
fof(f809,axiom,
! [X21,X7,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X21),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff) ).
fof(f10867,plain,
spl47_623,
inference(avatar_split_clause,[],[f4963,f10865]) ).
fof(f10865,plain,
( spl47_623
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_623])]) ).
fof(f4963,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(cnf_transformation,[],[f2940]) ).
fof(f2940,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(ennf_transformation,[],[f1867]) ).
fof(f1867,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) ),
inference(rectify,[],[f473]) ).
fof(f473,axiom,
! [X20,X33,X32] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X32,X33)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X20,X32),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X20,X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__mono) ).
fof(f10863,plain,
spl47_622,
inference(avatar_split_clause,[],[f4931,f10861]) ).
fof(f10861,plain,
( spl47_622
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_622])]) ).
fof(f4931,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ),
inference(cnf_transformation,[],[f3748]) ).
fof(f3748,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
| ~ class_Orderings_Opreorder(X2) ),
inference(flattening,[],[f3747]) ).
fof(f3747,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
| ~ class_Orderings_Opreorder(X2) ),
inference(nnf_transformation,[],[f2905]) ).
fof(f2905,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) )
| ~ class_Orderings_Opreorder(X2) ),
inference(ennf_transformation,[],[f1846]) ).
fof(f1846,plain,
! [X0,X1,X2] :
( class_Orderings_Opreorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X0)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ) ),
inference(rectify,[],[f199]) ).
fof(f199,axiom,
! [X25,X15,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X15,X25)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(X5,X25,X15)
& c_Orderings_Oord__class_Oless__eq(X5,X15,X25) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(f10859,plain,
spl47_621,
inference(avatar_split_clause,[],[f4911,f10857]) ).
fof(f10857,plain,
( spl47_621
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)))
| ~ class_Rings_Ocomm__semiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_621])]) ).
fof(f4911,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(cnf_transformation,[],[f2881]) ).
fof(f2881,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f1829]) ).
fof(f1829,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1))) ),
inference(rectify,[],[f526]) ).
fof(f526,axiom,
! [X17,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X17),X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__right) ).
fof(f10855,plain,
spl47_620,
inference(avatar_split_clause,[],[f4910,f10853]) ).
fof(f10853,plain,
( spl47_620
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)))
| ~ class_Rings_Ocomm__semiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_620])]) ).
fof(f4910,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(cnf_transformation,[],[f2880]) ).
fof(f2880,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f1828]) ).
fof(f1828,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))) ),
inference(rectify,[],[f525]) ).
fof(f525,axiom,
! [X17,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__left) ).
fof(f10851,plain,
spl47_619,
inference(avatar_split_clause,[],[f4894,f10849]) ).
fof(f10849,plain,
( spl47_619
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X1
| c_Polynomial_OpCons(X2,X1,X0) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Groups_Ozero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_619])]) ).
fof(f4894,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X1
| c_Polynomial_OpCons(X2,X1,X0) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f3744]) ).
fof(f10847,plain,
( spl47_618
| ~ spl47_126
| ~ spl47_316 ),
inference(avatar_split_clause,[],[f7665,f7494,f6661,f10845]) ).
fof(f10845,plain,
( spl47_618
<=> ! [X0] : c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_618])]) ).
fof(f7665,plain,
( ! [X0] : c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0) = X0
| ~ spl47_126
| ~ spl47_316 ),
inference(resolution,[],[f7495,f6663]) ).
fof(f10843,plain,
spl47_617,
inference(avatar_split_clause,[],[f4892,f10841]) ).
fof(f10841,plain,
( spl47_617
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_Omonom(X2,X1,X0)
| ~ class_Groups_Ozero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_617])]) ).
fof(f4892,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_Omonom(X2,X1,X0)
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f3742]) ).
fof(f3742,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Omonom(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(X2) != X1 )
& ( c_Groups_Ozero__class_Ozero(X2) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_Omonom(X2,X1,X0) ) )
| ~ class_Groups_Ozero(X2) ),
inference(nnf_transformation,[],[f2867]) ).
fof(f2867,plain,
! [X0,X1,X2] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Omonom(X2,X1,X0)
<=> c_Groups_Ozero__class_Ozero(X2) = X1 )
| ~ class_Groups_Ozero(X2) ),
inference(ennf_transformation,[],[f1815]) ).
fof(f1815,plain,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Omonom(X2,X1,X0)
<=> c_Groups_Ozero__class_Ozero(X2) = X1 ) ),
inference(rectify,[],[f276]) ).
fof(f276,axiom,
! [X11,X12,X5] :
( class_Groups_Ozero(X5)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_Omonom(X5,X12,X11)
<=> c_Groups_Ozero__class_Ozero(X5) = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__0__iff) ).
fof(f10839,plain,
spl47_616,
inference(avatar_split_clause,[],[f4883,f10837]) ).
fof(f10837,plain,
( spl47_616
<=> ! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Groups_Ozero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_616])]) ).
fof(f4883,plain,
! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f2856]) ).
fof(f2856,plain,
! [X0,X1,X2] :
( c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Groups_Ozero(X2) ),
inference(flattening,[],[f2855]) ).
fof(f2855,plain,
! [X0,X1,X2] :
( c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Groups_Ozero(X2) ),
inference(ennf_transformation,[],[f1808]) ).
fof(f1808,plain,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( c_Groups_Ozero__class_Ozero(X2) != X1
=> c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)) = X0 ) ),
inference(rectify,[],[f277]) ).
fof(f277,axiom,
! [X7,X4,X5] :
( class_Groups_Ozero(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X4
=> c_Polynomial_Odegree(X5,c_Polynomial_Omonom(X5,X4,X7)) = X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__monom__eq) ).
fof(f10835,plain,
spl47_615,
inference(avatar_split_clause,[],[f4821,f10833]) ).
fof(f10833,plain,
( spl47_615
<=> ! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| ~ class_Groups_Ogroup__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_615])]) ).
fof(f4821,plain,
! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| ~ class_Groups_Ogroup__add(X2) ),
inference(cnf_transformation,[],[f3721]) ).
fof(f3721,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0) )
& ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0)
| c_Groups_Ouminus__class_Ouminus(X2,X0) != X1 ) )
| ~ class_Groups_Ogroup__add(X2) ),
inference(nnf_transformation,[],[f2794]) ).
fof(f2794,plain,
! [X0,X1,X2] :
( ( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
<=> c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0) )
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f1763]) ).
fof(f1763,plain,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> ( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
<=> c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0) ) ),
inference(rectify,[],[f436]) ).
fof(f436,axiom,
! [X29,X12,X5] :
( class_Groups_Ogroup__add(X5)
=> ( c_Groups_Ouminus__class_Ouminus(X5,X29) = X12
<=> c_Groups_Ozero__class_Ozero(X5) = c_Groups_Oplus__class_Oplus(X5,X12,X29) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).
fof(f10831,plain,
spl47_614,
inference(avatar_split_clause,[],[f4813,f10829]) ).
fof(f10829,plain,
( spl47_614
<=> ! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,X1) = X0
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| ~ class_Groups_Ogroup__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_614])]) ).
fof(f4813,plain,
! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,X1) = X0
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| ~ class_Groups_Ogroup__add(X2) ),
inference(cnf_transformation,[],[f2787]) ).
fof(f2787,plain,
! [X0,X1,X2] :
( c_Groups_Ouminus__class_Ouminus(X2,X1) = X0
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| ~ class_Groups_Ogroup__add(X2) ),
inference(flattening,[],[f2786]) ).
fof(f2786,plain,
! [X0,X1,X2] :
( c_Groups_Ouminus__class_Ouminus(X2,X1) = X0
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f1758]) ).
fof(f1758,plain,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0)
=> c_Groups_Ouminus__class_Ouminus(X2,X1) = X0 ) ),
inference(rectify,[],[f440]) ).
fof(f440,axiom,
! [X17,X4,X5] :
( class_Groups_Ogroup__add(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) = c_Groups_Oplus__class_Oplus(X5,X4,X17)
=> c_Groups_Ouminus__class_Ouminus(X5,X4) = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__unique) ).
fof(f10827,plain,
spl47_613,
inference(avatar_split_clause,[],[f4738,f10825]) ).
fof(f10825,plain,
( spl47_613
<=> ! [X2,X0,X1] :
( c_Divides_Odiv__class_Omod(X2,X1,X0) = c_Divides_Odiv__class_Omod(X2,c_Divides_Odiv__class_Omod(X2,X1,X0),X0)
| ~ class_Divides_Osemiring__div(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_613])]) ).
fof(f4738,plain,
! [X2,X0,X1] :
( c_Divides_Odiv__class_Omod(X2,X1,X0) = c_Divides_Odiv__class_Omod(X2,c_Divides_Odiv__class_Omod(X2,X1,X0),X0)
| ~ class_Divides_Osemiring__div(X2) ),
inference(cnf_transformation,[],[f2695]) ).
fof(f2695,plain,
! [X0,X1,X2] :
( c_Divides_Odiv__class_Omod(X2,X1,X0) = c_Divides_Odiv__class_Omod(X2,c_Divides_Odiv__class_Omod(X2,X1,X0),X0)
| ~ class_Divides_Osemiring__div(X2) ),
inference(ennf_transformation,[],[f1699]) ).
fof(f1699,plain,
! [X0,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,X1,X0) = c_Divides_Odiv__class_Omod(X2,c_Divides_Odiv__class_Omod(X2,X1,X0),X0) ),
inference(rectify,[],[f994]) ).
fof(f994,axiom,
! [X17,X4,X5] :
( class_Divides_Osemiring__div(X5)
=> c_Divides_Odiv__class_Omod(X5,X4,X17) = c_Divides_Odiv__class_Omod(X5,c_Divides_Odiv__class_Omod(X5,X4,X17),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mod__trivial) ).
fof(f10823,plain,
spl47_612,
inference(avatar_split_clause,[],[f4722,f10821]) ).
fof(f10821,plain,
( spl47_612
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X2),X1,X0)
| ~ c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
| ~ class_Rings_Olinordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_612])]) ).
fof(f4722,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X2),X1,X0)
| ~ c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(cnf_transformation,[],[f3700]) ).
fof(f3700,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X2),X1,X0)
| ~ c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1)) )
& ( c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X2),X1,X0) ) )
| ~ class_Rings_Olinordered__idom(X2) ),
inference(nnf_transformation,[],[f2679]) ).
fof(f2679,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X2),X1,X0)
<=> c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1)) )
| ~ class_Rings_Olinordered__idom(X2) ),
inference(ennf_transformation,[],[f1689]) ).
fof(f1689,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X2),X1,X0)
<=> c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1)) ) ),
inference(rectify,[],[f887]) ).
fof(f887,axiom,
! [X25,X15,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X5),X15,X25)
<=> c_Polynomial_Opos__poly(X5,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5),X25,X15)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__poly__def) ).
fof(f10819,plain,
spl47_611,
inference(avatar_split_clause,[],[f4721,f10817]) ).
fof(f10817,plain,
( spl47_611
<=> ! [X2,X0,X1] :
( c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X2),X1,X0)
| ~ class_Rings_Olinordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_611])]) ).
fof(f4721,plain,
! [X2,X0,X1] :
( c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X2),X1,X0)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(cnf_transformation,[],[f3700]) ).
fof(f10815,plain,
spl47_610,
inference(avatar_split_clause,[],[f4720,f10813]) ).
fof(f10813,plain,
( spl47_610
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0)
| ~ c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
| ~ class_Rings_Olinordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_610])]) ).
fof(f4720,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0)
| ~ c_Polynomial_Opos__poly(X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2),X0,X1))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(cnf_transformation,[],[f3699]) ).
fof(f10811,plain,
spl47_609,
inference(avatar_split_clause,[],[f4712,f10809]) ).
fof(f10809,plain,
( spl47_609
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ class_Groups_Oordered__ab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_609])]) ).
fof(f4712,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(cnf_transformation,[],[f3697]) ).
fof(f3697,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1) )
& ( c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(nnf_transformation,[],[f2667]) ).
fof(f2667,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless(X2,X0,X1) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(ennf_transformation,[],[f1682]) ).
fof(f1682,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless(X2,X0,X1) ) ),
inference(rectify,[],[f417]) ).
fof(f417,axiom,
! [X12,X29,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ouminus__class_Ouminus(X5,X29),c_Groups_Ouminus__class_Ouminus(X5,X12))
<=> c_Orderings_Oord__class_Oless(X5,X12,X29) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).
fof(f10807,plain,
spl47_608,
inference(avatar_split_clause,[],[f4711,f10805]) ).
fof(f10805,plain,
( spl47_608
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Oordered__ab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_608])]) ).
fof(f4711,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(cnf_transformation,[],[f3697]) ).
fof(f10800,plain,
spl47_607,
inference(avatar_split_clause,[],[f4709,f10798]) ).
fof(f10798,plain,
( spl47_607
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Oordered__ab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_607])]) ).
fof(f4709,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(cnf_transformation,[],[f3696]) ).
fof(f3696,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1) )
& ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(nnf_transformation,[],[f2666]) ).
fof(f2666,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(X2,X0,X1) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(ennf_transformation,[],[f1681]) ).
fof(f1681,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(X2,X0,X1) ) ),
inference(rectify,[],[f413]) ).
fof(f413,axiom,
! [X12,X29,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X29),c_Groups_Ouminus__class_Ouminus(X5,X12))
<=> c_Orderings_Oord__class_Oless__eq(X5,X12,X29) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).
fof(f10796,plain,
spl47_606,
inference(avatar_split_clause,[],[f4708,f10794]) ).
fof(f10794,plain,
( spl47_606
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1)
| ~ class_Groups_Oordered__ab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_606])]) ).
fof(f4708,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1)
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(cnf_transformation,[],[f3695]) ).
fof(f3695,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) )
& ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) ) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(nnf_transformation,[],[f2665]) ).
fof(f2665,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
<=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(ennf_transformation,[],[f1680]) ).
fof(f1680,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
<=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) ) ),
inference(rectify,[],[f416]) ).
fof(f416,axiom,
! [X29,X12,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ouminus__class_Ouminus(X5,X12),X29)
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ouminus__class_Ouminus(X5,X29),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__less__iff) ).
fof(f10792,plain,
spl47_605,
inference(avatar_split_clause,[],[f4706,f10790]) ).
fof(f10790,plain,
( spl47_605
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ class_Groups_Oordered__ab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_605])]) ).
fof(f4706,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(cnf_transformation,[],[f3694]) ).
fof(f3694,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) )
& ( c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(nnf_transformation,[],[f2664]) ).
fof(f2664,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(ennf_transformation,[],[f1679]) ).
fof(f1679,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) ) ),
inference(rectify,[],[f415]) ).
fof(f415,axiom,
! [X29,X12,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X12,c_Groups_Ouminus__class_Ouminus(X5,X29))
<=> c_Orderings_Oord__class_Oless(X5,X29,c_Groups_Ouminus__class_Ouminus(X5,X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__iff) ).
fof(f10788,plain,
spl47_604,
inference(avatar_split_clause,[],[f4704,f10786]) ).
fof(f10786,plain,
( spl47_604
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1)
| ~ class_Groups_Oordered__ab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_604])]) ).
fof(f4704,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1)
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(cnf_transformation,[],[f3693]) ).
fof(f3693,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) )
& ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) ) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(nnf_transformation,[],[f2663]) ).
fof(f2663,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
<=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(ennf_transformation,[],[f1678]) ).
fof(f1678,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
<=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) ) ),
inference(rectify,[],[f412]) ).
fof(f412,axiom,
! [X29,X12,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X12),X29)
<=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X29),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__iff) ).
fof(f10784,plain,
spl47_603,
inference(avatar_split_clause,[],[f4702,f10782]) ).
fof(f10782,plain,
( spl47_603
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ class_Groups_Oordered__ab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_603])]) ).
fof(f4702,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(cnf_transformation,[],[f3692]) ).
fof(f3692,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) )
& ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(nnf_transformation,[],[f2662]) ).
fof(f2662,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(ennf_transformation,[],[f1677]) ).
fof(f1677,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) ) ),
inference(rectify,[],[f411]) ).
fof(f411,axiom,
! [X29,X12,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,c_Groups_Ouminus__class_Ouminus(X5,X29))
<=> c_Orderings_Oord__class_Oless__eq(X5,X29,c_Groups_Ouminus__class_Ouminus(X5,X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__iff) ).
fof(f10780,plain,
spl47_602,
inference(avatar_split_clause,[],[f4700,f10778]) ).
fof(f10778,plain,
( spl47_602
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__ab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_602])]) ).
fof(f4700,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(cnf_transformation,[],[f3691]) ).
fof(f3691,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) )
& ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(nnf_transformation,[],[f2661]) ).
fof(f2661,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
<=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(ennf_transformation,[],[f1676]) ).
fof(f1676,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X0)
<=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ) ),
inference(rectify,[],[f768]) ).
fof(f768,axiom,
! [X29,X12,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X12,X29)
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ominus__class_Ominus(X5,X12,X29),c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).
fof(f10776,plain,
spl47_601,
inference(avatar_split_clause,[],[f4699,f10774]) ).
fof(f4699,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(cnf_transformation,[],[f3691]) ).
fof(f10772,plain,
spl47_600,
inference(avatar_split_clause,[],[f4698,f10770]) ).
fof(f10770,plain,
( spl47_600
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__ab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_600])]) ).
fof(f4698,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(cnf_transformation,[],[f3690]) ).
fof(f3690,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) )
& ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(nnf_transformation,[],[f2660]) ).
fof(f2660,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
<=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(ennf_transformation,[],[f1675]) ).
fof(f1675,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
<=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2)) ) ),
inference(rectify,[],[f767]) ).
fof(f767,axiom,
! [X29,X12,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,X29)
<=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ominus__class_Ominus(X5,X12,X29),c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).
fof(f10768,plain,
spl47_599,
inference(avatar_split_clause,[],[f4697,f10766]) ).
fof(f10766,plain,
( spl47_599
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Groups_Oordered__ab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_599])]) ).
fof(f4697,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(cnf_transformation,[],[f3690]) ).
fof(f10764,plain,
spl47_598,
inference(avatar_split_clause,[],[f4696,f10762]) ).
fof(f10762,plain,
( spl47_598
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Groups_Oordered__ab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_598])]) ).
fof(f4696,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(cnf_transformation,[],[f2659]) ).
fof(f2659,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(flattening,[],[f2658]) ).
fof(f2658,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(ennf_transformation,[],[f1674]) ).
fof(f1674,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1)) ) ),
inference(rectify,[],[f414]) ).
fof(f414,axiom,
! [X17,X4,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X17)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X17),c_Groups_Ouminus__class_Ouminus(X5,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).
fof(f10760,plain,
( spl47_597
| ~ spl47_81
| ~ spl47_313 ),
inference(avatar_split_clause,[],[f7649,f7482,f6436,f10758]) ).
fof(f10758,plain,
( spl47_597
<=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_597])]) ).
fof(f6436,plain,
( spl47_81
<=> class_Groups_Omonoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_81])]) ).
fof(f7482,plain,
( spl47_313
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0
| ~ class_Groups_Omonoid__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_313])]) ).
fof(f7649,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0) = X0
| ~ spl47_81
| ~ spl47_313 ),
inference(resolution,[],[f7483,f6438]) ).
fof(f6438,plain,
( class_Groups_Omonoid__add(tc_Complex_Ocomplex)
| ~ spl47_81 ),
inference(avatar_component_clause,[],[f6436]) ).
fof(f7483,plain,
( ! [X0,X1] :
( ~ class_Groups_Omonoid__add(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 )
| ~ spl47_313 ),
inference(avatar_component_clause,[],[f7482]) ).
fof(f10756,plain,
spl47_596,
inference(avatar_split_clause,[],[f4685,f10754]) ).
fof(f10754,plain,
( spl47_596
<=> ! [X2,X0,X1] :
( sP9(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_596])]) ).
fof(f4685,plain,
! [X2,X0,X1] :
( sP9(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(cnf_transformation,[],[f3683]) ).
fof(f3683,plain,
! [X0,X1,X2] :
( ( sP9(X0,X1,X2)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
& c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) )
| ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
& c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) )
| ~ sP9(X0,X1,X2) ) ),
inference(rectify,[],[f3682]) ).
fof(f3682,plain,
! [X0,X2,X1] :
( ( sP9(X0,X2,X1)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) )
| ~ sP9(X0,X2,X1) ) ),
inference(flattening,[],[f3681]) ).
fof(f3681,plain,
! [X0,X2,X1] :
( ( sP9(X0,X2,X1)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) )
| ~ sP9(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f3490]) ).
fof(f3490,plain,
! [X0,X2,X1] :
( sP9(X0,X2,X1)
<=> ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f10752,plain,
spl47_595,
inference(avatar_split_clause,[],[f4684,f10750]) ).
fof(f10750,plain,
( spl47_595
<=> ! [X2,X0,X1] :
( sP9(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_595])]) ).
fof(f4684,plain,
! [X2,X0,X1] :
( sP9(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(cnf_transformation,[],[f3683]) ).
fof(f10748,plain,
spl47_594,
inference(avatar_split_clause,[],[f4683,f10746]) ).
fof(f10746,plain,
( spl47_594
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_594])]) ).
fof(f4683,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f3683]) ).
fof(f10744,plain,
spl47_593,
inference(avatar_split_clause,[],[f4682,f10742]) ).
fof(f10742,plain,
( spl47_593
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_593])]) ).
fof(f4682,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f3683]) ).
fof(f10740,plain,
spl47_592,
inference(avatar_split_clause,[],[f4681,f10738]) ).
fof(f10738,plain,
( spl47_592
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_592])]) ).
fof(f4681,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f3683]) ).
fof(f10736,plain,
spl47_591,
inference(avatar_split_clause,[],[f4680,f10734]) ).
fof(f10734,plain,
( spl47_591
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_591])]) ).
fof(f4680,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f3683]) ).
fof(f10732,plain,
spl47_590,
inference(avatar_split_clause,[],[f4676,f10730]) ).
fof(f10730,plain,
( spl47_590
<=> ! [X2,X0,X1] :
( sP7(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_590])]) ).
fof(f4676,plain,
! [X2,X0,X1] :
( sP7(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3678]) ).
fof(f3678,plain,
! [X0,X1,X2] :
( ( sP7(X0,X1,X2)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
& c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0)) )
| ( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
& c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2) )
| ~ sP7(X0,X1,X2) ) ),
inference(rectify,[],[f3677]) ).
fof(f3677,plain,
! [X2,X0,X1] :
( ( sP7(X2,X0,X1)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) )
| ~ sP7(X2,X0,X1) ) ),
inference(flattening,[],[f3676]) ).
fof(f3676,plain,
! [X2,X0,X1] :
( ( sP7(X2,X0,X1)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) )
| ~ sP7(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f3487]) ).
fof(f3487,plain,
! [X2,X0,X1] :
( sP7(X2,X0,X1)
<=> ( ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f10728,plain,
spl47_589,
inference(avatar_split_clause,[],[f4675,f10726]) ).
fof(f10726,plain,
( spl47_589
<=> ! [X2,X0,X1] :
( sP7(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_589])]) ).
fof(f4675,plain,
! [X2,X0,X1] :
( sP7(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2) ),
inference(cnf_transformation,[],[f3678]) ).
fof(f10724,plain,
spl47_588,
inference(avatar_split_clause,[],[f4674,f10722]) ).
fof(f10722,plain,
( spl47_588
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_588])]) ).
fof(f4674,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f3678]) ).
fof(f10720,plain,
spl47_587,
inference(avatar_split_clause,[],[f4673,f10718]) ).
fof(f10718,plain,
( spl47_587
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_587])]) ).
fof(f4673,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f3678]) ).
fof(f10716,plain,
( spl47_586
| ~ spl47_81
| ~ spl47_312 ),
inference(avatar_split_clause,[],[f7645,f7478,f6436,f10714]) ).
fof(f10714,plain,
( spl47_586
<=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_586])]) ).
fof(f7478,plain,
( spl47_312
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Groups_Omonoid__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_312])]) ).
fof(f7645,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X0
| ~ spl47_81
| ~ spl47_312 ),
inference(resolution,[],[f7479,f6438]) ).
fof(f7479,plain,
( ! [X0,X1] :
( ~ class_Groups_Omonoid__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 )
| ~ spl47_312 ),
inference(avatar_component_clause,[],[f7478]) ).
fof(f10712,plain,
spl47_585,
inference(avatar_split_clause,[],[f4672,f10710]) ).
fof(f10710,plain,
( spl47_585
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_585])]) ).
fof(f4672,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f3678]) ).
fof(f10708,plain,
spl47_584,
inference(avatar_split_clause,[],[f4671,f10706]) ).
fof(f10706,plain,
( spl47_584
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_584])]) ).
fof(f4671,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f3678]) ).
fof(f10704,plain,
spl47_583,
inference(avatar_split_clause,[],[f4663,f10702]) ).
fof(f10702,plain,
( spl47_583
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Lattices_Oboolean__algebra(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_583])]) ).
fof(f4663,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(cnf_transformation,[],[f3673]) ).
fof(f3673,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1) )
& ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ) )
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(nnf_transformation,[],[f2646]) ).
fof(f2646,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(X2,X0,X1) )
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(ennf_transformation,[],[f1665]) ).
fof(f1665,plain,
! [X0,X1,X2] :
( class_Lattices_Oboolean__algebra(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(X2,X0,X1) ) ),
inference(rectify,[],[f466]) ).
fof(f466,axiom,
! [X25,X15,X5] :
( class_Lattices_Oboolean__algebra(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X15),c_Groups_Ouminus__class_Ouminus(X5,X25))
<=> c_Orderings_Oord__class_Oless__eq(X5,X25,X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__le__compl__iff) ).
fof(f10700,plain,
spl47_582,
inference(avatar_split_clause,[],[f4660,f10698]) ).
fof(f10698,plain,
( spl47_582
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Lattices_Oboolean__algebra(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_582])]) ).
fof(f4660,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(cnf_transformation,[],[f2644]) ).
fof(f2644,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(flattening,[],[f2643]) ).
fof(f2643,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(ennf_transformation,[],[f1663]) ).
fof(f1663,plain,
! [X0,X1,X2] :
( class_Lattices_Oboolean__algebra(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1)) ) ),
inference(rectify,[],[f465]) ).
fof(f465,axiom,
! [X10,X6,X5] :
( class_Lattices_Oboolean__algebra(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X6,X10)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X10),c_Groups_Ouminus__class_Ouminus(X5,X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__mono) ).
fof(f10696,plain,
spl47_581,
inference(avatar_split_clause,[],[f4496,f10694]) ).
fof(f10694,plain,
( spl47_581
<=> ! [X0,X1] :
( X0 = X1
| hAPP(X1,sK34(X0,X1)) != hAPP(X0,sK34(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_581])]) ).
fof(f4496,plain,
! [X0,X1] :
( X0 = X1
| hAPP(X1,sK34(X0,X1)) != hAPP(X0,sK34(X0,X1)) ),
inference(cnf_transformation,[],[f3588]) ).
fof(f3588,plain,
! [X0,X1] :
( X0 = X1
| hAPP(X1,sK34(X0,X1)) != hAPP(X0,sK34(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK34])],[f2623,f3587]) ).
fof(f3587,plain,
! [X0,X1] :
( ? [X2] : hAPP(X1,X2) != hAPP(X0,X2)
=> hAPP(X1,sK34(X0,X1)) != hAPP(X0,sK34(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f2623,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] : hAPP(X1,X2) != hAPP(X0,X2) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( ! [X2] : hAPP(X1,X2) = hAPP(X0,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
fof(f10692,plain,
spl47_580,
inference(avatar_split_clause,[],[f4399,f10690]) ).
fof(f10690,plain,
( spl47_580
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_580])]) ).
fof(f4399,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2502]) ).
fof(f2502,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(flattening,[],[f2501]) ).
fof(f2501,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1485]) ).
fof(f1485,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X0))
=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),c_Groups_Ozero__class_Ozero(X5)),X4))
=> c_Groups_Ozero__class_Ozero(X5) = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__left) ).
fof(f10688,plain,
spl47_579,
inference(avatar_split_clause,[],[f4365,f10686]) ).
fof(f10686,plain,
( spl47_579
<=> ! [X0,X1] :
( c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Polynomial_Omonom(X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Groups_Ozero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_579])]) ).
fof(f4365,plain,
! [X0,X1] :
( c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Polynomial_Omonom(X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Groups_Ozero(X1) ),
inference(cnf_transformation,[],[f2471]) ).
fof(f2471,plain,
! [X0,X1] :
( c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Polynomial_Omonom(X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Groups_Ozero(X1) ),
inference(ennf_transformation,[],[f1456]) ).
fof(f1456,plain,
! [X0,X1] :
( class_Groups_Ozero(X1)
=> c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Polynomial_Omonom(X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(rectify,[],[f129]) ).
fof(f129,axiom,
! [X4,X5] :
( class_Groups_Ozero(X5)
=> c_Polynomial_OpCons(X5,X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) = c_Polynomial_Omonom(X5,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__0) ).
fof(f10684,plain,
spl47_578,
inference(avatar_split_clause,[],[f4343,f10682]) ).
fof(f10682,plain,
( spl47_578
<=> ! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
| ~ class_Groups_Oab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_578])]) ).
fof(f4343,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
| ~ class_Groups_Oab__group__add(X1) ),
inference(cnf_transformation,[],[f2450]) ).
fof(f2450,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
| ~ class_Groups_Oab__group__add(X1) ),
inference(ennf_transformation,[],[f1435]) ).
fof(f1435,plain,
! [X0,X1] :
( class_Groups_Oab__group__add(X1)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) ),
inference(rectify,[],[f898]) ).
fof(f898,axiom,
! [X13,X5] :
( class_Groups_Oab__group__add(X5)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X13) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__poly__code_I1_J) ).
fof(f10680,plain,
spl47_577,
inference(avatar_split_clause,[],[f4314,f10678]) ).
fof(f10678,plain,
( spl47_577
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_577])]) ).
fof(f4314,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3565]) ).
fof(f3565,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
& ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1)) ) )
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f2427]) ).
fof(f2427,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f1413]) ).
fof(f1413,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
inference(rectify,[],[f433]) ).
fof(f433,axiom,
! [X12,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ouminus__class_Ouminus(X5,X12),c_Groups_Ozero__class_Ozero(X5))
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).
fof(f10676,plain,
spl47_576,
inference(avatar_split_clause,[],[f4313,f10674]) ).
fof(f10674,plain,
( spl47_576
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_576])]) ).
fof(f4313,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3565]) ).
fof(f10672,plain,
( spl47_575
| ~ spl47_58
| ~ spl47_311 ),
inference(avatar_split_clause,[],[f7643,f7474,f6321,f10670]) ).
fof(f10670,plain,
( spl47_575
<=> ! [X0] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_575])]) ).
fof(f6321,plain,
( spl47_58
<=> class_Groups_Ogroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_58])]) ).
fof(f7474,plain,
( spl47_311
<=> ! [X0,X1] :
( c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Groups_Ogroup__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_311])]) ).
fof(f7643,plain,
( ! [X0] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0
| ~ spl47_58
| ~ spl47_311 ),
inference(resolution,[],[f7475,f6323]) ).
fof(f6323,plain,
( class_Groups_Ogroup__add(tc_Int_Oint)
| ~ spl47_58 ),
inference(avatar_component_clause,[],[f6321]) ).
fof(f7475,plain,
( ! [X0,X1] :
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 )
| ~ spl47_311 ),
inference(avatar_component_clause,[],[f7474]) ).
fof(f10668,plain,
spl47_574,
inference(avatar_split_clause,[],[f4312,f10666]) ).
fof(f10666,plain,
( spl47_574
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_574])]) ).
fof(f4312,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3564]) ).
fof(f3564,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
& ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0)) ) )
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f2426]) ).
fof(f2426,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
<=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f1412]) ).
fof(f1412,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
<=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
inference(rectify,[],[f432]) ).
fof(f432,axiom,
! [X12,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Ouminus__class_Ouminus(X5,X12))
<=> c_Orderings_Oord__class_Oless(X5,X12,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).
fof(f10664,plain,
spl47_573,
inference(avatar_split_clause,[],[f4311,f10662]) ).
fof(f10662,plain,
( spl47_573
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_Groups_Oordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_573])]) ).
fof(f4311,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3564]) ).
fof(f10660,plain,
spl47_572,
inference(avatar_split_clause,[],[f4310,f10658]) ).
fof(f10658,plain,
( spl47_572
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_572])]) ).
fof(f4310,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3563]) ).
fof(f3563,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
& ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1)) ) )
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f2425]) ).
fof(f2425,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f1411]) ).
fof(f1411,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
inference(rectify,[],[f429]) ).
fof(f429,axiom,
! [X12,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X12),c_Groups_Ozero__class_Ozero(X5))
<=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).
fof(f10656,plain,
spl47_571,
inference(avatar_split_clause,[],[f4309,f10654]) ).
fof(f10654,plain,
( spl47_571
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_571])]) ).
fof(f4309,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3563]) ).
fof(f10652,plain,
spl47_570,
inference(avatar_split_clause,[],[f4308,f10650]) ).
fof(f10650,plain,
( spl47_570
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_570])]) ).
fof(f4308,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3562]) ).
fof(f3562,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
& ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0)) ) )
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f2424]) ).
fof(f2424,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
<=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f1410]) ).
fof(f1410,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
<=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
inference(rectify,[],[f427]) ).
fof(f427,axiom,
! [X12,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Ouminus__class_Ouminus(X5,X12))
<=> c_Orderings_Oord__class_Oless__eq(X5,X12,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).
fof(f10648,plain,
spl47_569,
inference(avatar_split_clause,[],[f4307,f10646]) ).
fof(f10646,plain,
( spl47_569
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_Groups_Oordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_569])]) ).
fof(f4307,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3562]) ).
fof(f10644,plain,
spl47_568,
inference(avatar_split_clause,[],[f4280,f10642]) ).
fof(f10642,plain,
( spl47_568
<=> ! [X0,X1] :
( c_Polynomial_Opdivmod__rel(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Fields_Ofield(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_568])]) ).
fof(f4280,plain,
! [X0,X1] :
( c_Polynomial_Opdivmod__rel(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Fields_Ofield(X1) ),
inference(cnf_transformation,[],[f2408]) ).
fof(f2408,plain,
! [X0,X1] :
( c_Polynomial_Opdivmod__rel(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Fields_Ofield(X1) ),
inference(ennf_transformation,[],[f1394]) ).
fof(f1394,plain,
! [X0,X1] :
( class_Fields_Ofield(X1)
=> c_Polynomial_Opdivmod__rel(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(rectify,[],[f734]) ).
fof(f734,axiom,
! [X10,X5] :
( class_Fields_Ofield(X5)
=> c_Polynomial_Opdivmod__rel(X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__0) ).
fof(f10640,plain,
spl47_567,
inference(avatar_split_clause,[],[f4134,f10638]) ).
fof(f10638,plain,
( spl47_567
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_567])]) ).
fof(f4134,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0))),
inference(cnf_transformation,[],[f1258]) ).
fof(f1258,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0))),
inference(rectify,[],[f663]) ).
fof(f663,axiom,
! [X21] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X21))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__cube) ).
fof(f10632,plain,
( spl47_566
| ~ spl47_55
| ~ spl47_311 ),
inference(avatar_split_clause,[],[f7642,f7474,f6306,f10630]) ).
fof(f10630,plain,
( spl47_566
<=> ! [X0] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_566])]) ).
fof(f6306,plain,
( spl47_55
<=> class_Groups_Ogroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_55])]) ).
fof(f7642,plain,
( ! [X0] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X0
| ~ spl47_55
| ~ spl47_311 ),
inference(resolution,[],[f7475,f6308]) ).
fof(f6308,plain,
( class_Groups_Ogroup__add(tc_Complex_Ocomplex)
| ~ spl47_55 ),
inference(avatar_component_clause,[],[f6306]) ).
fof(f10517,plain,
( spl47_565
| ~ spl47_55
| ~ spl47_310 ),
inference(avatar_split_clause,[],[f7639,f7470,f6306,f10515]) ).
fof(f10515,plain,
( spl47_565
<=> ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_565])]) ).
fof(f7470,plain,
( spl47_310
<=> ! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0
| ~ class_Groups_Ogroup__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_310])]) ).
fof(f7639,plain,
( ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = X0
| ~ spl47_55
| ~ spl47_310 ),
inference(resolution,[],[f7471,f6308]) ).
fof(f7471,plain,
( ! [X0,X1] :
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0 )
| ~ spl47_310 ),
inference(avatar_component_clause,[],[f7470]) ).
fof(f10383,plain,
( spl47_564
| ~ spl47_58
| ~ spl47_309 ),
inference(avatar_split_clause,[],[f7637,f7466,f6321,f10381]) ).
fof(f10381,plain,
( spl47_564
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_564])]) ).
fof(f7466,plain,
( spl47_309
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ominus__class_Ominus(X1,X0,X0)
| ~ class_Groups_Ogroup__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_309])]) ).
fof(f7637,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X0)
| ~ spl47_58
| ~ spl47_309 ),
inference(resolution,[],[f7467,f6323]) ).
fof(f7467,plain,
( ! [X0,X1] :
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ominus__class_Ominus(X1,X0,X0) )
| ~ spl47_309 ),
inference(avatar_component_clause,[],[f7466]) ).
fof(f10160,plain,
( spl47_563
| ~ spl47_55
| ~ spl47_309 ),
inference(avatar_split_clause,[],[f7636,f7466,f6306,f10158]) ).
fof(f10158,plain,
( spl47_563
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_563])]) ).
fof(f7636,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X0)
| ~ spl47_55
| ~ spl47_309 ),
inference(resolution,[],[f7467,f6308]) ).
fof(f10019,plain,
( spl47_562
| ~ spl47_42
| ~ spl47_308 ),
inference(avatar_split_clause,[],[f7634,f7461,f6241,f10017]) ).
fof(f10017,plain,
( spl47_562
<=> ! [X0] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_562])]) ).
fof(f7634,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| ~ spl47_42
| ~ spl47_308 ),
inference(resolution,[],[f7462,f6243]) ).
fof(f9979,plain,
spl47_561,
inference(avatar_split_clause,[],[f5869,f9977]) ).
fof(f9977,plain,
( spl47_561
<=> ! [X4,X0,X1,X3] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X3
| ~ sP25(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_561])]) ).
fof(f5869,plain,
! [X3,X0,X1,X4] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X3
| ~ sP25(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X3,X4) ),
inference(equality_resolution,[],[f5405]) ).
fof(f5405,plain,
! [X2,X3,X0,X1,X4] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X3
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X2
| ~ sP25(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f3884]) ).
fof(f9975,plain,
spl47_560,
inference(avatar_split_clause,[],[f5677,f9973]) ).
fof(f9973,plain,
( spl47_560
<=> ! [X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_560])]) ).
fof(f5677,plain,
! [X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(equality_resolution,[],[f4397]) ).
fof(f4397,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2500]) ).
fof(f9971,plain,
spl47_559,
inference(avatar_split_clause,[],[f5667,f9969]) ).
fof(f9969,plain,
( spl47_559
<=> ! [X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_559])]) ).
fof(f5667,plain,
! [X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(equality_resolution,[],[f4324]) ).
fof(f4324,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = c_Groups_Oone__class_Oone(X1)
| c_Groups_Oone__class_Oone(X1) != X0
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(cnf_transformation,[],[f3570]) ).
fof(f9967,plain,
spl47_558,
inference(avatar_split_clause,[],[f5525,f9965]) ).
fof(f9965,plain,
( spl47_558
<=> ! [X0] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK32(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_558])]) ).
fof(f5525,plain,
! [X0] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK32(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(definition_unfolding,[],[f4221,f4118]) ).
fof(f4221,plain,
! [X0] :
( c_Nat_OSuc(sK32(X0)) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(cnf_transformation,[],[f3546]) ).
fof(f3546,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ! [X1] : c_Nat_OSuc(X1) != X0 )
& ( c_Nat_OSuc(sK32(X0)) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f3544,f3545]) ).
fof(f3545,plain,
! [X0] :
( ? [X2] : c_Nat_OSuc(X2) = X0
=> c_Nat_OSuc(sK32(X0)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f3544,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ! [X1] : c_Nat_OSuc(X1) != X0 )
& ( ? [X2] : c_Nat_OSuc(X2) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
inference(rectify,[],[f3543]) ).
fof(f3543,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ! [X1] : c_Nat_OSuc(X1) != X0 )
& ( ? [X1] : c_Nat_OSuc(X1) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
inference(nnf_transformation,[],[f1342]) ).
fof(f1342,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
<=> ? [X1] : c_Nat_OSuc(X1) = X0 ),
inference(rectify,[],[f257]) ).
fof(f257,axiom,
! [X11] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X11)
<=> ? [X41] : c_Nat_OSuc(X41) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
fof(f9963,plain,
spl47_557,
inference(avatar_split_clause,[],[f5220,f9961]) ).
fof(f9961,plain,
( spl47_557
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ sP22(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_557])]) ).
fof(f5220,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ sP22(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3856]) ).
fof(f9959,plain,
spl47_556,
inference(avatar_split_clause,[],[f5211,f9957]) ).
fof(f9957,plain,
( spl47_556
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ sP20(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_556])]) ).
fof(f5211,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ sP20(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3851]) ).
fof(f9955,plain,
spl47_555,
inference(avatar_split_clause,[],[f5180,f9953]) ).
fof(f9953,plain,
( spl47_555
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| ~ c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0)
| ~ class_Fields_Ofield(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_555])]) ).
fof(f5180,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| ~ c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X0)
| ~ class_Fields_Ofield(X3) ),
inference(cnf_transformation,[],[f3835]) ).
fof(f9951,plain,
( spl47_554
| ~ spl47_41
| ~ spl47_308 ),
inference(avatar_split_clause,[],[f7633,f7461,f6236,f9949]) ).
fof(f9949,plain,
( spl47_554
<=> ! [X0] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_554])]) ).
fof(f7633,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0
| ~ spl47_41
| ~ spl47_308 ),
inference(resolution,[],[f7462,f6238]) ).
fof(f9947,plain,
spl47_553,
inference(avatar_split_clause,[],[f5070,f9945]) ).
fof(f9945,plain,
( spl47_553
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ sP13(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_553])]) ).
fof(f5070,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ sP13(X0,X1,X2) ),
inference(cnf_transformation,[],[f3793]) ).
fof(f9943,plain,
spl47_552,
inference(avatar_split_clause,[],[f5062,f9941]) ).
fof(f9941,plain,
( spl47_552
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ sP12(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_552])]) ).
fof(f5062,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f3787]) ).
fof(f9939,plain,
spl47_551,
inference(avatar_split_clause,[],[f4937,f9937]) ).
fof(f9937,plain,
( spl47_551
<=> ! [X2,X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_551])]) ).
fof(f4937,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f2917]) ).
fof(f2917,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f2916]) ).
fof(f2916,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f1852]) ).
fof(f1852,plain,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
=> X0 = X1 ) ) ),
inference(rectify,[],[f286]) ).
fof(f286,axiom,
! [X6,X10,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X10,X6)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X6,X10)
=> X6 = X10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
fof(f9935,plain,
spl47_550,
inference(avatar_split_clause,[],[f4932,f9933]) ).
fof(f9933,plain,
( spl47_550
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| X0 = X1
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_550])]) ).
fof(f4932,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| X0 = X1
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f2907]) ).
fof(f2907,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| X0 = X1
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f2906]) ).
fof(f2906,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| X0 = X1
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f1847]) ).
fof(f1847,plain,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( X0 != X1
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
=> c_Orderings_Oord__class_Oless(X2,X1,X0) ) ) ),
inference(rectify,[],[f194]) ).
fof(f194,axiom,
! [X17,X4,X5] :
( class_Orderings_Oorder(X5)
=> ( X4 != X17
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X17)
=> c_Orderings_Oord__class_Oless(X5,X4,X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
fof(f9931,plain,
spl47_549,
inference(avatar_split_clause,[],[f4898,f9929]) ).
fof(f9929,plain,
( spl47_549
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)),c_Polynomial_Odegree(X2,X0))
| ~ class_Rings_Ocomm__semiring__0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_549])]) ).
fof(f4898,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)),c_Polynomial_Odegree(X2,X0))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(cnf_transformation,[],[f2870]) ).
fof(f2870,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)),c_Polynomial_Odegree(X2,X0))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(ennf_transformation,[],[f1818]) ).
fof(f1818,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__0(X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0)),c_Polynomial_Odegree(X2,X0)) ),
inference(rectify,[],[f89]) ).
fof(f89,axiom,
! [X8,X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X5,c_Polynomial_Osmult(X5,X4,X8)),c_Polynomial_Odegree(X5,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__smult__le) ).
fof(f9927,plain,
spl47_548,
inference(avatar_split_clause,[],[f4878,f9925]) ).
fof(f9925,plain,
( spl47_548
<=> ! [X2,X0,X1] :
( hAPP(c_Polynomial_Ocoeff(X2,c_Polynomial_OpCons(X2,X1,X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ class_Groups_Ozero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_548])]) ).
fof(f4878,plain,
! [X2,X0,X1] :
( hAPP(c_Polynomial_Ocoeff(X2,c_Polynomial_OpCons(X2,X1,X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f2851]) ).
fof(f2851,plain,
! [X0,X1,X2] :
( hAPP(c_Polynomial_Ocoeff(X2,c_Polynomial_OpCons(X2,X1,X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ class_Groups_Ozero(X2) ),
inference(ennf_transformation,[],[f1804]) ).
fof(f1804,plain,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> hAPP(c_Polynomial_Ocoeff(X2,c_Polynomial_OpCons(X2,X1,X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ),
inference(rectify,[],[f804]) ).
fof(f804,axiom,
! [X8,X4,X5] :
( class_Groups_Ozero(X5)
=> hAPP(c_Polynomial_Ocoeff(X5,c_Polynomial_OpCons(X5,X4,X8)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__pCons__0) ).
fof(f9923,plain,
spl47_547,
inference(avatar_split_clause,[],[f4845,f9921]) ).
fof(f9921,plain,
( spl47_547
<=> ! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,X0,X1)
| ~ class_Groups_Oab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_547])]) ).
fof(f4845,plain,
! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,X0,X1)
| ~ class_Groups_Oab__group__add(X2) ),
inference(cnf_transformation,[],[f2805]) ).
fof(f2805,plain,
! [X0,X1,X2] :
( c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,X0,X1)
| ~ class_Groups_Oab__group__add(X2) ),
inference(ennf_transformation,[],[f1774]) ).
fof(f1774,plain,
! [X0,X1,X2] :
( class_Groups_Oab__group__add(X2)
=> c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,X0,X1) ),
inference(rectify,[],[f759]) ).
fof(f759,axiom,
! [X17,X4,X5] :
( class_Groups_Oab__group__add(X5)
=> c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Ominus__class_Ominus(X5,X4,X17)) = c_Groups_Ominus__class_Ominus(X5,X17,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__diff__eq) ).
fof(f9919,plain,
spl47_546,
inference(avatar_split_clause,[],[f4844,f9917]) ).
fof(f9917,plain,
( spl47_546
<=> ! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Oab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_546])]) ).
fof(f4844,plain,
! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Oab__group__add(X2) ),
inference(cnf_transformation,[],[f2804]) ).
fof(f2804,plain,
! [X0,X1,X2] :
( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Oab__group__add(X2) ),
inference(ennf_transformation,[],[f1773]) ).
fof(f1773,plain,
! [X0,X1,X2] :
( class_Groups_Oab__group__add(X2)
=> c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(rectify,[],[f834]) ).
fof(f834,axiom,
! [X17,X4,X5] :
( class_Groups_Oab__group__add(X5)
=> c_Groups_Ominus__class_Ominus(X5,X4,X17) = c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Ouminus__class_Ouminus(X5,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__diff__minus) ).
fof(f9915,plain,
spl47_545,
inference(avatar_split_clause,[],[f4803,f9913]) ).
fof(f9913,plain,
( spl47_545
<=> ! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = X0
| ~ class_Groups_Ogroup__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_545])]) ).
fof(f4803,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = X0
| ~ class_Groups_Ogroup__add(X2) ),
inference(cnf_transformation,[],[f2774]) ).
fof(f2774,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = X0
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f1750]) ).
fof(f1750,plain,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = X0 ),
inference(rectify,[],[f421]) ).
fof(f421,axiom,
! [X17,X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),c_Groups_Oplus__class_Oplus(X5,X4,X17)) = X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__cancel) ).
fof(f9911,plain,
spl47_544,
inference(avatar_split_clause,[],[f4802,f9909]) ).
fof(f9909,plain,
( spl47_544
<=> ! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)) = X0
| ~ class_Groups_Ogroup__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_544])]) ).
fof(f4802,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)) = X0
| ~ class_Groups_Ogroup__add(X2) ),
inference(cnf_transformation,[],[f2773]) ).
fof(f2773,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)) = X0
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f1749]) ).
fof(f1749,plain,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)) = X0 ),
inference(rectify,[],[f420]) ).
fof(f420,axiom,
! [X17,X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Oplus__class_Oplus(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),X17)) = X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__minus__cancel) ).
fof(f9907,plain,
( spl47_543
| ~ spl47_42
| ~ spl47_307 ),
inference(avatar_split_clause,[],[f7631,f7457,f6241,f9905]) ).
fof(f9905,plain,
( spl47_543
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_543])]) ).
fof(f7631,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X0)
| ~ spl47_42
| ~ spl47_307 ),
inference(resolution,[],[f7458,f6243]) ).
fof(f9903,plain,
spl47_542,
inference(avatar_split_clause,[],[f4801,f9901]) ).
fof(f9901,plain,
( spl47_542
<=> ! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ominus__class_Ominus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Ogroup__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_542])]) ).
fof(f4801,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ominus__class_Ominus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Ogroup__add(X2) ),
inference(cnf_transformation,[],[f2772]) ).
fof(f2772,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ominus__class_Ominus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f1748]) ).
fof(f1748,plain,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ominus__class_Ominus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(rectify,[],[f832]) ).
fof(f832,axiom,
! [X17,X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,X4,X17) = c_Groups_Ominus__class_Ominus(X5,X4,c_Groups_Ouminus__class_Ouminus(X5,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).
fof(f9899,plain,
spl47_541,
inference(avatar_split_clause,[],[f4800,f9897]) ).
fof(f9897,plain,
( spl47_541
<=> ! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Ogroup__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_541])]) ).
fof(f4800,plain,
! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Ogroup__add(X2) ),
inference(cnf_transformation,[],[f2771]) ).
fof(f2771,plain,
! [X0,X1,X2] :
( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f1747]) ).
fof(f1747,plain,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(rectify,[],[f835]) ).
fof(f835,axiom,
! [X17,X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ominus__class_Ominus(X5,X4,X17) = c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Ouminus__class_Ouminus(X5,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__def) ).
fof(f9895,plain,
spl47_540,
inference(avatar_split_clause,[],[f4777,f9893]) ).
fof(f9893,plain,
( spl47_540
<=> ! [X2,X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_540])]) ).
fof(f4777,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f3711]) ).
fof(f3711,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| X0 != X1 )
& ( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) )
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(nnf_transformation,[],[f2748]) ).
fof(f2748,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
<=> X0 = X1 )
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(flattening,[],[f2747]) ).
fof(f2747,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
<=> X0 = X1 )
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f1732]) ).
fof(f1732,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
<=> X0 = X1 ) ) ),
inference(rectify,[],[f195]) ).
fof(f195,axiom,
! [X25,X15,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X15,X25)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X15,X25)
<=> X15 = X25 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(f9891,plain,
spl47_539,
inference(avatar_split_clause,[],[f4769,f9889]) ).
fof(f9889,plain,
( spl47_539
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| X0 = X1
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_539])]) ).
fof(f4769,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| X0 = X1
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f2734]) ).
fof(f2734,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| X0 = X1
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(flattening,[],[f2733]) ).
fof(f2733,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| X0 = X1
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f1725]) ).
fof(f1725,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X0,X1)
| X0 = X1
| c_Orderings_Oord__class_Oless(X2,X1,X0) ) ),
inference(rectify,[],[f166]) ).
fof(f166,axiom,
! [X10,X6,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X10,X6)
| X6 = X10
| c_Orderings_Oord__class_Oless(X5,X6,X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
fof(f9887,plain,
spl47_538,
inference(avatar_split_clause,[],[f4746,f9885]) ).
fof(f9885,plain,
( spl47_538
<=> ! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Rings_Ocomm__ring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_538])]) ).
fof(f4746,plain,
! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(cnf_transformation,[],[f2703]) ).
fof(f2703,plain,
! [X0,X1,X2] :
( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(ennf_transformation,[],[f1706]) ).
fof(f1706,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__ring__1(X2)
=> c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(rectify,[],[f833]) ).
fof(f833,axiom,
! [X10,X6,X5] :
( class_Rings_Ocomm__ring__1(X5)
=> c_Groups_Ominus__class_Ominus(X5,X6,X10) = c_Groups_Oplus__class_Oplus(X5,X6,c_Groups_Ouminus__class_Ouminus(X5,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).
fof(f9883,plain,
spl47_537,
inference(avatar_split_clause,[],[f4713,f9881]) ).
fof(f9881,plain,
( spl47_537
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| X0 = X1
| ~ class_Rings_Olinordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_537])]) ).
fof(f4713,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| X0 = X1
| ~ class_Rings_Olinordered__idom(X2) ),
inference(cnf_transformation,[],[f2669]) ).
fof(f2669,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| X0 = X1
| ~ class_Rings_Olinordered__idom(X2) ),
inference(flattening,[],[f2668]) ).
fof(f2668,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| X0 = X1
| ~ class_Rings_Olinordered__idom(X2) ),
inference(ennf_transformation,[],[f1683]) ).
fof(f1683,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( X0 != X1
=> ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
=> c_Orderings_Oord__class_Oless(X2,X0,X1) ) ) ),
inference(rectify,[],[f148]) ).
fof(f148,axiom,
! [X10,X6,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( X6 != X10
=> ( ~ c_Orderings_Oord__class_Oless(X5,X6,X10)
=> c_Orderings_Oord__class_Oless(X5,X10,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(f9879,plain,
spl47_536,
inference(avatar_split_clause,[],[f4590,f9877]) ).
fof(f9877,plain,
( spl47_536
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_536])]) ).
fof(f4590,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ),
inference(cnf_transformation,[],[f3651]) ).
fof(f3651,plain,
! [X0,X1] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1 )
& ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 )
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ) ),
inference(flattening,[],[f3650]) ).
fof(f3650,plain,
! [X0,X1] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1 )
& ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 )
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ) ),
inference(nnf_transformation,[],[f1600]) ).
fof(f1600,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
<=> ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 ) ),
inference(rectify,[],[f668]) ).
fof(f668,axiom,
! [X11,X14] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X11)
<=> ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X11
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
fof(f9875,plain,
spl47_535,
inference(avatar_split_clause,[],[f4589,f9873]) ).
fof(f9873,plain,
( spl47_535
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_535])]) ).
fof(f4589,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ),
inference(cnf_transformation,[],[f3651]) ).
fof(f9871,plain,
spl47_534,
inference(avatar_split_clause,[],[f4421,f9869]) ).
fof(f9869,plain,
( spl47_534
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_534])]) ).
fof(f4421,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2526]) ).
fof(f2526,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1505]) ).
fof(f1505,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X0 ),
inference(rectify,[],[f810]) ).
fof(f810,axiom,
! [X21,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X21)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X7)) = X21 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).
fof(f9867,plain,
spl47_533,
inference(avatar_split_clause,[],[f4420,f9865]) ).
fof(f9865,plain,
( spl47_533
<=> ! [X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_533])]) ).
fof(f4420,plain,
! [X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2525]) ).
fof(f2525,plain,
! [X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1504]) ).
fof(f1504,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X1 ),
inference(rectify,[],[f786]) ).
fof(f786,axiom,
! [X7,X32] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32,X7)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,X32)) = X32 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
fof(f9863,plain,
( spl47_532
| ~ spl47_41
| ~ spl47_307 ),
inference(avatar_split_clause,[],[f7630,f7457,f6236,f9861]) ).
fof(f9861,plain,
( spl47_532
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_532])]) ).
fof(f7630,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0)
| ~ spl47_41
| ~ spl47_307 ),
inference(resolution,[],[f7458,f6238]) ).
fof(f9859,plain,
spl47_531,
inference(avatar_split_clause,[],[f4412,f9857]) ).
fof(f9857,plain,
( spl47_531
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_531])]) ).
fof(f4412,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2516]) ).
fof(f2516,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1497]) ).
fof(f1497,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1 ),
inference(rectify,[],[f822]) ).
fof(f822,axiom,
! [X7,X21] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X7)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X7)) = X21 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
fof(f9855,plain,
spl47_530,
inference(avatar_split_clause,[],[f4371,f9853]) ).
fof(f9853,plain,
( spl47_530
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0)
| ~ class_Groups_Ozero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_530])]) ).
fof(f4371,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0)
| ~ class_Groups_Ozero(X1) ),
inference(cnf_transformation,[],[f3575]) ).
fof(f3575,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0) ) )
| ~ class_Groups_Ozero(X1) ),
inference(nnf_transformation,[],[f2476]) ).
fof(f2476,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0)
<=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0 )
| ~ class_Groups_Ozero(X1) ),
inference(ennf_transformation,[],[f1460]) ).
fof(f1460,plain,
! [X0,X1] :
( class_Groups_Ozero(X1)
=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0)
<=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0 ) ),
inference(rectify,[],[f69]) ).
fof(f69,axiom,
! [X9,X5] :
( class_Groups_Ozero(X5)
=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X5,X9)
<=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psize__eq__0__iff) ).
fof(f9851,plain,
spl47_529,
inference(avatar_split_clause,[],[f4364,f9849]) ).
fof(f9849,plain,
( spl47_529
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X1,c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))
| ~ class_Groups_Ozero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_529])]) ).
fof(f4364,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X1,c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))
| ~ class_Groups_Ozero(X1) ),
inference(cnf_transformation,[],[f2470]) ).
fof(f2470,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X1,c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))
| ~ class_Groups_Ozero(X1) ),
inference(ennf_transformation,[],[f1455]) ).
fof(f1455,plain,
! [X0,X1] :
( class_Groups_Ozero(X1)
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X1,c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))) ),
inference(rectify,[],[f118]) ).
fof(f118,axiom,
! [X4,X5] :
( class_Groups_Ozero(X5)
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X5,c_Polynomial_OpCons(X5,X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__pCons__0) ).
fof(f9847,plain,
spl47_528,
inference(avatar_split_clause,[],[f4319,f9845]) ).
fof(f9845,plain,
( spl47_528
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_528])]) ).
fof(f4319,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(cnf_transformation,[],[f3567]) ).
fof(f3567,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
& ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0)) ) )
| ~ class_Rings_Olinordered__idom(X1) ),
inference(nnf_transformation,[],[f2431]) ).
fof(f2431,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
<=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
| ~ class_Rings_Olinordered__idom(X1) ),
inference(ennf_transformation,[],[f1416]) ).
fof(f1416,plain,
! [X0,X1] :
( class_Rings_Olinordered__idom(X1)
=> ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
<=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
inference(rectify,[],[f431]) ).
fof(f431,axiom,
! [X12,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X12,c_Groups_Ouminus__class_Ouminus(X5,X12))
<=> c_Orderings_Oord__class_Oless(X5,X12,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).
fof(f9843,plain,
spl47_527,
inference(avatar_split_clause,[],[f4318,f9841]) ).
fof(f9841,plain,
( spl47_527
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_Rings_Olinordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_527])]) ).
fof(f4318,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(cnf_transformation,[],[f3567]) ).
fof(f9839,plain,
spl47_526,
inference(avatar_split_clause,[],[f4295,f9837]) ).
fof(f9837,plain,
( spl47_526
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oplus__class_Oplus(X1,X0,X0)
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_526])]) ).
fof(f4295,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oplus__class_Oplus(X1,X0,X0)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3556]) ).
fof(f3556,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X0,X0)
| c_Groups_Ozero__class_Ozero(X1) != X0 )
& ( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oplus__class_Oplus(X1,X0,X0) ) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f2418]) ).
fof(f2418,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X0,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f1404]) ).
fof(f1404,plain,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X0,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f356]) ).
fof(f356,axiom,
! [X12,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) = c_Groups_Oplus__class_Oplus(X5,X12,X12)
<=> c_Groups_Ozero__class_Ozero(X5) = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__zero__sym) ).
fof(f9835,plain,
spl47_525,
inference(avatar_split_clause,[],[f4294,f9833]) ).
fof(f9833,plain,
( spl47_525
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_525])]) ).
fof(f4294,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3555]) ).
fof(f3555,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
& ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0) ) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f2417]) ).
fof(f2417,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f1403]) ).
fof(f1403,plain,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
inference(rectify,[],[f434]) ).
fof(f434,axiom,
! [X12,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ouminus__class_Ouminus(X5,X12),X12)
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).
fof(f9831,plain,
spl47_524,
inference(avatar_split_clause,[],[f4293,f9829]) ).
fof(f9829,plain,
( spl47_524
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_524])]) ).
fof(f4293,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3555]) ).
fof(f9827,plain,
spl47_523,
inference(avatar_split_clause,[],[f4292,f9825]) ).
fof(f9825,plain,
( spl47_523
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_523])]) ).
fof(f4292,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3554]) ).
fof(f3554,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
& ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0) ) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f2416]) ).
fof(f2416,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f1402]) ).
fof(f1402,plain,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
inference(rectify,[],[f430]) ).
fof(f430,axiom,
! [X12,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X12),X12)
<=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).
fof(f9823,plain,
spl47_522,
inference(avatar_split_clause,[],[f4291,f9821]) ).
fof(f9821,plain,
( spl47_522
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_522])]) ).
fof(f4291,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3554]) ).
fof(f9819,plain,
spl47_521,
inference(avatar_split_clause,[],[f4290,f9817]) ).
fof(f9817,plain,
( spl47_521
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_521])]) ).
fof(f4290,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3553]) ).
fof(f3553,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
& ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0)) ) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f2415]) ).
fof(f2415,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
<=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f1401]) ).
fof(f1401,plain,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
<=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
inference(rectify,[],[f428]) ).
fof(f428,axiom,
! [X12,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,c_Groups_Ouminus__class_Ouminus(X5,X12))
<=> c_Orderings_Oord__class_Oless__eq(X5,X12,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).
fof(f9815,plain,
spl47_520,
inference(avatar_split_clause,[],[f4289,f9813]) ).
fof(f9813,plain,
( spl47_520
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_520])]) ).
fof(f4289,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3553]) ).
fof(f9811,plain,
spl47_519,
inference(avatar_split_clause,[],[f4274,f9809]) ).
fof(f9809,plain,
( spl47_519
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = c_Rings_Oinverse__class_Odivide(X1,X0,X0)
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Rings_Odivision__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_519])]) ).
fof(f4274,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = c_Rings_Oinverse__class_Odivide(X1,X0,X0)
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Rings_Odivision__ring(X1) ),
inference(cnf_transformation,[],[f2402]) ).
fof(f2402,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = c_Rings_Oinverse__class_Odivide(X1,X0,X0)
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Rings_Odivision__ring(X1) ),
inference(flattening,[],[f2401]) ).
fof(f2401,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = c_Rings_Oinverse__class_Odivide(X1,X0,X0)
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Rings_Odivision__ring(X1) ),
inference(ennf_transformation,[],[f1388]) ).
fof(f1388,plain,
! [X0,X1] :
( class_Rings_Odivision__ring(X1)
=> ( c_Groups_Ozero__class_Ozero(X1) != X0
=> c_Groups_Oone__class_Oone(X1) = c_Rings_Oinverse__class_Odivide(X1,X0,X0) ) ),
inference(rectify,[],[f908]) ).
fof(f908,axiom,
! [X4,X5] :
( class_Rings_Odivision__ring(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X4
=> c_Groups_Oone__class_Oone(X5) = c_Rings_Oinverse__class_Odivide(X5,X4,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self) ).
fof(f9807,plain,
spl47_518,
inference(avatar_split_clause,[],[f4270,f9805]) ).
fof(f9805,plain,
( spl47_518
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = c_Rings_Oinverse__class_Odivide(X1,X0,X0)
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_518])]) ).
fof(f4270,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = c_Rings_Oinverse__class_Odivide(X1,X0,X0)
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(cnf_transformation,[],[f2397]) ).
fof(f2397,plain,
! [X0,X1] :
( ( ( c_Groups_Oone__class_Oone(X1) = c_Rings_Oinverse__class_Odivide(X1,X0,X0)
| c_Groups_Ozero__class_Ozero(X1) = X0 )
& ( c_Groups_Ozero__class_Ozero(X1) = c_Rings_Oinverse__class_Odivide(X1,X0,X0)
| c_Groups_Ozero__class_Ozero(X1) != X0 ) )
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(ennf_transformation,[],[f1384]) ).
fof(f1384,plain,
! [X0,X1] :
( class_Rings_Odivision__ring__inverse__zero(X1)
=> ( ( c_Groups_Ozero__class_Ozero(X1) != X0
=> c_Groups_Oone__class_Oone(X1) = c_Rings_Oinverse__class_Odivide(X1,X0,X0) )
& ( c_Groups_Ozero__class_Ozero(X1) = X0
=> c_Groups_Ozero__class_Ozero(X1) = c_Rings_Oinverse__class_Odivide(X1,X0,X0) ) ) ),
inference(rectify,[],[f907]) ).
fof(f907,axiom,
! [X4,X5] :
( class_Rings_Odivision__ring__inverse__zero(X5)
=> ( ( c_Groups_Ozero__class_Ozero(X5) != X4
=> c_Groups_Oone__class_Oone(X5) = c_Rings_Oinverse__class_Odivide(X5,X4,X4) )
& ( c_Groups_Ozero__class_Ozero(X5) = X4
=> c_Groups_Ozero__class_Ozero(X5) = c_Rings_Oinverse__class_Odivide(X5,X4,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self__if) ).
fof(f9803,plain,
spl47_517,
inference(avatar_split_clause,[],[f4251,f9801]) ).
fof(f9801,plain,
( spl47_517
<=> ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_517])]) ).
fof(f4251,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),
inference(cnf_transformation,[],[f1367]) ).
fof(f1367,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),
inference(rectify,[],[f717]) ).
fof(f717,axiom,
! [X7,X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
fof(f9799,plain,
spl47_516,
inference(avatar_split_clause,[],[f4250,f9797]) ).
fof(f4250,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1),
inference(cnf_transformation,[],[f1366]) ).
fof(f1366,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1),
inference(rectify,[],[f715]) ).
fof(f715,axiom,
! [X48,X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X48) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X26),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).
fof(f9795,plain,
spl47_515,
inference(avatar_split_clause,[],[f4207,f9793]) ).
fof(f9793,plain,
( spl47_515
<=> ! [X0] :
( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_515])]) ).
fof(f4207,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2383]) ).
fof(f2383,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1331]) ).
fof(f1331,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
inference(rectify,[],[f209]) ).
fof(f209,axiom,
! [X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Polynomial_OpCons(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__poly__def) ).
fof(f9791,plain,
spl47_514,
inference(avatar_split_clause,[],[f4192,f9789]) ).
fof(f9789,plain,
( spl47_514
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Groups_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_514])]) ).
fof(f4192,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f2368]) ).
fof(f2368,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Groups_Ozero(X0) ),
inference(ennf_transformation,[],[f1316]) ).
fof(f1316,plain,
! [X0] :
( class_Groups_Ozero(X0)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
inference(rectify,[],[f106]) ).
fof(f106,axiom,
! [X5] :
( class_Groups_Ozero(X5)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_OpCons(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__0__0) ).
fof(f9778,plain,
( ~ spl47_513
| spl47_512
| ~ spl47_265
| ~ spl47_484 ),
inference(avatar_split_clause,[],[f9506,f9100,f7262,f9526,f9775]) ).
fof(f9775,plain,
( spl47_513
<=> class_Groups_Oab__group__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_513])]) ).
fof(f9526,plain,
( spl47_512
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_512])]) ).
fof(f7262,plain,
( spl47_265
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_265])]) ).
fof(f9100,plain,
( spl47_484
<=> ! [X2,X0,X1] :
( X0 = X1
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Ominus__class_Ominus(X2,X1,X0)
| ~ class_Groups_Oab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_484])]) ).
fof(f9506,plain,
( ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ class_Groups_Oab__group__add(tc_Nat_Onat) )
| ~ spl47_265
| ~ spl47_484 ),
inference(trivial_inequality_removal,[],[f9503]) ).
fof(f9503,plain,
( ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ class_Groups_Oab__group__add(tc_Nat_Onat) )
| ~ spl47_265
| ~ spl47_484 ),
inference(superposition,[],[f9101,f7263]) ).
fof(f7263,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ spl47_265 ),
inference(avatar_component_clause,[],[f7262]) ).
fof(f9101,plain,
( ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) != c_Groups_Ominus__class_Ominus(X2,X1,X0)
| X0 = X1
| ~ class_Groups_Oab__group__add(X2) )
| ~ spl47_484 ),
inference(avatar_component_clause,[],[f9100]) ).
fof(f9528,plain,
( ~ spl47_511
| spl47_512
| ~ spl47_265
| ~ spl47_482 ),
inference(avatar_split_clause,[],[f9491,f9092,f7262,f9526,f9522]) ).
fof(f9522,plain,
( spl47_511
<=> class_Groups_Ogroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_511])]) ).
fof(f9092,plain,
( spl47_482
<=> ! [X2,X0,X1] :
( X0 = X1
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Ominus__class_Ominus(X2,X1,X0)
| ~ class_Groups_Ogroup__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_482])]) ).
fof(f9491,plain,
( ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ class_Groups_Ogroup__add(tc_Nat_Onat) )
| ~ spl47_265
| ~ spl47_482 ),
inference(trivial_inequality_removal,[],[f9488]) ).
fof(f9488,plain,
( ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ class_Groups_Ogroup__add(tc_Nat_Onat) )
| ~ spl47_265
| ~ spl47_482 ),
inference(superposition,[],[f9093,f7263]) ).
fof(f9093,plain,
( ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) != c_Groups_Ominus__class_Ominus(X2,X1,X0)
| X0 = X1
| ~ class_Groups_Ogroup__add(X2) )
| ~ spl47_482 ),
inference(avatar_component_clause,[],[f9092]) ).
fof(f9416,plain,
( spl47_510
| ~ spl47_11
| ~ spl47_306 ),
inference(avatar_split_clause,[],[f7628,f7453,f6086,f9414]) ).
fof(f9414,plain,
( spl47_510
<=> ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_510])]) ).
fof(f6086,plain,
( spl47_11
<=> class_Lattices_Oboolean__algebra(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_11])]) ).
fof(f7453,plain,
( spl47_306
<=> ! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0
| ~ class_Lattices_Oboolean__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_306])]) ).
fof(f7628,plain,
( ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0)) = X0
| ~ spl47_11
| ~ spl47_306 ),
inference(resolution,[],[f7454,f6088]) ).
fof(f6088,plain,
( class_Lattices_Oboolean__algebra(tc_HOL_Obool)
| ~ spl47_11 ),
inference(avatar_component_clause,[],[f6086]) ).
fof(f7454,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0 )
| ~ spl47_306 ),
inference(avatar_component_clause,[],[f7453]) ).
fof(f9311,plain,
( spl47_509
| ~ spl47_5
| ~ spl47_305 ),
inference(avatar_split_clause,[],[f7627,f7449,f6056,f9309]) ).
fof(f9309,plain,
( spl47_509
<=> ! [X0] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_509])]) ).
fof(f6056,plain,
( spl47_5
<=> class_Rings_Odivision__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_5])]) ).
fof(f7449,plain,
( spl47_305
<=> ! [X0,X1] :
( c_Rings_Oinverse__class_Odivide(X1,X0,c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Rings_Odivision__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_305])]) ).
fof(f7627,plain,
( ! [X0] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = X0
| ~ spl47_5
| ~ spl47_305 ),
inference(resolution,[],[f7450,f6058]) ).
fof(f6058,plain,
( class_Rings_Odivision__ring(tc_Complex_Ocomplex)
| ~ spl47_5 ),
inference(avatar_component_clause,[],[f6056]) ).
fof(f7450,plain,
( ! [X0,X1] :
( ~ class_Rings_Odivision__ring(X1)
| c_Rings_Oinverse__class_Odivide(X1,X0,c_Groups_Oone__class_Oone(X1)) = X0 )
| ~ spl47_305 ),
inference(avatar_component_clause,[],[f7449]) ).
fof(f9207,plain,
spl47_508,
inference(avatar_split_clause,[],[f5856,f9205]) ).
fof(f9205,plain,
( spl47_508
<=> ! [X2,X0,X3] :
( hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X0,X2)),X2) = X0
| ~ class_Groups_Ozero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_508])]) ).
fof(f5856,plain,
! [X2,X3,X0] :
( hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X0,X2)),X2) = X0
| ~ class_Groups_Ozero(X3) ),
inference(equality_resolution,[],[f5311]) ).
fof(f5311,plain,
! [X2,X3,X0,X1] :
( hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X0,X2)),X1) = X0
| X1 != X2
| ~ class_Groups_Ozero(X3) ),
inference(cnf_transformation,[],[f3256]) ).
fof(f9203,plain,
spl47_507,
inference(avatar_split_clause,[],[f5829,f9201]) ).
fof(f5829,plain,
! [X2,X1] : sP16(c_Groups_Ozero__class_Ozero(X1),X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)),
inference(equality_resolution,[],[f5828]) ).
fof(f5828,plain,
! [X2,X3,X1] :
( sP16(c_Groups_Ozero__class_Ozero(X1),X1,X2,X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) != X3 ),
inference(equality_resolution,[],[f5147]) ).
fof(f5147,plain,
! [X2,X3,X0,X1] :
( sP16(X0,X1,X2,X3)
| c_Groups_Ozero__class_Ozero(X1) != X0
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2) != X3 ),
inference(cnf_transformation,[],[f3830]) ).
fof(f9199,plain,
spl47_506,
inference(avatar_split_clause,[],[f5821,f9197]) ).
fof(f5821,plain,
! [X2,X1] : sP14(c_Groups_Ozero__class_Ozero(X1),X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)),
inference(equality_resolution,[],[f5820]) ).
fof(f5820,plain,
! [X2,X3,X1] :
( sP14(c_Groups_Ozero__class_Ozero(X1),X1,X2,X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) != X3 ),
inference(equality_resolution,[],[f5138]) ).
fof(f5138,plain,
! [X2,X3,X0,X1] :
( sP14(X0,X1,X2,X3)
| c_Groups_Ozero__class_Ozero(X1) != X0
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2) != X3 ),
inference(cnf_transformation,[],[f3825]) ).
fof(f9195,plain,
spl47_505,
inference(avatar_split_clause,[],[f5766,f9193]) ).
fof(f9193,plain,
( spl47_505
<=> ! [X2,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)))
| ~ class_Rings_Oidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_505])]) ).
fof(f5766,plain,
! [X2,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)))
| ~ class_Rings_Oidom(X2) ),
inference(equality_resolution,[],[f4835]) ).
fof(f4835,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f3729]) ).
fof(f9191,plain,
spl47_504,
inference(avatar_split_clause,[],[f5765,f9189]) ).
fof(f9189,plain,
( spl47_504
<=> ! [X2,X0] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0)
| ~ class_Rings_Oidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_504])]) ).
fof(f5765,plain,
! [X2,X0] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0)
| ~ class_Rings_Oidom(X2) ),
inference(equality_resolution,[],[f4831]) ).
fof(f4831,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f3727]) ).
fof(f9187,plain,
spl47_503,
inference(avatar_split_clause,[],[f5756,f9185]) ).
fof(f9185,plain,
( spl47_503
<=> ! [X2,X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,c_Groups_Ozero__class_Ozero(X2),X0))
| ~ class_Rings_Oidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_503])]) ).
fof(f5756,plain,
! [X2,X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,c_Groups_Ozero__class_Ozero(X2),X0))
| ~ class_Rings_Oidom(X2) ),
inference(equality_resolution,[],[f4806]) ).
fof(f4806,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X2,c_Polynomial_Osmult(X2,X1,X0))
| c_Groups_Ozero__class_Ozero(X2) != X1
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f2777]) ).
fof(f9183,plain,
spl47_502,
inference(avatar_split_clause,[],[f5747,f9181]) ).
fof(f9181,plain,
( spl47_502
<=> ! [X2,X0] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),X0)
| ~ class_Rings_Oring__no__zero__divisors(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_502])]) ).
fof(f5747,plain,
! [X2,X0] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),X0)
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(equality_resolution,[],[f4728]) ).
fof(f4728,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Ozero__class_Ozero(X2) != X1
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(cnf_transformation,[],[f3704]) ).
fof(f9179,plain,
spl47_501,
inference(avatar_split_clause,[],[f5746,f9177]) ).
fof(f9177,plain,
( spl47_501
<=> ! [X2,X1] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Oring__no__zero__divisors(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_501])]) ).
fof(f5746,plain,
! [X2,X1] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(equality_resolution,[],[f4729]) ).
fof(f4729,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Ozero__class_Ozero(X2) != X0
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(cnf_transformation,[],[f3704]) ).
fof(f9175,plain,
spl47_500,
inference(avatar_split_clause,[],[f5583,f9173]) ).
fof(f9173,plain,
( spl47_500
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_500])]) ).
fof(f5583,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(definition_unfolding,[],[f4533,f4118]) ).
fof(f4533,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
inference(cnf_transformation,[],[f3619]) ).
fof(f3619,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
inference(nnf_transformation,[],[f1582]) ).
fof(f1582,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f261]) ).
fof(f261,axiom,
! [X11,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,c_Nat_OSuc(X11))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
fof(f9171,plain,
spl47_499,
inference(avatar_split_clause,[],[f5570,f9169]) ).
fof(f9169,plain,
( spl47_499
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_499])]) ).
fof(f5570,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f4505,f4118]) ).
fof(f4505,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3594]) ).
fof(f3594,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f1570]) ).
fof(f1570,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ),
inference(rectify,[],[f230]) ).
fof(f230,axiom,
! [X11,X14] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X11)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,c_Nat_OSuc(X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).
fof(f9167,plain,
spl47_498,
inference(avatar_split_clause,[],[f5569,f9165]) ).
fof(f5569,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(definition_unfolding,[],[f4506,f4118]) ).
fof(f4506,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ),
inference(cnf_transformation,[],[f3594]) ).
fof(f9163,plain,
spl47_497,
inference(avatar_split_clause,[],[f5568,f9161]) ).
fof(f5568,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f4503,f4118]) ).
fof(f4503,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3593]) ).
fof(f3593,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f1569]) ).
fof(f1569,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1) ),
inference(rectify,[],[f95]) ).
fof(f95,axiom,
! [X11,X14] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X11)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X11),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
fof(f9159,plain,
spl47_496,
inference(avatar_split_clause,[],[f5567,f9157]) ).
fof(f5567,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(definition_unfolding,[],[f4504,f4118]) ).
fof(f4504,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1) ),
inference(cnf_transformation,[],[f3593]) ).
fof(f9155,plain,
spl47_495,
inference(avatar_split_clause,[],[f5558,f9153]) ).
fof(f5558,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
inference(definition_unfolding,[],[f4460,f4118]) ).
fof(f4460,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ),
inference(cnf_transformation,[],[f2570]) ).
fof(f2570,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ),
inference(ennf_transformation,[],[f1537]) ).
fof(f1537,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f266]) ).
fof(f266,axiom,
! [X7,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X21),X7)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
fof(f9151,plain,
spl47_494,
inference(avatar_split_clause,[],[f5550,f9149]) ).
fof(f5550,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f4434,f4118]) ).
fof(f4434,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2540]) ).
fof(f2540,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1517]) ).
fof(f1517,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ),
inference(rectify,[],[f264]) ).
fof(f264,axiom,
! [X7,X21] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X21),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leI) ).
fof(f9147,plain,
spl47_493,
inference(avatar_split_clause,[],[f5546,f9145]) ).
fof(f9145,plain,
( spl47_493
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_493])]) ).
fof(f5546,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f4418,f4118]) ).
fof(f4418,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2523]) ).
fof(f2523,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1502]) ).
fof(f1502,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
inference(rectify,[],[f263]) ).
fof(f263,axiom,
! [X7,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X7)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,c_Nat_OSuc(X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
fof(f9143,plain,
spl47_492,
inference(avatar_split_clause,[],[f5412,f9141]) ).
fof(f9141,plain,
( spl47_492
<=> ! [X2,X0,X1] :
( sP24(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_492])]) ).
fof(f5412,plain,
! [X2,X0,X1] :
( sP24(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X1,X0)) ),
inference(cnf_transformation,[],[f3887]) ).
fof(f9130,plain,
spl47_491,
inference(avatar_split_clause,[],[f5084,f9128]) ).
fof(f9128,plain,
( spl47_491
<=> ! [X2,X0,X1] :
( X0 = X2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_491])]) ).
fof(f5084,plain,
! [X2,X0,X1] :
( X0 = X2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f3798]) ).
fof(f3798,plain,
! [X0,X1,X2] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)
| X0 != X2 )
& ( X0 = X2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) ) ),
inference(nnf_transformation,[],[f1945]) ).
fof(f1945,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)
<=> X0 = X2 ),
inference(rectify,[],[f396]) ).
fof(f396,axiom,
! [X11,X44,X14] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X44) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X44)
<=> X11 = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
fof(f9126,plain,
spl47_490,
inference(avatar_split_clause,[],[f5082,f9124]) ).
fof(f9124,plain,
( spl47_490
<=> ! [X2,X0,X1] :
( X0 = X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_490])]) ).
fof(f5082,plain,
! [X2,X0,X1] :
( X0 = X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0) ),
inference(cnf_transformation,[],[f3797]) ).
fof(f3797,plain,
! [X0,X1,X2] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)
| X0 != X1 )
& ( X0 = X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0) ) ),
inference(nnf_transformation,[],[f1944]) ).
fof(f1944,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)
<=> X0 = X1 ),
inference(rectify,[],[f395]) ).
fof(f395,axiom,
! [X11,X14,X44] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X44,X14) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X44,X11)
<=> X11 = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
fof(f9122,plain,
spl47_489,
inference(avatar_split_clause,[],[f4982,f9120]) ).
fof(f9120,plain,
( spl47_489
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_489])]) ).
fof(f4982,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2961]) ).
fof(f2961,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(flattening,[],[f2960]) ).
fof(f2960,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1886]) ).
fof(f1886,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ) ),
inference(rectify,[],[f83]) ).
fof(f83,axiom,
! [X20,X33,X32] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32,X33)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32,X20) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).
fof(f9118,plain,
spl47_488,
inference(avatar_split_clause,[],[f4964,f9116]) ).
fof(f9116,plain,
( spl47_488
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_488])]) ).
fof(f4964,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(cnf_transformation,[],[f2942]) ).
fof(f2942,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(flattening,[],[f2941]) ).
fof(f2941,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(ennf_transformation,[],[f1868]) ).
fof(f1868,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0) ) ),
inference(rectify,[],[f474]) ).
fof(f474,axiom,
! [X20,X33,X32] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X32,X33)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X33,X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X32,X20) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__trans) ).
fof(f9114,plain,
spl47_487,
inference(avatar_split_clause,[],[f4897,f9112]) ).
fof(f9112,plain,
( spl47_487
<=> ! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,X1) = c_Polynomial_Odegree(X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0))
| ~ class_Rings_Ocomm__semiring__0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_487])]) ).
fof(f4897,plain,
! [X2,X0,X1] :
( c_Polynomial_Odegree(X2,X1) = c_Polynomial_Odegree(X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(cnf_transformation,[],[f2869]) ).
fof(f2869,plain,
! [X0,X1,X2] :
( c_Polynomial_Odegree(X2,X1) = c_Polynomial_Odegree(X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(ennf_transformation,[],[f1817]) ).
fof(f1817,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__0(X2)
=> c_Polynomial_Odegree(X2,X1) = c_Polynomial_Odegree(X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0)) ),
inference(rectify,[],[f274]) ).
fof(f274,axiom,
! [X35,X8,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Polynomial_Odegree(X5,X8) = c_Polynomial_Odegree(X5,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5,X8,X35)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__offset__poly) ).
fof(f9110,plain,
spl47_486,
inference(avatar_split_clause,[],[f4890,f9108]) ).
fof(f9108,plain,
( spl47_486
<=> ! [X2,X0,X1] :
( X0 = X1
| c_Polynomial_Ocoeff(X2,X1) != c_Polynomial_Ocoeff(X2,X0)
| ~ class_Groups_Ozero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_486])]) ).
fof(f4890,plain,
! [X2,X0,X1] :
( X0 = X1
| c_Polynomial_Ocoeff(X2,X1) != c_Polynomial_Ocoeff(X2,X0)
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f3741]) ).
fof(f3741,plain,
! [X0,X1,X2] :
( ( ( c_Polynomial_Ocoeff(X2,X1) = c_Polynomial_Ocoeff(X2,X0)
| X0 != X1 )
& ( X0 = X1
| c_Polynomial_Ocoeff(X2,X1) != c_Polynomial_Ocoeff(X2,X0) ) )
| ~ class_Groups_Ozero(X2) ),
inference(nnf_transformation,[],[f2866]) ).
fof(f2866,plain,
! [X0,X1,X2] :
( ( c_Polynomial_Ocoeff(X2,X1) = c_Polynomial_Ocoeff(X2,X0)
<=> X0 = X1 )
| ~ class_Groups_Ozero(X2) ),
inference(ennf_transformation,[],[f1814]) ).
fof(f1814,plain,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( c_Polynomial_Ocoeff(X2,X1) = c_Polynomial_Ocoeff(X2,X0)
<=> X0 = X1 ) ),
inference(rectify,[],[f779]) ).
fof(f779,axiom,
! [X25,X15,X5] :
( class_Groups_Ozero(X5)
=> ( c_Polynomial_Ocoeff(X5,X15) = c_Polynomial_Ocoeff(X5,X25)
<=> X15 = X25 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__inject) ).
fof(f9106,plain,
spl47_485,
inference(avatar_split_clause,[],[f4867,f9104]) ).
fof(f9104,plain,
( spl47_485
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X0
| c_Groups_Oplus__class_Oplus(X2,X1,X0) != X1
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_485])]) ).
fof(f4867,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X0
| c_Groups_Oplus__class_Oplus(X2,X1,X0) != X1
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(cnf_transformation,[],[f3736]) ).
fof(f3736,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Oplus__class_Oplus(X2,X1,X0) = X1
| c_Groups_Ozero__class_Ozero(X2) != X0 )
& ( c_Groups_Ozero__class_Ozero(X2) = X0
| c_Groups_Oplus__class_Oplus(X2,X1,X0) != X1 ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(nnf_transformation,[],[f2839]) ).
fof(f2839,plain,
! [X0,X1,X2] :
( ( c_Groups_Oplus__class_Oplus(X2,X1,X0) = X1
<=> c_Groups_Ozero__class_Ozero(X2) = X0 )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(ennf_transformation,[],[f1795]) ).
fof(f1795,plain,
! [X0,X1,X2] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)
=> ( c_Groups_Oplus__class_Oplus(X2,X1,X0) = X1
<=> c_Groups_Ozero__class_Ozero(X2) = X0 ) ),
inference(rectify,[],[f459]) ).
fof(f459,axiom,
! [X12,X29,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,X29,X12) = X29
<=> c_Groups_Ozero__class_Ozero(X5) = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(f9102,plain,
spl47_484,
inference(avatar_split_clause,[],[f4853,f9100]) ).
fof(f4853,plain,
! [X2,X0,X1] :
( X0 = X1
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Ominus__class_Ominus(X2,X1,X0)
| ~ class_Groups_Oab__group__add(X2) ),
inference(cnf_transformation,[],[f3735]) ).
fof(f3735,plain,
! [X0,X1,X2] :
( ( ( X0 = X1
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Ominus__class_Ominus(X2,X1,X0) )
& ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Ominus__class_Ominus(X2,X1,X0)
| X0 != X1 ) )
| ~ class_Groups_Oab__group__add(X2) ),
inference(nnf_transformation,[],[f2812]) ).
fof(f2812,plain,
! [X0,X1,X2] :
( ( X0 = X1
<=> c_Groups_Ozero__class_Ozero(X2) = c_Groups_Ominus__class_Ominus(X2,X1,X0) )
| ~ class_Groups_Oab__group__add(X2) ),
inference(ennf_transformation,[],[f1781]) ).
fof(f1781,plain,
! [X0,X1,X2] :
( class_Groups_Oab__group__add(X2)
=> ( X0 = X1
<=> c_Groups_Ozero__class_Ozero(X2) = c_Groups_Ominus__class_Ominus(X2,X1,X0) ) ),
inference(rectify,[],[f800]) ).
fof(f800,axiom,
! [X29,X12,X5] :
( class_Groups_Oab__group__add(X5)
=> ( X12 = X29
<=> c_Groups_Ozero__class_Ozero(X5) = c_Groups_Ominus__class_Ominus(X5,X12,X29) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).
fof(f9098,plain,
spl47_483,
inference(avatar_split_clause,[],[f4826,f9096]) ).
fof(f9096,plain,
( spl47_483
<=> ! [X2,X0,X1] :
( X0 = X1
| c_Groups_Ouminus__class_Ouminus(X2,X1) != c_Groups_Ouminus__class_Ouminus(X2,X0)
| ~ class_Groups_Ogroup__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_483])]) ).
fof(f4826,plain,
! [X2,X0,X1] :
( X0 = X1
| c_Groups_Ouminus__class_Ouminus(X2,X1) != c_Groups_Ouminus__class_Ouminus(X2,X0)
| ~ class_Groups_Ogroup__add(X2) ),
inference(cnf_transformation,[],[f3724]) ).
fof(f3724,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ouminus__class_Ouminus(X2,X1) = c_Groups_Ouminus__class_Ouminus(X2,X0)
| X0 != X1 )
& ( X0 = X1
| c_Groups_Ouminus__class_Ouminus(X2,X1) != c_Groups_Ouminus__class_Ouminus(X2,X0) ) )
| ~ class_Groups_Ogroup__add(X2) ),
inference(nnf_transformation,[],[f2797]) ).
fof(f2797,plain,
! [X0,X1,X2] :
( ( c_Groups_Ouminus__class_Ouminus(X2,X1) = c_Groups_Ouminus__class_Ouminus(X2,X0)
<=> X0 = X1 )
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f1766]) ).
fof(f1766,plain,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> ( c_Groups_Ouminus__class_Ouminus(X2,X1) = c_Groups_Ouminus__class_Ouminus(X2,X0)
<=> X0 = X1 ) ),
inference(rectify,[],[f400]) ).
fof(f400,axiom,
! [X29,X12,X5] :
( class_Groups_Ogroup__add(X5)
=> ( c_Groups_Ouminus__class_Ouminus(X5,X29) = c_Groups_Ouminus__class_Ouminus(X5,X12)
<=> X12 = X29 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).
fof(f9094,plain,
spl47_482,
inference(avatar_split_clause,[],[f4822,f9092]) ).
fof(f4822,plain,
! [X2,X0,X1] :
( X0 = X1
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Ominus__class_Ominus(X2,X1,X0)
| ~ class_Groups_Ogroup__add(X2) ),
inference(cnf_transformation,[],[f3722]) ).
fof(f3722,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Ominus__class_Ominus(X2,X1,X0)
| X0 != X1 )
& ( X0 = X1
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Ominus__class_Ominus(X2,X1,X0) ) )
| ~ class_Groups_Ogroup__add(X2) ),
inference(nnf_transformation,[],[f2795]) ).
fof(f2795,plain,
! [X0,X1,X2] :
( ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Ominus__class_Ominus(X2,X1,X0)
<=> X0 = X1 )
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f1764]) ).
fof(f1764,plain,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Ominus__class_Ominus(X2,X1,X0)
<=> X0 = X1 ) ),
inference(rectify,[],[f801]) ).
fof(f801,axiom,
! [X29,X12,X5] :
( class_Groups_Ogroup__add(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) = c_Groups_Ominus__class_Ominus(X5,X12,X29)
<=> X12 = X29 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus__eq) ).
fof(f9087,plain,
spl47_481,
inference(avatar_split_clause,[],[f4661,f9085]) ).
fof(f9085,plain,
( spl47_481
<=> ! [X2,X0,X1] :
( X0 = X1
| c_Groups_Ouminus__class_Ouminus(X2,X1) != c_Groups_Ouminus__class_Ouminus(X2,X0)
| ~ class_Lattices_Oboolean__algebra(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_481])]) ).
fof(f4661,plain,
! [X2,X0,X1] :
( X0 = X1
| c_Groups_Ouminus__class_Ouminus(X2,X1) != c_Groups_Ouminus__class_Ouminus(X2,X0)
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(cnf_transformation,[],[f3672]) ).
fof(f3672,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ouminus__class_Ouminus(X2,X1) = c_Groups_Ouminus__class_Ouminus(X2,X0)
| X0 != X1 )
& ( X0 = X1
| c_Groups_Ouminus__class_Ouminus(X2,X1) != c_Groups_Ouminus__class_Ouminus(X2,X0) ) )
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(nnf_transformation,[],[f2645]) ).
fof(f2645,plain,
! [X0,X1,X2] :
( ( c_Groups_Ouminus__class_Ouminus(X2,X1) = c_Groups_Ouminus__class_Ouminus(X2,X0)
<=> X0 = X1 )
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(ennf_transformation,[],[f1664]) ).
fof(f1664,plain,
! [X0,X1,X2] :
( class_Lattices_Oboolean__algebra(X2)
=> ( c_Groups_Ouminus__class_Ouminus(X2,X1) = c_Groups_Ouminus__class_Ouminus(X2,X0)
<=> X0 = X1 ) ),
inference(rectify,[],[f631]) ).
fof(f631,axiom,
! [X25,X15,X5] :
( class_Lattices_Oboolean__algebra(X5)
=> ( c_Groups_Ouminus__class_Ouminus(X5,X25) = c_Groups_Ouminus__class_Ouminus(X5,X15)
<=> X15 = X25 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).
fof(f9083,plain,
spl47_480,
inference(avatar_split_clause,[],[f4585,f9081]) ).
fof(f9081,plain,
( spl47_480
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_480])]) ).
fof(f4585,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3647]) ).
fof(f3647,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ) ),
inference(nnf_transformation,[],[f1598]) ).
fof(f1598,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(rectify,[],[f831]) ).
fof(f831,axiom,
! [X14,X11] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X14))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__diff) ).
fof(f9079,plain,
spl47_479,
inference(avatar_split_clause,[],[f4584,f9077]) ).
fof(f9077,plain,
( spl47_479
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_479])]) ).
fof(f4584,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ),
inference(cnf_transformation,[],[f3647]) ).
fof(f9075,plain,
spl47_478,
inference(avatar_split_clause,[],[f4582,f9073]) ).
fof(f4582,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3646]) ).
fof(f9071,plain,
spl47_477,
inference(avatar_split_clause,[],[f4580,f9069]) ).
fof(f4580,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3644]) ).
fof(f3644,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(nnf_transformation,[],[f1596]) ).
fof(f1596,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(rectify,[],[f470]) ).
fof(f470,axiom,
! [X30,X49] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X30,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X49,X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).
fof(f9067,plain,
spl47_476,
inference(avatar_split_clause,[],[f4579,f9065]) ).
fof(f9065,plain,
( spl47_476
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_476])]) ).
fof(f4579,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f3644]) ).
fof(f9063,plain,
spl47_475,
inference(avatar_split_clause,[],[f4577,f9061]) ).
fof(f9061,plain,
( spl47_475
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_475])]) ).
fof(f4577,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) ),
inference(cnf_transformation,[],[f3643]) ).
fof(f3643,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) ) ),
inference(nnf_transformation,[],[f1595]) ).
fof(f1595,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(rectify,[],[f471]) ).
fof(f471,axiom,
! [X30,X49] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X49,c_Groups_Oone__class_Oone(tc_Int_Oint)),X30)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add1__zle__eq) ).
fof(f9059,plain,
spl47_474,
inference(avatar_split_clause,[],[f4576,f9057]) ).
fof(f9057,plain,
( spl47_474
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_474])]) ).
fof(f4576,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3642]) ).
fof(f3642,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(nnf_transformation,[],[f1594]) ).
fof(f1594,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(rectify,[],[f899]) ).
fof(f899,axiom,
! [X30,X49] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X49,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X30,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).
fof(f9055,plain,
spl47_473,
inference(avatar_split_clause,[],[f4575,f9053]) ).
fof(f4575,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f3642]) ).
fof(f9051,plain,
spl47_472,
inference(avatar_split_clause,[],[f4515,f9049]) ).
fof(f9049,plain,
( spl47_472
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_472])]) ).
fof(f4515,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3605]) ).
fof(f3605,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
inference(nnf_transformation,[],[f1574]) ).
fof(f1574,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(rectify,[],[f895]) ).
fof(f895,axiom,
! [X47,X44] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X44,X47)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X44,X47),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__bin__lemma) ).
fof(f9044,plain,
spl47_471,
inference(avatar_split_clause,[],[f4514,f9042]) ).
fof(f9042,plain,
( spl47_471
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_471])]) ).
fof(f4514,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3605]) ).
fof(f9040,plain,
spl47_470,
inference(avatar_split_clause,[],[f4512,f9038]) ).
fof(f4512,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK36(X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3604]) ).
fof(f3604,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0 )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK36(X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK36])],[f3602,f3603]) ).
fof(f3603,plain,
! [X0,X1] :
( ? [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) = X0
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK36(X0,X1)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f3602,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0 )
& ( ? [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(rectify,[],[f3601]) ).
fof(f3601,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0 )
& ( ? [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f1573]) ).
fof(f1573,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
<=> ? [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = X0 ),
inference(rectify,[],[f463]) ).
fof(f463,axiom,
! [X47,X44] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X47)
<=> ? [X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X44,X19) = X47 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).
fof(f9036,plain,
spl47_469,
inference(avatar_split_clause,[],[f4510,f9034]) ).
fof(f4510,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK35(X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3600]) ).
fof(f3600,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0 )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK35(X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35])],[f3598,f3599]) ).
fof(f3599,plain,
! [X0,X1] :
( ? [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) = X0
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK35(X0,X1)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f3598,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0 )
& ( ? [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(rectify,[],[f3597]) ).
fof(f3597,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0 )
& ( ? [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f1572]) ).
fof(f1572,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
<=> ? [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = X0 ),
inference(rectify,[],[f337]) ).
fof(f337,axiom,
! [X11,X14] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X11)
<=> ? [X45] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X45) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).
fof(f9032,plain,
spl47_468,
inference(avatar_split_clause,[],[f4428,f9030]) ).
fof(f9030,plain,
( spl47_468
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_468])]) ).
fof(f4428,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f2534]) ).
fof(f2534,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(ennf_transformation,[],[f1511]) ).
fof(f1511,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) ),
inference(rectify,[],[f472]) ).
fof(f472,axiom,
! [X26,X48] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,X26)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X48,c_Groups_Oone__class_Oone(tc_Int_Oint)),X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).
fof(f9028,plain,
spl47_467,
inference(avatar_split_clause,[],[f4395,f9026]) ).
fof(f9026,plain,
( spl47_467
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_467])]) ).
fof(f4395,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2498]) ).
fof(f2498,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1482]) ).
fof(f1482,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0) ),
inference(rectify,[],[f513]) ).
fof(f513,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ozero__class_Ozero(X5)),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(f9024,plain,
spl47_466,
inference(avatar_split_clause,[],[f4394,f9022]) ).
fof(f9022,plain,
( spl47_466
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_466])]) ).
fof(f4394,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2497]) ).
fof(f2497,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1481]) ).
fof(f1481,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) ),
inference(rectify,[],[f512]) ).
fof(f512,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(f9020,plain,
spl47_465,
inference(avatar_split_clause,[],[f4393,f9018]) ).
fof(f9018,plain,
( spl47_465
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_465])]) ).
fof(f4393,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2496]) ).
fof(f2496,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1480]) ).
fof(f1480,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Groups_Oone__class_Oone(X1) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X0) ),
inference(rectify,[],[f204]) ).
fof(f204,axiom,
! [X6,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oone__class_Oone(X5) = hAPP(c_Polynomial_Opoly(X5,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X5))),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__1) ).
fof(f9016,plain,
spl47_464,
inference(avatar_split_clause,[],[f4392,f9014]) ).
fof(f9014,plain,
( spl47_464
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_464])]) ).
fof(f4392,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2495]) ).
fof(f2495,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1479]) ).
fof(f1479,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(rectify,[],[f386]) ).
fof(f386,axiom,
! [X6,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oone__class_Oone(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(f9012,plain,
spl47_463,
inference(avatar_split_clause,[],[f4380,f9010]) ).
fof(f9010,plain,
( spl47_463
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Rings_Ocomm__semiring__0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_463])]) ).
fof(f4380,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(cnf_transformation,[],[f2483]) ).
fof(f2483,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(ennf_transformation,[],[f1467]) ).
fof(f1467,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(rectify,[],[f101]) ).
fof(f101,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_Osmult(X5,X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__0__right) ).
fof(f9008,plain,
spl47_462,
inference(avatar_split_clause,[],[f4379,f9006]) ).
fof(f9006,plain,
( spl47_462
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osynthetic__div(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
| ~ class_Rings_Ocomm__semiring__0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_462])]) ).
fof(f4379,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osynthetic__div(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(cnf_transformation,[],[f2482]) ).
fof(f2482,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osynthetic__div(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(ennf_transformation,[],[f1466]) ).
fof(f1466,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osynthetic__div(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) ),
inference(rectify,[],[f64]) ).
fof(f64,axiom,
! [X16,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_Osynthetic__div(X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__0) ).
fof(f9000,plain,
spl47_461,
inference(avatar_split_clause,[],[f4378,f8998]) ).
fof(f8998,plain,
( spl47_461
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
| ~ class_Rings_Ocomm__semiring__0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_461])]) ).
fof(f4378,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(cnf_transformation,[],[f2481]) ).
fof(f2481,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(ennf_transformation,[],[f1465]) ).
fof(f1465,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) ),
inference(rectify,[],[f272]) ).
fof(f272,axiom,
! [X35,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__0) ).
fof(f8996,plain,
spl47_460,
inference(avatar_split_clause,[],[f4377,f8994]) ).
fof(f8994,plain,
( spl47_460
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Opcompose(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
| ~ class_Rings_Ocomm__semiring__0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_460])]) ).
fof(f4377,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Opcompose(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(cnf_transformation,[],[f2480]) ).
fof(f2480,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Opcompose(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(ennf_transformation,[],[f1464]) ).
fof(f1464,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Opcompose(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) ),
inference(rectify,[],[f692]) ).
fof(f692,axiom,
! [X13,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_Opcompose(X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pcompose__0) ).
fof(f8992,plain,
spl47_459,
inference(avatar_split_clause,[],[f4376,f8990]) ).
fof(f8990,plain,
( spl47_459
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0)
| ~ class_Rings_Ocomm__semiring__0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_459])]) ).
fof(f4376,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(cnf_transformation,[],[f2479]) ).
fof(f2479,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(ennf_transformation,[],[f1463]) ).
fof(f1463,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X6,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Polynomial_Opoly(X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__0) ).
fof(f8988,plain,
spl47_458,
inference(avatar_split_clause,[],[f4363,f8986]) ).
fof(f8986,plain,
( spl47_458
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0)
| ~ class_Groups_Ozero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_458])]) ).
fof(f4363,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0)
| ~ class_Groups_Ozero(X1) ),
inference(cnf_transformation,[],[f2469]) ).
fof(f2469,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0)
| ~ class_Groups_Ozero(X1) ),
inference(ennf_transformation,[],[f1454]) ).
fof(f1454,plain,
! [X0,X1] :
( class_Groups_Ozero(X1)
=> c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X0) ),
inference(rectify,[],[f824]) ).
fof(f824,axiom,
! [X7,X5] :
( class_Groups_Ozero(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Polynomial_Ocoeff(X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__0) ).
fof(f8984,plain,
spl47_457,
inference(avatar_split_clause,[],[f4357,f8982]) ).
fof(f8982,plain,
( spl47_457
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X0)
| ~ class_Groups_Omonoid__mult(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_457])]) ).
fof(f4357,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X0)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(cnf_transformation,[],[f2463]) ).
fof(f2463,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X0)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(ennf_transformation,[],[f1448]) ).
fof(f1448,plain,
! [X0,X1] :
( class_Groups_Omonoid__mult(X1)
=> c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X0) ),
inference(rectify,[],[f214]) ).
fof(f214,axiom,
! [X7,X5] :
( class_Groups_Omonoid__mult(X5)
=> c_Groups_Oone__class_Oone(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Oone__class_Oone(X5)),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).
fof(f8980,plain,
spl47_456,
inference(avatar_split_clause,[],[f4353,f8978]) ).
fof(f8978,plain,
( spl47_456
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Power_Opower(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_456])]) ).
fof(f4353,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Power_Opower(X1) ),
inference(cnf_transformation,[],[f2459]) ).
fof(f2459,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Power_Opower(X1) ),
inference(ennf_transformation,[],[f1444]) ).
fof(f1444,plain,
! [X0,X1] :
( class_Power_Opower(X1)
=> c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(rectify,[],[f254]) ).
fof(f254,axiom,
! [X4,X5] :
( class_Power_Opower(X5)
=> c_Groups_Oone__class_Oone(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0) ).
fof(f8976,plain,
spl47_455,
inference(avatar_split_clause,[],[f4352,f8974]) ).
fof(f8974,plain,
( spl47_455
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| ~ class_Rings_Omult__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_455])]) ).
fof(f4352,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| ~ class_Rings_Omult__zero(X1) ),
inference(cnf_transformation,[],[f2458]) ).
fof(f2458,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| ~ class_Rings_Omult__zero(X1) ),
inference(ennf_transformation,[],[f1443]) ).
fof(f1443,plain,
! [X0,X1] :
( class_Rings_Omult__zero(X1)
=> c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0) ),
inference(rectify,[],[f514]) ).
fof(f514,axiom,
! [X4,X5] :
( class_Rings_Omult__zero(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ozero__class_Ozero(X5)),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).
fof(f8972,plain,
spl47_454,
inference(avatar_split_clause,[],[f4351,f8970]) ).
fof(f4351,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Omult__zero(X1) ),
inference(cnf_transformation,[],[f2457]) ).
fof(f2457,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Omult__zero(X1) ),
inference(ennf_transformation,[],[f1442]) ).
fof(f1442,plain,
! [X0,X1] :
( class_Rings_Omult__zero(X1)
=> c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) ),
inference(rectify,[],[f515]) ).
fof(f515,axiom,
! [X4,X5] :
( class_Rings_Omult__zero(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__right) ).
fof(f8968,plain,
spl47_453,
inference(avatar_split_clause,[],[f4342,f8966]) ).
fof(f8966,plain,
( spl47_453
<=> ! [X0,X1] :
( c_Polynomial_Odegree(X1,X0) = c_Polynomial_Odegree(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0))
| ~ class_Groups_Oab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_453])]) ).
fof(f4342,plain,
! [X0,X1] :
( c_Polynomial_Odegree(X1,X0) = c_Polynomial_Odegree(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0))
| ~ class_Groups_Oab__group__add(X1) ),
inference(cnf_transformation,[],[f2449]) ).
fof(f2449,plain,
! [X0,X1] :
( c_Polynomial_Odegree(X1,X0) = c_Polynomial_Odegree(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0))
| ~ class_Groups_Oab__group__add(X1) ),
inference(ennf_transformation,[],[f1434]) ).
fof(f1434,plain,
! [X0,X1] :
( class_Groups_Oab__group__add(X1)
=> c_Polynomial_Odegree(X1,X0) = c_Polynomial_Odegree(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0)) ),
inference(rectify,[],[f425]) ).
fof(f425,axiom,
! [X8,X5] :
( class_Groups_Oab__group__add(X5)
=> c_Polynomial_Odegree(X5,X8) = c_Polynomial_Odegree(X5,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__minus) ).
fof(f8964,plain,
spl47_452,
inference(avatar_split_clause,[],[f4336,f8962]) ).
fof(f8962,plain,
( spl47_452
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Ouminus__class_Ouminus(X1,X0)
| ~ class_Groups_Ogroup__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_452])]) ).
fof(f4336,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Ouminus__class_Ouminus(X1,X0)
| ~ class_Groups_Ogroup__add(X1) ),
inference(cnf_transformation,[],[f3571]) ).
fof(f3571,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,X0)
| c_Groups_Ozero__class_Ozero(X1) != X0 )
& ( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Ouminus__class_Ouminus(X1,X0) ) )
| ~ class_Groups_Ogroup__add(X1) ),
inference(nnf_transformation,[],[f2445]) ).
fof(f2445,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_Groups_Ogroup__add(X1) ),
inference(ennf_transformation,[],[f1430]) ).
fof(f1430,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f409]) ).
fof(f409,axiom,
! [X12,X5] :
( class_Groups_Ogroup__add(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) = c_Groups_Ouminus__class_Ouminus(X5,X12)
<=> c_Groups_Ozero__class_Ozero(X5) = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).
fof(f8952,plain,
spl47_451,
inference(avatar_split_clause,[],[f4282,f8950]) ).
fof(f8950,plain,
( spl47_451
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0))
| ~ class_Rings_Olinordered__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_451])]) ).
fof(f4282,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0))
| ~ class_Rings_Olinordered__ring(X1) ),
inference(cnf_transformation,[],[f2410]) ).
fof(f2410,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0))
| ~ class_Rings_Olinordered__ring(X1) ),
inference(ennf_transformation,[],[f1396]) ).
fof(f1396,plain,
! [X0,X1] :
( class_Rings_Olinordered__ring(X1)
=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0)) ),
inference(rectify,[],[f547]) ).
fof(f547,axiom,
! [X4,X5] :
( class_Rings_Olinordered__ring(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__square) ).
fof(f8948,plain,
spl47_450,
inference(avatar_split_clause,[],[f4281,f8946]) ).
fof(f8946,plain,
( spl47_450
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_450])]) ).
fof(f4281,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring(X1) ),
inference(cnf_transformation,[],[f2409]) ).
fof(f2409,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring(X1) ),
inference(ennf_transformation,[],[f1395]) ).
fof(f1395,plain,
! [X0,X1] :
( class_Rings_Olinordered__ring(X1)
=> ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0),c_Groups_Ozero__class_Ozero(X1)) ),
inference(rectify,[],[f580]) ).
fof(f580,axiom,
! [X4,X5] :
( class_Rings_Olinordered__ring(X5)
=> ~ c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X4),c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
fof(f8944,plain,
spl47_449,
inference(avatar_split_clause,[],[f4279,f8942]) ).
fof(f8942,plain,
( spl47_449
<=> ! [X0,X1] :
( c_Polynomial_Opdivmod__rel(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
| ~ class_Fields_Ofield(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_449])]) ).
fof(f4279,plain,
! [X0,X1] :
( c_Polynomial_Opdivmod__rel(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
| ~ class_Fields_Ofield(X1) ),
inference(cnf_transformation,[],[f2407]) ).
fof(f2407,plain,
! [X0,X1] :
( c_Polynomial_Opdivmod__rel(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0)
| ~ class_Fields_Ofield(X1) ),
inference(ennf_transformation,[],[f1393]) ).
fof(f1393,plain,
! [X0,X1] :
( class_Fields_Ofield(X1)
=> c_Polynomial_Opdivmod__rel(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) ),
inference(rectify,[],[f735]) ).
fof(f735,axiom,
! [X6,X5] :
( class_Fields_Ofield(X5)
=> c_Polynomial_Opdivmod__rel(X5,X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__by__0) ).
fof(f8940,plain,
spl47_448,
inference(avatar_split_clause,[],[f4277,f8938]) ).
fof(f8938,plain,
( spl47_448
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| ~ class_RealVector_Oreal__normed__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_448])]) ).
fof(f4277,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(cnf_transformation,[],[f2405]) ).
fof(f2405,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(ennf_transformation,[],[f1391]) ).
fof(f1391,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__algebra(X1)
=> c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0) ),
inference(rectify,[],[f742]) ).
fof(f742,axiom,
! [X10,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ozero__class_Ozero(X5)),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).
fof(f8936,plain,
spl47_447,
inference(avatar_split_clause,[],[f4275,f8934]) ).
fof(f8934,plain,
( spl47_447
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_447])]) ).
fof(f4275,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(cnf_transformation,[],[f2403]) ).
fof(f2403,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(ennf_transformation,[],[f1389]) ).
fof(f1389,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__algebra(X1)
=> c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) ),
inference(rectify,[],[f743]) ).
fof(f743,axiom,
! [X4,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).
fof(f8932,plain,
spl47_446,
inference(avatar_split_clause,[],[f4225,f8930]) ).
fof(f8930,plain,
( spl47_446
<=> ! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_446])]) ).
fof(f4225,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(cnf_transformation,[],[f3548]) ).
fof(f3548,plain,
! [X0] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0 )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(nnf_transformation,[],[f1344]) ).
fof(f1344,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 ),
inference(rectify,[],[f239]) ).
fof(f239,axiom,
! [X14] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X14),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__1__iff__1) ).
fof(f8928,plain,
spl47_445,
inference(avatar_split_clause,[],[f4180,f8926]) ).
fof(f8926,plain,
( spl47_445
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0)))
| ~ class_Rings_Olinordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_445])]) ).
fof(f4180,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0)))
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(cnf_transformation,[],[f2356]) ).
fof(f2356,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0)))
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(ennf_transformation,[],[f1304]) ).
fof(f1304,plain,
! [X0] :
( class_Rings_Olinordered__semidom(X0)
=> c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0))) ),
inference(rectify,[],[f144]) ).
fof(f144,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Oone__class_Oone(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).
fof(f8924,plain,
spl47_444,
inference(avatar_split_clause,[],[f4175,f8922]) ).
fof(f8922,plain,
( spl47_444
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Groups_Oab__group__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_444])]) ).
fof(f4175,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f2351]) ).
fof(f2351,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Groups_Oab__group__add(X0) ),
inference(ennf_transformation,[],[f1299]) ).
fof(f1299,plain,
! [X0] :
( class_Groups_Oab__group__add(X0)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
inference(rectify,[],[f424]) ).
fof(f424,axiom,
! [X5] :
( class_Groups_Oab__group__add(X5)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I1_J) ).
fof(f8858,plain,
( spl47_443
| ~ spl47_268
| ~ spl47_356 ),
inference(avatar_split_clause,[],[f8026,f7822,f7275,f8856]) ).
fof(f8856,plain,
( spl47_443
<=> ! [X0] : ~ sP11(X0,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_443])]) ).
fof(f8026,plain,
( ! [X0] : ~ sP11(X0,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Rings_Odvd__class_Odvd(tc_Nat_Onat))
| ~ spl47_268
| ~ spl47_356 ),
inference(resolution,[],[f7823,f7276]) ).
fof(f8721,plain,
( spl47_442
| ~ spl47_266
| ~ spl47_356 ),
inference(avatar_split_clause,[],[f8025,f7822,f7266,f8719]) ).
fof(f8719,plain,
( spl47_442
<=> ! [X0] : ~ sP11(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0,c_Rings_Odvd__class_Odvd(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_442])]) ).
fof(f7266,plain,
( spl47_266
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_266])]) ).
fof(f8025,plain,
( ! [X0] : ~ sP11(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0,c_Rings_Odvd__class_Odvd(tc_Nat_Onat))
| ~ spl47_266
| ~ spl47_356 ),
inference(resolution,[],[f7823,f7267]) ).
fof(f7267,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ spl47_266 ),
inference(avatar_component_clause,[],[f7266]) ).
fof(f8532,plain,
( spl47_441
| ~ spl47_347 ),
inference(avatar_split_clause,[],[f7939,f7786,f8530]) ).
fof(f8530,plain,
( spl47_441
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X1)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_441])]) ).
fof(f7786,plain,
( spl47_347
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_347])]) ).
fof(f7939,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X1)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl47_347 ),
inference(factoring,[],[f7787]) ).
fof(f7787,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl47_347 ),
inference(avatar_component_clause,[],[f7786]) ).
fof(f8358,plain,
spl47_440,
inference(avatar_split_clause,[],[f5968,f8356]) ).
fof(f8356,plain,
( spl47_440
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_440])]) ).
fof(f5968,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ sP6(X0,X1) ),
inference(forward_demodulation,[],[f5967,f4114]) ).
fof(f5967,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ sP6(X0,X1) ),
inference(forward_demodulation,[],[f5606,f4240]) ).
fof(f5606,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
| ~ sP6(X0,X1) ),
inference(definition_unfolding,[],[f4567,f4118]) ).
fof(f4567,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f3640]) ).
fof(f3640,plain,
! [X0,X1] :
( ( sP6(X0,X1)
| ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
& ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ sP6(X0,X1) ) ),
inference(flattening,[],[f3639]) ).
fof(f3639,plain,
! [X0,X1] :
( ( sP6(X0,X1)
| ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
& ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ sP6(X0,X1) ) ),
inference(nnf_transformation,[],[f3485]) ).
fof(f3485,plain,
! [X0,X1] :
( sP6(X0,X1)
<=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f8354,plain,
spl47_439,
inference(avatar_split_clause,[],[f5966,f8352]) ).
fof(f8352,plain,
( spl47_439
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_439])]) ).
fof(f5966,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP6(X0,X1) ),
inference(forward_demodulation,[],[f5965,f4114]) ).
fof(f5965,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP6(X0,X1) ),
inference(forward_demodulation,[],[f5964,f4240]) ).
fof(f5964,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
| ~ sP6(X0,X1) ),
inference(forward_demodulation,[],[f5963,f4114]) ).
fof(f5963,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
| ~ sP6(X0,X1) ),
inference(forward_demodulation,[],[f5605,f4240]) ).
fof(f5605,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
| ~ sP6(X0,X1) ),
inference(definition_unfolding,[],[f4569,f4118,f4118]) ).
fof(f4569,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f3640]) ).
fof(f8350,plain,
spl47_438,
inference(avatar_split_clause,[],[f5962,f8348]) ).
fof(f8348,plain,
( spl47_438
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_438])]) ).
fof(f5962,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP6(X0,X1) ),
inference(forward_demodulation,[],[f5961,f4114]) ).
fof(f5961,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP6(X0,X1) ),
inference(forward_demodulation,[],[f5604,f4240]) ).
fof(f5604,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP6(X0,X1) ),
inference(definition_unfolding,[],[f4570,f4118]) ).
fof(f4570,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f3640]) ).
fof(f8346,plain,
spl47_437,
inference(avatar_split_clause,[],[f5952,f8344]) ).
fof(f8344,plain,
( spl47_437
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_437])]) ).
fof(f5952,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ sP5(X0,X1) ),
inference(forward_demodulation,[],[f5951,f4114]) ).
fof(f5951,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ sP5(X0,X1) ),
inference(forward_demodulation,[],[f5599,f4240]) ).
fof(f5599,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
| ~ sP5(X0,X1) ),
inference(definition_unfolding,[],[f4559,f4118]) ).
fof(f4559,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f3637]) ).
fof(f3637,plain,
! [X0,X1] :
( ( sP5(X0,X1)
| ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
& ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ sP5(X0,X1) ) ),
inference(flattening,[],[f3636]) ).
fof(f3636,plain,
! [X0,X1] :
( ( sP5(X0,X1)
| ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
& ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ sP5(X0,X1) ) ),
inference(nnf_transformation,[],[f3483]) ).
fof(f3483,plain,
! [X0,X1] :
( sP5(X0,X1)
<=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f8342,plain,
spl47_436,
inference(avatar_split_clause,[],[f5950,f8340]) ).
fof(f8340,plain,
( spl47_436
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_436])]) ).
fof(f5950,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP5(X0,X1) ),
inference(forward_demodulation,[],[f5949,f4114]) ).
fof(f5949,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP5(X0,X1) ),
inference(forward_demodulation,[],[f5948,f4240]) ).
fof(f5948,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
| ~ sP5(X0,X1) ),
inference(forward_demodulation,[],[f5947,f4114]) ).
fof(f5947,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
| ~ sP5(X0,X1) ),
inference(forward_demodulation,[],[f5598,f4240]) ).
fof(f5598,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
| ~ sP5(X0,X1) ),
inference(definition_unfolding,[],[f4561,f4118,f4118]) ).
fof(f4561,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f3637]) ).
fof(f8338,plain,
spl47_435,
inference(avatar_split_clause,[],[f5946,f8336]) ).
fof(f8336,plain,
( spl47_435
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_435])]) ).
fof(f5946,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP5(X0,X1) ),
inference(forward_demodulation,[],[f5945,f4114]) ).
fof(f5945,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP5(X0,X1) ),
inference(forward_demodulation,[],[f5597,f4240]) ).
fof(f5597,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP5(X0,X1) ),
inference(definition_unfolding,[],[f4562,f4118]) ).
fof(f4562,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f3637]) ).
fof(f8334,plain,
spl47_434,
inference(avatar_split_clause,[],[f5912,f8332]) ).
fof(f8332,plain,
( spl47_434
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_434])]) ).
fof(f5912,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
inference(forward_demodulation,[],[f5531,f5515]) ).
fof(f5531,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(definition_unfolding,[],[f4237,f4118]) ).
fof(f4237,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
inference(cnf_transformation,[],[f1353]) ).
fof(f1353,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
inference(rectify,[],[f344]) ).
fof(f344,axiom,
! [X21,X32] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X32))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
fof(f8330,plain,
( spl47_433
| ~ spl47_252
| ~ spl47_321 ),
inference(avatar_split_clause,[],[f7693,f7515,f7197,f8327]) ).
fof(f8327,plain,
( spl47_433
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK31,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_433])]) ).
fof(f7197,plain,
( spl47_252
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_252])]) ).
fof(f7515,plain,
( spl47_321
<=> c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK31,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_321])]) ).
fof(f7693,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK31,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))
| ~ spl47_252
| ~ spl47_321 ),
inference(superposition,[],[f7198,f7517]) ).
fof(f7517,plain,
( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK31,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl47_321 ),
inference(avatar_component_clause,[],[f7515]) ).
fof(f7198,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ spl47_252 ),
inference(avatar_component_clause,[],[f7197]) ).
fof(f8325,plain,
spl47_432,
inference(avatar_split_clause,[],[f5911,f8323]) ).
fof(f8323,plain,
( spl47_432
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_432])]) ).
fof(f5911,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))),
inference(forward_demodulation,[],[f5530,f5515]) ).
fof(f5530,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(definition_unfolding,[],[f4236,f4118]) ).
fof(f4236,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))),
inference(cnf_transformation,[],[f1352]) ).
fof(f1352,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))),
inference(rectify,[],[f343]) ).
fof(f343,axiom,
! [X21,X32] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X21))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
fof(f8321,plain,
spl47_431,
inference(avatar_split_clause,[],[f5849,f8319]) ).
fof(f8319,plain,
( spl47_431
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| ~ sP18(X0,X1,X2,c_Groups_Ozero__class_Ozero(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_431])]) ).
fof(f5849,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| ~ sP18(X0,X1,X2,c_Groups_Ozero__class_Ozero(X2)) ),
inference(equality_resolution,[],[f5187]) ).
fof(f5187,plain,
! [X2,X3,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Groups_Ozero__class_Ozero(X2) != X3
| ~ sP18(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3842]) ).
fof(f8317,plain,
spl47_430,
inference(avatar_split_clause,[],[f5808,f8315]) ).
fof(f8315,plain,
( spl47_430
<=> ! [X4,X0,X2] :
( hBOOL(hAPP(X0,X4))
| ~ sP13(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_430])]) ).
fof(f5808,plain,
! [X2,X0,X4] :
( hBOOL(hAPP(X0,X4))
| ~ sP13(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4),X2) ),
inference(equality_resolution,[],[f5071]) ).
fof(f5071,plain,
! [X2,X0,X1,X4] :
( hBOOL(hAPP(X0,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X1
| ~ sP13(X0,X1,X2) ),
inference(cnf_transformation,[],[f3793]) ).
fof(f8313,plain,
spl47_429,
inference(avatar_split_clause,[],[f5807,f8311]) ).
fof(f8311,plain,
( spl47_429
<=> ! [X4,X0,X2] :
( hBOOL(hAPP(X0,X4))
| ~ sP12(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_429])]) ).
fof(f5807,plain,
! [X2,X0,X4] :
( hBOOL(hAPP(X0,X4))
| ~ sP12(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4),X2) ),
inference(equality_resolution,[],[f5063]) ).
fof(f5063,plain,
! [X2,X0,X1,X4] :
( hBOOL(hAPP(X0,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X1
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f3787]) ).
fof(f8309,plain,
spl47_428,
inference(avatar_split_clause,[],[f5767,f8307]) ).
fof(f8307,plain,
( spl47_428
<=> ! [X2,X0] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ class_Rings_Oidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_428])]) ).
fof(f5767,plain,
! [X2,X0] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ class_Rings_Oidom(X2) ),
inference(equality_resolution,[],[f4834]) ).
fof(f4834,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(X2) != X1
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f3729]) ).
fof(f8305,plain,
spl47_427,
inference(avatar_split_clause,[],[f5664,f8303]) ).
fof(f8303,plain,
( spl47_427
<=> ! [X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_427])]) ).
fof(f5664,plain,
! [X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(equality_resolution,[],[f4296]) ).
fof(f4296,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X0,X0)
| c_Groups_Ozero__class_Ozero(X1) != X0
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3556]) ).
fof(f8301,plain,
spl47_426,
inference(avatar_split_clause,[],[f5532,f8299]) ).
fof(f8299,plain,
( spl47_426
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_426])]) ).
fof(f5532,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(definition_unfolding,[],[f4238,f4118]) ).
fof(f4238,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Nat_OSuc(X1)),
inference(cnf_transformation,[],[f1354]) ).
fof(f1354,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Nat_OSuc(X1)),
inference(rectify,[],[f829]) ).
fof(f829,axiom,
! [X7,X21] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X7),c_Nat_OSuc(X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
fof(f8297,plain,
spl47_425,
inference(avatar_split_clause,[],[f5122,f8295]) ).
fof(f8295,plain,
( spl47_425
<=> ! [X2,X0,X1,X3] : hAPP(hAPP(c_Power_Opower_Opower(X3,X2,X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_425])]) ).
fof(f5122,plain,
! [X2,X3,X0,X1] : hAPP(hAPP(c_Power_Opower_Opower(X3,X2,X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
inference(cnf_transformation,[],[f1960]) ).
fof(f1960,plain,
! [X0,X1,X2,X3] : hAPP(hAPP(c_Power_Opower_Opower(X3,X2,X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
inference(rectify,[],[f694]) ).
fof(f694,axiom,
! [X12,X65,X66,X5] : hAPP(hAPP(c_Power_Opower_Opower(X5,X66,X65),X12),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X66,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).
fof(f8293,plain,
spl47_424,
inference(avatar_split_clause,[],[f5077,f8291]) ).
fof(f5077,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP13(X2,X1,X0) ),
inference(cnf_transformation,[],[f3794]) ).
fof(f3794,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP13(X2,X1,X0) )
& ( sP13(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
inference(nnf_transformation,[],[f3498]) ).
fof(f3498,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
<=> sP13(X2,X1,X0) ),
inference(definition_folding,[],[f3052,f3497]) ).
fof(f3052,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
<=> ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ) ),
inference(ennf_transformation,[],[f1941]) ).
fof(f1941,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
<=> ~ ( ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X1 )
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ) ),
inference(rectify,[],[f857]) ).
fof(f857,axiom,
! [X29,X12,X39] :
( hBOOL(hAPP(X39,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X29)))
<=> ~ ( ? [X84] :
( ~ hBOOL(hAPP(X39,X84))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X84) = X12 )
| ( ~ hBOOL(hAPP(X39,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X29) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
fof(f8289,plain,
spl47_423,
inference(avatar_split_clause,[],[f5076,f8287]) ).
fof(f5076,plain,
! [X2,X0,X1] :
( sP13(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f3794]) ).
fof(f8285,plain,
( ~ spl47_422
| ~ spl47_250
| ~ spl47_321 ),
inference(avatar_split_clause,[],[f7691,f7515,f7189,f8282]) ).
fof(f8282,plain,
( spl47_422
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),sK31) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_422])]) ).
fof(f7189,plain,
( spl47_250
<=> ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_250])]) ).
fof(f7691,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),sK31)
| ~ spl47_250
| ~ spl47_321 ),
inference(superposition,[],[f7190,f7517]) ).
fof(f7190,plain,
( ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1)
| ~ spl47_250 ),
inference(avatar_component_clause,[],[f7189]) ).
fof(f8280,plain,
spl47_421,
inference(avatar_split_clause,[],[f5069,f8278]) ).
fof(f5069,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP12(X2,X1,X0) ),
inference(cnf_transformation,[],[f3788]) ).
fof(f3788,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP12(X2,X1,X0) )
& ( sP12(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
inference(nnf_transformation,[],[f3496]) ).
fof(f3496,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
<=> sP12(X2,X1,X0) ),
inference(definition_folding,[],[f3051,f3495]) ).
fof(f3051,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
<=> ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ) ),
inference(ennf_transformation,[],[f1940]) ).
fof(f1940,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
<=> ( ! [X3] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X1
=> hBOOL(hAPP(X2,X3)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
inference(rectify,[],[f858]) ).
fof(f858,axiom,
! [X29,X12,X39] :
( hBOOL(hAPP(X39,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X29)))
<=> ( ! [X84] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X84) = X12
=> hBOOL(hAPP(X39,X84)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X29)
=> hBOOL(hAPP(X39,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split) ).
fof(f8276,plain,
spl47_420,
inference(avatar_split_clause,[],[f5068,f8274]) ).
fof(f5068,plain,
! [X2,X0,X1] :
( sP12(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f3788]) ).
fof(f8272,plain,
spl47_419,
inference(avatar_split_clause,[],[f5029,f8270]) ).
fof(f8270,plain,
( spl47_419
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_419])]) ).
fof(f5029,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) ),
inference(cnf_transformation,[],[f3014]) ).
fof(f3014,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) ),
inference(ennf_transformation,[],[f1921]) ).
fof(f1921,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) ),
inference(rectify,[],[f319]) ).
fof(f319,axiom,
! [X20,X33,X32] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X33),X20)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32,X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).
fof(f8268,plain,
spl47_418,
inference(avatar_split_clause,[],[f5026,f8266]) ).
fof(f8266,plain,
( spl47_418
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_418])]) ).
fof(f5026,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) ),
inference(cnf_transformation,[],[f3012]) ).
fof(f3012,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) ),
inference(ennf_transformation,[],[f1919]) ).
fof(f1919,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ),
inference(rectify,[],[f330]) ).
fof(f330,axiom,
! [X7,X20,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X20),X7)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).
fof(f8264,plain,
spl47_417,
inference(avatar_split_clause,[],[f5025,f8262]) ).
fof(f8262,plain,
( spl47_417
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_417])]) ).
fof(f5025,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) ),
inference(cnf_transformation,[],[f3011]) ).
fof(f3011,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) ),
inference(ennf_transformation,[],[f1918]) ).
fof(f1918,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f331]) ).
fof(f331,axiom,
! [X7,X20,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X20),X7)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).
fof(f8260,plain,
spl47_416,
inference(avatar_split_clause,[],[f5000,f8258]) ).
fof(f5000,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2979]) ).
fof(f2979,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1899]) ).
fof(f1899,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),X1) ),
inference(rectify,[],[f791]) ).
fof(f791,axiom,
! [X7,X20,X33] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,X20)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,X7),X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
fof(f8256,plain,
spl47_415,
inference(avatar_split_clause,[],[f4997,f8254]) ).
fof(f8254,plain,
( spl47_415
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_415])]) ).
fof(f4997,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2976]) ).
fof(f2976,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1896]) ).
fof(f1896,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(rectify,[],[f449]) ).
fof(f449,axiom,
! [X10,X26,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X26)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(f8252,plain,
spl47_414,
inference(avatar_split_clause,[],[f4996,f8250]) ).
fof(f4996,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2975]) ).
fof(f2975,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1895]) ).
fof(f1895,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(rectify,[],[f324]) ).
fof(f324,axiom,
! [X21,X33,X32] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32,X33)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).
fof(f8248,plain,
spl47_413,
inference(avatar_split_clause,[],[f4966,f8246]) ).
fof(f8246,plain,
( spl47_413
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_413])]) ).
fof(f4966,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2944]) ).
fof(f2944,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1870]) ).
fof(f1870,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(rectify,[],[f451]) ).
fof(f451,axiom,
! [X10,X26,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X26)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
fof(f8244,plain,
spl47_412,
inference(avatar_split_clause,[],[f4965,f8242]) ).
fof(f8242,plain,
( spl47_412
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_412])]) ).
fof(f4965,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2943]) ).
fof(f2943,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1869]) ).
fof(f1869,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(rectify,[],[f335]) ).
fof(f335,axiom,
! [X21,X33,X32] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32,X33)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).
fof(f8240,plain,
( ~ spl47_411
| ~ spl47_280
| ~ spl47_321 ),
inference(avatar_split_clause,[],[f7688,f7515,f7323,f8237]) ).
fof(f8237,plain,
( spl47_411
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),sK31) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_411])]) ).
fof(f7688,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),sK31)
| ~ spl47_280
| ~ spl47_321 ),
inference(superposition,[],[f7324,f7517]) ).
fof(f8235,plain,
spl47_410,
inference(avatar_split_clause,[],[f4909,f8233]) ).
fof(f8233,plain,
( spl47_410
<=> ! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_410])]) ).
fof(f4909,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(cnf_transformation,[],[f2879]) ).
fof(f2879,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f1827]) ).
fof(f1827,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1) ),
inference(rectify,[],[f447]) ).
fof(f447,axiom,
! [X16,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,X4,X16) = c_Groups_Oplus__class_Oplus(X5,X16,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f8231,plain,
spl47_409,
inference(avatar_split_clause,[],[f4877,f8229]) ).
fof(f8229,plain,
( spl47_409
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)),X0)
| ~ class_Groups_Ozero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_409])]) ).
fof(f4877,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)),X0)
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f2850]) ).
fof(f2850,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)),X0)
| ~ class_Groups_Ozero(X2) ),
inference(ennf_transformation,[],[f1803]) ).
fof(f1803,plain,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X2,c_Polynomial_Omonom(X2,X1,X0)),X0) ),
inference(rectify,[],[f278]) ).
fof(f278,axiom,
! [X7,X4,X5] :
( class_Groups_Ozero(X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X5,c_Polynomial_Omonom(X5,X4,X7)),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__monom__le) ).
fof(f8227,plain,
spl47_408,
inference(avatar_split_clause,[],[f4799,f8225]) ).
fof(f8225,plain,
( spl47_408
<=> ! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1
| ~ class_Groups_Ogroup__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_408])]) ).
fof(f4799,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1
| ~ class_Groups_Ogroup__add(X2) ),
inference(cnf_transformation,[],[f2770]) ).
fof(f2770,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f1746]) ).
fof(f1746,plain,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1 ),
inference(rectify,[],[f761]) ).
fof(f761,axiom,
! [X17,X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Ominus__class_Ominus(X5,X4,X17),X17) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
fof(f8223,plain,
spl47_407,
inference(avatar_split_clause,[],[f4798,f8221]) ).
fof(f8221,plain,
( spl47_407
<=> ! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) = X1
| ~ class_Groups_Ogroup__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_407])]) ).
fof(f4798,plain,
! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) = X1
| ~ class_Groups_Ogroup__add(X2) ),
inference(cnf_transformation,[],[f2769]) ).
fof(f2769,plain,
! [X0,X1,X2] :
( c_Groups_Ominus__class_Ominus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) = X1
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f1745]) ).
fof(f1745,plain,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Ominus__class_Ominus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) = X1 ),
inference(rectify,[],[f760]) ).
fof(f760,axiom,
! [X17,X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ominus__class_Ominus(X5,c_Groups_Oplus__class_Oplus(X5,X4,X17),X17) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
fof(f8219,plain,
spl47_406,
inference(avatar_split_clause,[],[f4725,f8217]) ).
fof(f8217,plain,
( spl47_406
<=> ! [X2,X0,X1] :
( c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
| ~ c_Polynomial_Opos__poly(X2,X0)
| ~ class_Rings_Olinordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_406])]) ).
fof(f4725,plain,
! [X2,X0,X1] :
( c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X1,X0))
| ~ c_Polynomial_Opos__poly(X2,X0)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(cnf_transformation,[],[f3702]) ).
fof(f8215,plain,
spl47_405,
inference(avatar_split_clause,[],[f4568,f8213]) ).
fof(f8213,plain,
( spl47_405
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_405])]) ).
fof(f4568,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f3640]) ).
fof(f8211,plain,
spl47_404,
inference(avatar_split_clause,[],[f4560,f8209]) ).
fof(f8209,plain,
( spl47_404
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_404])]) ).
fof(f4560,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f3637]) ).
fof(f8207,plain,
spl47_403,
inference(avatar_split_clause,[],[f4549,f8205]) ).
fof(f8205,plain,
( spl47_403
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_403])]) ).
fof(f4549,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3631]) ).
fof(f3631,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ) ),
inference(flattening,[],[f3630]) ).
fof(f3630,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f1588]) ).
fof(f1588,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) ),
inference(rectify,[],[f312]) ).
fof(f312,axiom,
! [X11,X14] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X11)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X11
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).
fof(f8203,plain,
spl47_402,
inference(avatar_split_clause,[],[f4548,f8201]) ).
fof(f8201,plain,
( spl47_402
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_402])]) ).
fof(f4548,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3631]) ).
fof(f8199,plain,
spl47_401,
inference(avatar_split_clause,[],[f4546,f8197]) ).
fof(f8197,plain,
( spl47_401
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_401])]) ).
fof(f4546,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3629]) ).
fof(f3629,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f1587]) ).
fof(f1587,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f826]) ).
fof(f826,axiom,
! [X11,X14] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X14,X11)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
fof(f8195,plain,
( spl47_400
| ~ spl47_281
| ~ spl47_321 ),
inference(avatar_split_clause,[],[f7687,f7515,f7327,f8192]) ).
fof(f8192,plain,
( spl47_400
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK31,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_400])]) ).
fof(f7687,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK31,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))
| ~ spl47_281
| ~ spl47_321 ),
inference(superposition,[],[f7328,f7517]) ).
fof(f8190,plain,
spl47_399,
inference(avatar_split_clause,[],[f4518,f8188]) ).
fof(f8188,plain,
( spl47_399
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_399])]) ).
fof(f4518,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3607]) ).
fof(f3607,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
& ( ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
inference(flattening,[],[f3606]) ).
fof(f3606,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
& ( ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
inference(nnf_transformation,[],[f1575]) ).
fof(f1575,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
<=> ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
inference(rectify,[],[f469]) ).
fof(f469,axiom,
! [X49,X30] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X30,X49)
<=> ( X30 != X49
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X30,X49) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__le) ).
fof(f8186,plain,
spl47_398,
inference(avatar_split_clause,[],[f4425,f8184]) ).
fof(f8184,plain,
( spl47_398
<=> ! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_398])]) ).
fof(f4425,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2532]) ).
fof(f2532,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(flattening,[],[f2531]) ).
fof(f2531,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1509]) ).
fof(f1509,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
=> X0 = X1 ) ),
inference(rectify,[],[f82]) ).
fof(f82,axiom,
! [X7,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X21)
=> X7 = X21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).
fof(f8182,plain,
spl47_397,
inference(avatar_split_clause,[],[f4424,f8180]) ).
fof(f8180,plain,
( spl47_397
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_397])]) ).
fof(f4424,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2530]) ).
fof(f2530,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(flattening,[],[f2529]) ).
fof(f2529,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1508]) ).
fof(f1508,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> ( X0 != X1
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(rectify,[],[f234]) ).
fof(f234,axiom,
! [X7,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X7)
=> ( X7 != X21
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
fof(f8178,plain,
spl47_396,
inference(avatar_split_clause,[],[f4419,f8176]) ).
fof(f8176,plain,
( spl47_396
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_396])]) ).
fof(f4419,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2524]) ).
fof(f2524,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1503]) ).
fof(f1503,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f827]) ).
fof(f827,axiom,
! [X7,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X7)
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).
fof(f8174,plain,
spl47_395,
inference(avatar_split_clause,[],[f4416,f8172]) ).
fof(f8172,plain,
( spl47_395
<=> ! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_395])]) ).
fof(f4416,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f2521]) ).
fof(f2521,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(flattening,[],[f2520]) ).
fof(f2520,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(ennf_transformation,[],[f1500]) ).
fof(f1500,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
=> X0 = X1 ) ),
inference(rectify,[],[f475]) ).
fof(f475,axiom,
! [X48,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X26,X48)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X48,X26)
=> X26 = X48 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__antisym) ).
fof(f8170,plain,
spl47_394,
inference(avatar_split_clause,[],[f4407,f8168]) ).
fof(f8168,plain,
( spl47_394
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_394])]) ).
fof(f4407,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f2511]) ).
fof(f2511,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| X0 = X1 ),
inference(flattening,[],[f2510]) ).
fof(f2510,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| X0 = X1 ),
inference(ennf_transformation,[],[f1493]) ).
fof(f1493,plain,
! [X0,X1] :
( X0 != X1
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ) ),
inference(rectify,[],[f172]) ).
fof(f172,axiom,
! [X10,X6] :
( X6 != X10
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X10)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
fof(f8166,plain,
spl47_393,
inference(avatar_split_clause,[],[f4391,f8164]) ).
fof(f8164,plain,
( spl47_393
<=> ! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_393])]) ).
fof(f4391,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2494]) ).
fof(f2494,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1478]) ).
fof(f1478,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0 ),
inference(rectify,[],[f496]) ).
fof(f496,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oone__class_Oone(X5)),X4) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(f8162,plain,
spl47_392,
inference(avatar_split_clause,[],[f4390,f8160]) ).
fof(f8160,plain,
( spl47_392
<=> ! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_392])]) ).
fof(f4390,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2493]) ).
fof(f2493,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1477]) ).
fof(f1477,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0 ),
inference(rectify,[],[f495]) ).
fof(f495,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Oone__class_Oone(X5)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(f8158,plain,
spl47_391,
inference(avatar_split_clause,[],[f4389,f8156]) ).
fof(f8156,plain,
( spl47_391
<=> ! [X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_391])]) ).
fof(f4389,plain,
! [X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2492]) ).
fof(f2492,plain,
! [X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1476]) ).
fof(f1476,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 ),
inference(rectify,[],[f390]) ).
fof(f390,axiom,
! [X6,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(f8154,plain,
spl47_390,
inference(avatar_split_clause,[],[f4375,f8152]) ).
fof(f8152,plain,
( spl47_390
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Rings_Ocomm__semiring__0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_390])]) ).
fof(f4375,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(cnf_transformation,[],[f2478]) ).
fof(f2478,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(ennf_transformation,[],[f1462]) ).
fof(f1462,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(rectify,[],[f110]) ).
fof(f110,axiom,
! [X8,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_Osmult(X5,c_Groups_Ozero__class_Ozero(X5),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__0__left) ).
fof(f8150,plain,
( spl47_389
| ~ spl47_252
| ~ spl47_320 ),
inference(avatar_split_clause,[],[f7683,f7510,f7197,f8147]) ).
fof(f8147,plain,
( spl47_389
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_389])]) ).
fof(f7683,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_n____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))
| ~ spl47_252
| ~ spl47_320 ),
inference(superposition,[],[f7198,f7512]) ).
fof(f8145,plain,
spl47_388,
inference(avatar_split_clause,[],[f4362,f8143]) ).
fof(f8143,plain,
( spl47_388
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Omonom(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Ozero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_388])]) ).
fof(f4362,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Omonom(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Ozero(X1) ),
inference(cnf_transformation,[],[f2468]) ).
fof(f2468,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Omonom(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Ozero(X1) ),
inference(ennf_transformation,[],[f1453]) ).
fof(f1453,plain,
! [X0,X1] :
( class_Groups_Ozero(X1)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Omonom(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(rectify,[],[f275]) ).
fof(f275,axiom,
! [X7,X5] :
( class_Groups_Ozero(X5)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_Omonom(X5,c_Groups_Ozero__class_Ozero(X5),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__0) ).
fof(f8141,plain,
spl47_387,
inference(avatar_split_clause,[],[f4361,f8139]) ).
fof(f8139,plain,
( spl47_387
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = X0
| ~ class_Groups_Ocomm__monoid__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_387])]) ).
fof(f4361,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = X0
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(cnf_transformation,[],[f2467]) ).
fof(f2467,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = X0
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(ennf_transformation,[],[f1452]) ).
fof(f1452,plain,
! [X0,X1] :
( class_Groups_Ocomm__monoid__add(X1)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = X0 ),
inference(rectify,[],[f237]) ).
fof(f237,axiom,
! [X13,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X13) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).
fof(f8137,plain,
spl47_386,
inference(avatar_split_clause,[],[f4360,f8135]) ).
fof(f8135,plain,
( spl47_386
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0
| ~ class_Groups_Ocomm__monoid__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_386])]) ).
fof(f4360,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(cnf_transformation,[],[f2466]) ).
fof(f2466,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(ennf_transformation,[],[f1451]) ).
fof(f1451,plain,
! [X0,X1] :
( class_Groups_Ocomm__monoid__add(X1)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0 ),
inference(rectify,[],[f238]) ).
fof(f238,axiom,
! [X8,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),X8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).
fof(f8133,plain,
spl47_385,
inference(avatar_split_clause,[],[f4356,f8131]) ).
fof(f8131,plain,
( spl47_385
<=> ! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
| ~ class_Groups_Omonoid__mult(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_385])]) ).
fof(f4356,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
| ~ class_Groups_Omonoid__mult(X1) ),
inference(cnf_transformation,[],[f2462]) ).
fof(f2462,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
| ~ class_Groups_Omonoid__mult(X1) ),
inference(ennf_transformation,[],[f1447]) ).
fof(f1447,plain,
! [X0,X1] :
( class_Groups_Omonoid__mult(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0 ),
inference(rectify,[],[f521]) ).
fof(f521,axiom,
! [X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oone__class_Oone(X5)),X4) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__left) ).
fof(f8129,plain,
spl47_384,
inference(avatar_split_clause,[],[f4355,f8127]) ).
fof(f8127,plain,
( spl47_384
<=> ! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Groups_Omonoid__mult(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_384])]) ).
fof(f4355,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Groups_Omonoid__mult(X1) ),
inference(cnf_transformation,[],[f2461]) ).
fof(f2461,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Groups_Omonoid__mult(X1) ),
inference(ennf_transformation,[],[f1446]) ).
fof(f1446,plain,
! [X0,X1] :
( class_Groups_Omonoid__mult(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0 ),
inference(rectify,[],[f523]) ).
fof(f523,axiom,
! [X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Oone__class_Oone(X5)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).
fof(f8125,plain,
spl47_383,
inference(avatar_split_clause,[],[f4354,f8123]) ).
fof(f8123,plain,
( spl47_383
<=> ! [X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| ~ class_Groups_Omonoid__mult(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_383])]) ).
fof(f4354,plain,
! [X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| ~ class_Groups_Omonoid__mult(X1) ),
inference(cnf_transformation,[],[f2460]) ).
fof(f2460,plain,
! [X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| ~ class_Groups_Omonoid__mult(X1) ),
inference(ennf_transformation,[],[f1445]) ).
fof(f1445,plain,
! [X0,X1] :
( class_Groups_Omonoid__mult(X1)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 ),
inference(rectify,[],[f236]) ).
fof(f236,axiom,
! [X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__right) ).
fof(f8121,plain,
spl47_382,
inference(avatar_split_clause,[],[f4350,f8119]) ).
fof(f8119,plain,
( spl47_382
<=> ! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
| ~ class_Groups_Ocomm__monoid__mult(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_382])]) ).
fof(f4350,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(cnf_transformation,[],[f2456]) ).
fof(f2456,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(ennf_transformation,[],[f1441]) ).
fof(f1441,plain,
! [X0,X1] :
( class_Groups_Ocomm__monoid__mult(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0 ),
inference(rectify,[],[f522]) ).
fof(f522,axiom,
! [X4,X5] :
( class_Groups_Ocomm__monoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oone__class_Oone(X5)),X4) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).
fof(f8117,plain,
spl47_381,
inference(avatar_split_clause,[],[f4349,f8115]) ).
fof(f8115,plain,
( spl47_381
<=> ! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Groups_Ocomm__monoid__mult(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_381])]) ).
fof(f4349,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(cnf_transformation,[],[f2455]) ).
fof(f2455,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(ennf_transformation,[],[f1440]) ).
fof(f1440,plain,
! [X0,X1] :
( class_Groups_Ocomm__monoid__mult(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0 ),
inference(rectify,[],[f524]) ).
fof(f524,axiom,
! [X4,X5] :
( class_Groups_Ocomm__monoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Oone__class_Oone(X5)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
fof(f8113,plain,
spl47_380,
inference(avatar_split_clause,[],[f4341,f8111]) ).
fof(f8111,plain,
( spl47_380
<=> ! [X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0
| ~ class_Groups_Oab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_380])]) ).
fof(f4341,plain,
! [X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0
| ~ class_Groups_Oab__group__add(X1) ),
inference(cnf_transformation,[],[f2448]) ).
fof(f2448,plain,
! [X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0
| ~ class_Groups_Oab__group__add(X1) ),
inference(ennf_transformation,[],[f1433]) ).
fof(f1433,plain,
! [X0,X1] :
( class_Groups_Oab__group__add(X1)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X0 ),
inference(rectify,[],[f890]) ).
fof(f890,axiom,
! [X8,X5] :
( class_Groups_Oab__group__add(X5)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5),X8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__poly__code_I2_J) ).
fof(f8109,plain,
spl47_379,
inference(avatar_split_clause,[],[f4340,f8107]) ).
fof(f8107,plain,
( spl47_379
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Groups_Oab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_379])]) ).
fof(f4340,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Groups_Oab__group__add(X1) ),
inference(cnf_transformation,[],[f2447]) ).
fof(f2447,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Groups_Oab__group__add(X1) ),
inference(ennf_transformation,[],[f1432]) ).
fof(f1432,plain,
! [X0,X1] :
( class_Groups_Oab__group__add(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0) ),
inference(rectify,[],[f438]) ).
fof(f438,axiom,
! [X4,X5] :
( class_Groups_Oab__group__add(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Groups_Oplus__class_Oplus(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__left__minus) ).
fof(f8105,plain,
spl47_378,
inference(avatar_split_clause,[],[f4335,f8103]) ).
fof(f8103,plain,
( spl47_378
<=> ! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,X0) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Ogroup__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_378])]) ).
fof(f4335,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,X0) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Ogroup__add(X1) ),
inference(cnf_transformation,[],[f2444]) ).
fof(f2444,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,X0) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Ogroup__add(X1) ),
inference(ennf_transformation,[],[f1429]) ).
fof(f1429,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ouminus__class_Ouminus(X1,X0) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(rectify,[],[f836]) ).
fof(f836,axiom,
! [X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ouminus__class_Ouminus(X5,X4) = c_Groups_Ominus__class_Ominus(X5,c_Groups_Ozero__class_Ozero(X5),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0) ).
fof(f8101,plain,
spl47_377,
inference(avatar_split_clause,[],[f4334,f8099]) ).
fof(f8099,plain,
( spl47_377
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Groups_Ogroup__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_377])]) ).
fof(f4334,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Groups_Ogroup__add(X1) ),
inference(cnf_transformation,[],[f2443]) ).
fof(f2443,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Groups_Ogroup__add(X1) ),
inference(ennf_transformation,[],[f1428]) ).
fof(f1428,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0) ),
inference(rectify,[],[f437]) ).
fof(f437,axiom,
! [X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Groups_Oplus__class_Oplus(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__minus) ).
fof(f8097,plain,
spl47_376,
inference(avatar_split_clause,[],[f4333,f8095]) ).
fof(f8095,plain,
( spl47_376
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_Groups_Ogroup__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_376])]) ).
fof(f4333,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_Groups_Ogroup__add(X1) ),
inference(cnf_transformation,[],[f2442]) ).
fof(f2442,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_Groups_Ogroup__add(X1) ),
inference(ennf_transformation,[],[f1427]) ).
fof(f1427,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0)) ),
inference(rectify,[],[f435]) ).
fof(f435,axiom,
! [X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Ouminus__class_Ouminus(X5,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus) ).
fof(f8093,plain,
spl47_375,
inference(avatar_split_clause,[],[f4285,f8091]) ).
fof(f8091,plain,
( spl47_375
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ouminus__class_Ouminus(X1,X0) != X0
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_375])]) ).
fof(f4285,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ouminus__class_Ouminus(X1,X0) != X0
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3551]) ).
fof(f3551,plain,
! [X0,X1] :
( ( ( c_Groups_Ouminus__class_Ouminus(X1,X0) = X0
| c_Groups_Ozero__class_Ozero(X1) != X0 )
& ( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ouminus__class_Ouminus(X1,X0) != X0 ) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f2413]) ).
fof(f2413,plain,
! [X0,X1] :
( ( c_Groups_Ouminus__class_Ouminus(X1,X0) = X0
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f1399]) ).
fof(f1399,plain,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( c_Groups_Ouminus__class_Ouminus(X1,X0) = X0
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f408]) ).
fof(f408,axiom,
! [X12,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Groups_Ouminus__class_Ouminus(X5,X12) = X12
<=> c_Groups_Ozero__class_Ozero(X5) = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equal__neg__zero) ).
fof(f8089,plain,
spl47_374,
inference(avatar_split_clause,[],[f4267,f8087]) ).
fof(f8087,plain,
( spl47_374
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| X0 = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_374])]) ).
fof(f4267,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| X0 = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f1380]) ).
fof(f1380,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| X0 = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(rectify,[],[f494]) ).
fof(f494,axiom,
! [X10,X6] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X10,X6)
| X6 = X10
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__linear) ).
fof(f8085,plain,
spl47_373,
inference(avatar_split_clause,[],[f4248,f8083]) ).
fof(f8083,plain,
( spl47_373
<=> ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_373])]) ).
fof(f4248,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),
inference(cnf_transformation,[],[f1364]) ).
fof(f1364,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),
inference(rectify,[],[f891]) ).
fof(f891,axiom,
! [X48,X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X48)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X26,X48),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).
fof(f8081,plain,
spl47_372,
inference(avatar_split_clause,[],[f4186,f8079]) ).
fof(f8079,plain,
( spl47_372
<=> ! [X0] :
( c_Power_Opower__class_Opower(X0) = c_Power_Opower_Opower(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Otimes__class_Otimes(X0))
| ~ class_Power_Opower(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_372])]) ).
fof(f4186,plain,
! [X0] :
( c_Power_Opower__class_Opower(X0) = c_Power_Opower_Opower(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Otimes__class_Otimes(X0))
| ~ class_Power_Opower(X0) ),
inference(cnf_transformation,[],[f2362]) ).
fof(f2362,plain,
! [X0] :
( c_Power_Opower__class_Opower(X0) = c_Power_Opower_Opower(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Otimes__class_Otimes(X0))
| ~ class_Power_Opower(X0) ),
inference(ennf_transformation,[],[f1310]) ).
fof(f1310,plain,
! [X0] :
( class_Power_Opower(X0)
=> c_Power_Opower__class_Opower(X0) = c_Power_Opower_Opower(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Otimes__class_Otimes(X0)) ),
inference(rectify,[],[f641]) ).
fof(f641,axiom,
! [X5] :
( class_Power_Opower(X5)
=> c_Power_Opower__class_Opower(X5) = c_Power_Opower_Opower(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Otimes__class_Otimes(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__power__power) ).
fof(f8077,plain,
spl47_371,
inference(avatar_split_clause,[],[f4132,f8075]) ).
fof(f8075,plain,
( spl47_371
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_371])]) ).
fof(f4132,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
inference(cnf_transformation,[],[f1256]) ).
fof(f1256,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
inference(rectify,[],[f480]) ).
fof(f480,axiom,
! [X26] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26),X26),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nonzero) ).
fof(f8065,plain,
( spl47_370
| ~ spl47_247
| ~ spl47_356 ),
inference(avatar_split_clause,[],[f8024,f7822,f7177,f8063]) ).
fof(f8063,plain,
( spl47_370
<=> ! [X0] : ~ sP11(X0,X0,c_Rings_Odvd__class_Odvd(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_370])]) ).
fof(f7177,plain,
( spl47_247
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_247])]) ).
fof(f8024,plain,
( ! [X0] : ~ sP11(X0,X0,c_Rings_Odvd__class_Odvd(tc_Nat_Onat))
| ~ spl47_247
| ~ spl47_356 ),
inference(resolution,[],[f7823,f7178]) ).
fof(f7178,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X0))
| ~ spl47_247 ),
inference(avatar_component_clause,[],[f7177]) ).
fof(f8014,plain,
( ~ spl47_369
| ~ spl47_250
| ~ spl47_320 ),
inference(avatar_split_clause,[],[f7681,f7510,f7189,f8011]) ).
fof(f8011,plain,
( spl47_369
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),v_n____) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_369])]) ).
fof(f7681,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),v_n____)
| ~ spl47_250
| ~ spl47_320 ),
inference(superposition,[],[f7190,f7512]) ).
fof(f7922,plain,
( ~ spl47_368
| ~ spl47_280
| ~ spl47_320 ),
inference(avatar_split_clause,[],[f7678,f7510,f7323,f7919]) ).
fof(f7919,plain,
( spl47_368
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),v_n____) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_368])]) ).
fof(f7678,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),v_n____)
| ~ spl47_280
| ~ spl47_320 ),
inference(superposition,[],[f7324,f7512]) ).
fof(f7875,plain,
( spl47_367
| ~ spl47_281
| ~ spl47_320 ),
inference(avatar_split_clause,[],[f7677,f7510,f7327,f7872]) ).
fof(f7872,plain,
( spl47_367
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_367])]) ).
fof(f7677,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_n____,c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))
| ~ spl47_281
| ~ spl47_320 ),
inference(superposition,[],[f7328,f7512]) ).
fof(f7864,plain,
spl47_366,
inference(avatar_split_clause,[],[f5972,f7862]) ).
fof(f5972,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| sP6(X0,X1) ),
inference(forward_demodulation,[],[f5971,f4114]) ).
fof(f5971,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP6(X0,X1) ),
inference(forward_demodulation,[],[f5608,f4240]) ).
fof(f5608,plain,
! [X0,X1] :
( sP6(X0,X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(definition_unfolding,[],[f4573,f4118]) ).
fof(f4573,plain,
! [X0,X1] :
( sP6(X0,X1)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3641]) ).
fof(f3641,plain,
! [X0,X1] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ sP6(X0,X1) )
& ( sP6(X0,X1)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f3486]) ).
fof(f3486,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
<=> sP6(X0,X1) ),
inference(definition_folding,[],[f1593,f3485]) ).
fof(f1593,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
<=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ) ) ),
inference(rectify,[],[f340]) ).
fof(f340,axiom,
! [X11,X14] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X11)
<=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X11
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X14 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X11
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).
fof(f7860,plain,
spl47_365,
inference(avatar_split_clause,[],[f5970,f7858]) ).
fof(f7858,plain,
( spl47_365
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_365])]) ).
fof(f5970,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ sP6(X0,X1) ),
inference(forward_demodulation,[],[f5969,f4114]) ).
fof(f5969,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP6(X0,X1) ),
inference(forward_demodulation,[],[f5607,f4240]) ).
fof(f5607,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ sP6(X0,X1) ),
inference(definition_unfolding,[],[f4574,f4118]) ).
fof(f4574,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f3641]) ).
fof(f7856,plain,
spl47_364,
inference(avatar_split_clause,[],[f5956,f7854]) ).
fof(f5956,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| sP5(X0,X1) ),
inference(forward_demodulation,[],[f5955,f4114]) ).
fof(f5955,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP5(X0,X1) ),
inference(forward_demodulation,[],[f5601,f4240]) ).
fof(f5601,plain,
! [X0,X1] :
( sP5(X0,X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(definition_unfolding,[],[f4565,f4118]) ).
fof(f4565,plain,
! [X0,X1] :
( sP5(X0,X1)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3638]) ).
fof(f3638,plain,
! [X0,X1] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ sP5(X0,X1) )
& ( sP5(X0,X1)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f3484]) ).
fof(f3484,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
<=> sP5(X0,X1) ),
inference(definition_folding,[],[f1592,f3483]) ).
fof(f1592,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
<=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ) ) ),
inference(rectify,[],[f341]) ).
fof(f341,axiom,
! [X11,X14] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X11)
<=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X11
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X14 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X11
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__1) ).
fof(f7852,plain,
spl47_363,
inference(avatar_split_clause,[],[f5954,f7850]) ).
fof(f7850,plain,
( spl47_363
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_363])]) ).
fof(f5954,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ sP5(X0,X1) ),
inference(forward_demodulation,[],[f5953,f4114]) ).
fof(f5953,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP5(X0,X1) ),
inference(forward_demodulation,[],[f5600,f4240]) ).
fof(f5600,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ sP5(X0,X1) ),
inference(definition_unfolding,[],[f4566,f4118]) ).
fof(f4566,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f3638]) ).
fof(f7848,plain,
spl47_362,
inference(avatar_split_clause,[],[f5893,f7846]) ).
fof(f7846,plain,
( spl47_362
<=> ! [X0] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_362])]) ).
fof(f5893,plain,
! [X0] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),
inference(forward_demodulation,[],[f5892,f4114]) ).
fof(f5892,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X0),
inference(forward_demodulation,[],[f5518,f5515]) ).
fof(f5518,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0),
inference(definition_unfolding,[],[f4133,f4118,f4118]) ).
fof(f4133,plain,
! [X0] : c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X0),
inference(cnf_transformation,[],[f1257]) ).
fof(f1257,plain,
! [X0] : c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X0),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X7] : c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__0) ).
fof(f7844,plain,
spl47_361,
inference(avatar_split_clause,[],[f5834,f7842]) ).
fof(f7842,plain,
( spl47_361
<=> ! [X0,X1,X3] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ sP16(X0,X1,c_Groups_Ozero__class_Ozero(X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_361])]) ).
fof(f5834,plain,
! [X3,X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ sP16(X0,X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(equality_resolution,[],[f5143]) ).
fof(f5143,plain,
! [X2,X3,X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != X2
| ~ sP16(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3830]) ).
fof(f7840,plain,
spl47_360,
inference(avatar_split_clause,[],[f5826,f7838]) ).
fof(f7838,plain,
( spl47_360
<=> ! [X0,X1,X3] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ sP14(X0,X1,c_Groups_Ozero__class_Ozero(X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_360])]) ).
fof(f5826,plain,
! [X3,X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ sP14(X0,X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(equality_resolution,[],[f5134]) ).
fof(f5134,plain,
! [X2,X3,X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != X2
| ~ sP14(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3825]) ).
fof(f7836,plain,
spl47_359,
inference(avatar_split_clause,[],[f5672,f7834]) ).
fof(f5672,plain,
! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Groups_Ozero(X1) ),
inference(equality_resolution,[],[f4366]) ).
fof(f4366,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X0
| ~ class_Groups_Ozero(X1) ),
inference(cnf_transformation,[],[f2472]) ).
fof(f7832,plain,
spl47_358,
inference(avatar_split_clause,[],[f5658,f7830]) ).
fof(f7830,plain,
( spl47_358
<=> ! [X0] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_358])]) ).
fof(f5658,plain,
! [X0] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f4259]) ).
fof(f4259,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f2394]) ).
fof(f7828,plain,
spl47_357,
inference(avatar_split_clause,[],[f5406,f7826]) ).
fof(f7826,plain,
( spl47_357
<=> ! [X4,X0,X3,X2,X1] :
( sP24(X2,X1,X0)
| ~ sP25(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_357])]) ).
fof(f5406,plain,
! [X2,X3,X0,X1,X4] :
( sP24(X2,X1,X0)
| ~ sP25(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f3884]) ).
fof(f7824,plain,
spl47_356,
inference(avatar_split_clause,[],[f5055,f7822]) ).
fof(f5055,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f3780]) ).
fof(f3780,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
| ~ sP11(X0,X1,X2) ),
inference(rectify,[],[f3779]) ).
fof(f3779,plain,
! [X2,X1,X0] :
( ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
| ~ sP11(X2,X1,X0) ),
inference(nnf_transformation,[],[f3493]) ).
fof(f7820,plain,
spl47_355,
inference(avatar_split_clause,[],[f4949,f7818]) ).
fof(f7818,plain,
( spl47_355
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_355])]) ).
fof(f4949,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f3753]) ).
fof(f3753,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ( X0 != X1
& ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
& ( X0 = X1
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) )
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f3752]) ).
fof(f3752,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ( X0 != X1
& ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
& ( X0 = X1
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) )
| ~ class_Orderings_Oorder(X2) ),
inference(nnf_transformation,[],[f2931]) ).
fof(f2931,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
<=> ( X0 = X1
| c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f1860]) ).
fof(f1860,plain,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
<=> ( X0 = X1
| c_Orderings_Oord__class_Oless(X2,X1,X0) ) ) ),
inference(rectify,[],[f198]) ).
fof(f198,axiom,
! [X25,X15,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X15,X25)
<=> ( X15 = X25
| c_Orderings_Oord__class_Oless(X5,X15,X25) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).
fof(f7816,plain,
spl47_354,
inference(avatar_split_clause,[],[f4944,f7814]) ).
fof(f7814,plain,
( spl47_354
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_354])]) ).
fof(f4944,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f2929]) ).
fof(f2929,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f2928]) ).
fof(f2928,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f1858]) ).
fof(f1858,plain,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X0)
=> ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ) ),
inference(rectify,[],[f157]) ).
fof(f157,axiom,
! [X4,X17,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X17,X4)
=> ~ c_Orderings_Oord__class_Oless(X5,X4,X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
fof(f7812,plain,
spl47_353,
inference(avatar_split_clause,[],[f4930,f7810]) ).
fof(f7810,plain,
( spl47_353
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_353])]) ).
fof(f4930,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ),
inference(cnf_transformation,[],[f3748]) ).
fof(f7808,plain,
spl47_352,
inference(avatar_split_clause,[],[f4928,f7806]) ).
fof(f7806,plain,
( spl47_352
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_352])]) ).
fof(f4928,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ),
inference(cnf_transformation,[],[f2904]) ).
fof(f2904,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ),
inference(flattening,[],[f2903]) ).
fof(f2903,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ),
inference(ennf_transformation,[],[f1845]) ).
fof(f1845,plain,
! [X0,X1,X2] :
( class_Orderings_Opreorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ),
inference(rectify,[],[f191]) ).
fof(f191,axiom,
! [X10,X6,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X6,X10)
=> c_Orderings_Oord__class_Oless__eq(X5,X6,X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
fof(f7804,plain,
spl47_351,
inference(avatar_split_clause,[],[f4924,f7802]) ).
fof(f7802,plain,
( spl47_351
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_351])]) ).
fof(f4924,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ),
inference(cnf_transformation,[],[f2896]) ).
fof(f2896,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ),
inference(flattening,[],[f2895]) ).
fof(f2895,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Opreorder(X2) ),
inference(ennf_transformation,[],[f1841]) ).
fof(f1841,plain,
! [X0,X1,X2] :
( class_Orderings_Opreorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X0)
=> ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ) ),
inference(rectify,[],[f150]) ).
fof(f150,axiom,
! [X10,X6,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X6,X10)
=> ~ c_Orderings_Oord__class_Oless(X5,X10,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).
fof(f7800,plain,
spl47_350,
inference(avatar_split_clause,[],[f4796,f7798]) ).
fof(f4796,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f3718]) ).
fof(f3718,plain,
! [X0,X1,X2] :
( ( ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ( X0 != X1
& ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ) )
& ( X0 = X1
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(flattening,[],[f3717]) ).
fof(f3717,plain,
! [X0,X1,X2] :
( ( ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ( X0 != X1
& ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ) )
& ( X0 = X1
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(nnf_transformation,[],[f2768]) ).
fof(f2768,plain,
! [X0,X1,X2] :
( ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
<=> ( X0 = X1
| c_Orderings_Oord__class_Oless(X2,X0,X1) ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f1744]) ).
fof(f1744,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
<=> ( X0 = X1
| c_Orderings_Oord__class_Oless(X2,X0,X1) ) ) ),
inference(rectify,[],[f167]) ).
fof(f167,axiom,
! [X25,X15,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X15,X25)
<=> ( X15 = X25
| c_Orderings_Oord__class_Oless(X5,X25,X15) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(f7796,plain,
spl47_349,
inference(avatar_split_clause,[],[f4779,f7794]) ).
fof(f4779,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f2750]) ).
fof(f2750,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(flattening,[],[f2749]) ).
fof(f2749,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f1733]) ).
fof(f1733,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
=> ~ c_Orderings_Oord__class_Oless(X2,X0,X1) ) ),
inference(rectify,[],[f192]) ).
fof(f192,axiom,
! [X6,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X10,X6)
=> ~ c_Orderings_Oord__class_Oless(X5,X6,X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).
fof(f7792,plain,
spl47_348,
inference(avatar_split_clause,[],[f4768,f7790]) ).
fof(f7790,plain,
( spl47_348
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_348])]) ).
fof(f4768,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f2732]) ).
fof(f2732,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(flattening,[],[f2731]) ).
fof(f2731,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f1724]) ).
fof(f1724,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ),
inference(rectify,[],[f201]) ).
fof(f201,axiom,
! [X10,X6,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X10,X6)
| c_Orderings_Oord__class_Oless__eq(X5,X6,X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
fof(f7788,plain,
spl47_347,
inference(avatar_split_clause,[],[f4767,f7786]) ).
fof(f4767,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f2730]) ).
fof(f2730,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(flattening,[],[f2729]) ).
fof(f2729,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f1723]) ).
fof(f1723,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ),
inference(rectify,[],[f297]) ).
fof(f297,axiom,
! [X10,X6,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X10,X6)
| c_Orderings_Oord__class_Oless__eq(X5,X6,X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).
fof(f7784,plain,
spl47_346,
inference(avatar_split_clause,[],[f4463,f7782]) ).
fof(f7782,plain,
( spl47_346
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_346])]) ).
fof(f4463,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != X1 ),
inference(cnf_transformation,[],[f2574]) ).
fof(f2574,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != X1 ),
inference(ennf_transformation,[],[f1540]) ).
fof(f1540,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = X1
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(rectify,[],[f313]) ).
fof(f313,axiom,
! [X7,X21] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X7) = X21
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
fof(f7780,plain,
spl47_345,
inference(avatar_split_clause,[],[f4388,f7778]) ).
fof(f4388,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Oone__class_Oone(X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2491]) ).
fof(f2491,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Oone__class_Oone(X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1475]) ).
fof(f1475,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Oone__class_Oone(X1)),X0)) ),
inference(rectify,[],[f213]) ).
fof(f213,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),c_Groups_Oone__class_Oone(X5)),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__dvd) ).
fof(f7776,plain,
spl47_344,
inference(avatar_split_clause,[],[f4387,f7774]) ).
fof(f4387,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2490]) ).
fof(f2490,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1474]) ).
fof(f1474,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),c_Groups_Ozero__class_Ozero(X1))) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X4),c_Groups_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__right) ).
fof(f7772,plain,
spl47_343,
inference(avatar_split_clause,[],[f4344,f7770]) ).
fof(f7770,plain,
( spl47_343
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Olinordered__semidom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_343])]) ).
fof(f4344,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(cnf_transformation,[],[f2451]) ).
fof(f2451,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(ennf_transformation,[],[f1436]) ).
fof(f1436,plain,
! [X0,X1] :
( class_Rings_Olinordered__semidom(X1)
=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Oone__class_Oone(X1))) ),
inference(rectify,[],[f145]) ).
fof(f145,axiom,
! [X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> c_Orderings_Oord__class_Oless(X5,X4,c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Oone__class_Oone(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).
fof(f7768,plain,
spl47_342,
inference(avatar_split_clause,[],[f4328,f7766]) ).
fof(f4328,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Divides_Osemiring__div(X1) ),
inference(cnf_transformation,[],[f2437]) ).
fof(f2437,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Divides_Osemiring__div(X1) ),
inference(ennf_transformation,[],[f1422]) ).
fof(f1422,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(rectify,[],[f989]) ).
fof(f989,axiom,
! [X4,X5] :
( class_Divides_Osemiring__div(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Divides_Odiv__class_Omod(X5,c_Groups_Ozero__class_Ozero(X5),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__0) ).
fof(f7764,plain,
spl47_341,
inference(avatar_split_clause,[],[f4273,f7762]) ).
fof(f7762,plain,
( spl47_341
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Rings_Odivision__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_341])]) ).
fof(f4273,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Rings_Odivision__ring(X1) ),
inference(cnf_transformation,[],[f2400]) ).
fof(f2400,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Rings_Odivision__ring(X1) ),
inference(ennf_transformation,[],[f1387]) ).
fof(f1387,plain,
! [X0,X1] :
( class_Rings_Odivision__ring(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(rectify,[],[f912]) ).
fof(f912,axiom,
! [X4,X5] :
( class_Rings_Odivision__ring(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ozero__class_Ozero(X5),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero__left) ).
fof(f7760,plain,
spl47_340,
inference(avatar_split_clause,[],[f4271,f7758]) ).
fof(f4271,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(cnf_transformation,[],[f2398]) ).
fof(f2398,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(ennf_transformation,[],[f1385]) ).
fof(f1385,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__field(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(rectify,[],[f922]) ).
fof(f922,axiom,
! [X10,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ozero__class_Ozero(X5),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Ozero) ).
fof(f7756,plain,
( ~ spl47_339
| ~ spl47_261
| ~ spl47_321 ),
inference(avatar_split_clause,[],[f7690,f7515,f7233,f7753]) ).
fof(f7753,plain,
( spl47_339
<=> c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = sK31 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_339])]) ).
fof(f7233,plain,
( spl47_261
<=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_261])]) ).
fof(f7690,plain,
( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != sK31
| ~ spl47_261
| ~ spl47_321 ),
inference(superposition,[],[f7234,f7517]) ).
fof(f7234,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X0
| ~ spl47_261 ),
inference(avatar_component_clause,[],[f7233]) ).
fof(f7751,plain,
spl47_338,
inference(avatar_split_clause,[],[f4268,f7749]) ).
fof(f4268,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Rings_Oinverse__class_Odivide(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(cnf_transformation,[],[f2396]) ).
fof(f2396,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Rings_Oinverse__class_Odivide(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(ennf_transformation,[],[f1383]) ).
fof(f1383,plain,
! [X0,X1] :
( class_Rings_Odivision__ring__inverse__zero(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Rings_Oinverse__class_Odivide(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ),
inference(rectify,[],[f911]) ).
fof(f911,axiom,
! [X4,X5] :
( class_Rings_Odivision__ring__inverse__zero(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Rings_Oinverse__class_Odivide(X5,X4,c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero) ).
fof(f7747,plain,
spl47_337,
inference(avatar_split_clause,[],[f4243,f7745]) ).
fof(f7745,plain,
( spl47_337
<=> ! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_337])]) ).
fof(f4243,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
inference(cnf_transformation,[],[f1359]) ).
fof(f1359,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
inference(rectify,[],[f828]) ).
fof(f828,axiom,
! [X21,X7] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__0) ).
fof(f7743,plain,
spl47_336,
inference(avatar_split_clause,[],[f4218,f7741]) ).
fof(f7741,plain,
( spl47_336
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_336])]) ).
fof(f4218,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(cnf_transformation,[],[f3541]) ).
fof(f3541,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ) ),
inference(nnf_transformation,[],[f1340]) ).
fof(f1340,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(rectify,[],[f478]) ).
fof(f478,axiom,
! [X30] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X30)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).
fof(f7739,plain,
spl47_335,
inference(avatar_split_clause,[],[f4217,f7737]) ).
fof(f7737,plain,
( spl47_335
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_335])]) ).
fof(f4217,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
inference(cnf_transformation,[],[f3541]) ).
fof(f7735,plain,
spl47_334,
inference(avatar_split_clause,[],[f4206,f7733]) ).
fof(f4206,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2382]) ).
fof(f2382,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1330]) ).
fof(f1330,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0))) ),
inference(rectify,[],[f269]) ).
fof(f269,axiom,
! [X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X5,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__1) ).
fof(f7731,plain,
spl47_333,
inference(avatar_split_clause,[],[f4191,f7729]) ).
fof(f4191,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f2367]) ).
fof(f2367,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Groups_Ozero(X0) ),
inference(ennf_transformation,[],[f1315]) ).
fof(f1315,plain,
! [X0] :
( class_Groups_Ozero(X0)
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X5] :
( class_Groups_Ozero(X5)
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__0) ).
fof(f7727,plain,
spl47_332,
inference(avatar_split_clause,[],[f4131,f7725]) ).
fof(f4131,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(cnf_transformation,[],[f1255]) ).
fof(f1255,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(rectify,[],[f654]) ).
fof(f654,axiom,
! [X7] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0) ).
fof(f7723,plain,
spl47_331,
inference(avatar_split_clause,[],[f4130,f7721]) ).
fof(f7721,plain,
( spl47_331
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_331])]) ).
fof(f4130,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f1254]) ).
fof(f1254,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rectify,[],[f653]) ).
fof(f653,axiom,
! [X21] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0__right) ).
fof(f7712,plain,
( ~ spl47_330
| ~ spl47_261
| ~ spl47_320 ),
inference(avatar_split_clause,[],[f7680,f7510,f7233,f7709]) ).
fof(f7709,plain,
( spl47_330
<=> c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = v_n____ ),
introduced(avatar_definition,[new_symbols(naming,[spl47_330])]) ).
fof(f7680,plain,
( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != v_n____
| ~ spl47_261
| ~ spl47_320 ),
inference(superposition,[],[f7234,f7512]) ).
fof(f7660,plain,
( spl47_329
| ~ spl47_261
| ~ spl47_302 ),
inference(avatar_split_clause,[],[f7596,f7437,f7233,f7658]) ).
fof(f7658,plain,
( spl47_329
<=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_329])]) ).
fof(f7596,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) != X0
| ~ spl47_261
| ~ spl47_302 ),
inference(superposition,[],[f7234,f7438]) ).
fof(f7626,plain,
( spl47_328
| ~ spl47_55
| ~ spl47_297 ),
inference(avatar_split_clause,[],[f7552,f7417,f6306,f7623]) ).
fof(f7623,plain,
( spl47_328
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_328])]) ).
fof(f7417,plain,
( spl47_297
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Ogroup__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_297])]) ).
fof(f7552,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ spl47_55
| ~ spl47_297 ),
inference(resolution,[],[f7418,f6308]) ).
fof(f7418,plain,
( ! [X0] :
( ~ class_Groups_Ogroup__add(X0)
| c_Groups_Ozero__class_Ozero(X0) = c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ozero__class_Ozero(X0)) )
| ~ spl47_297 ),
inference(avatar_component_clause,[],[f7417]) ).
fof(f7549,plain,
( spl47_327
| ~ spl47_282
| ~ spl47_291 ),
inference(avatar_split_clause,[],[f7544,f7393,f7331,f7546]) ).
fof(f7546,plain,
( spl47_327
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_327])]) ).
fof(f7393,plain,
( spl47_291
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_291])]) ).
fof(f7544,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ spl47_282
| ~ spl47_291 ),
inference(superposition,[],[f7332,f7394]) ).
fof(f7394,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0)
| ~ spl47_291 ),
inference(avatar_component_clause,[],[f7393]) ).
fof(f7538,plain,
spl47_326,
inference(avatar_split_clause,[],[f5906,f7536]) ).
fof(f7536,plain,
( spl47_326
<=> ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_326])]) ).
fof(f5906,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(forward_demodulation,[],[f5905,f4114]) ).
fof(f5905,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(forward_demodulation,[],[f5527,f5515]) ).
fof(f5527,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(definition_unfolding,[],[f4223,f4118]) ).
fof(f4223,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(cnf_transformation,[],[f3547]) ).
fof(f3547,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(nnf_transformation,[],[f1343]) ).
fof(f1343,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(rectify,[],[f256]) ).
fof(f256,axiom,
! [X11] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).
fof(f7534,plain,
spl47_325,
inference(avatar_split_clause,[],[f5773,f7532]) ).
fof(f7532,plain,
( spl47_325
<=> ! [X2,X1] :
( c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ozero__class_Ozero(X2)) = X1
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_325])]) ).
fof(f5773,plain,
! [X2,X1] :
( c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ozero__class_Ozero(X2)) = X1
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(equality_resolution,[],[f4868]) ).
fof(f4868,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(X2,X1,X0) = X1
| c_Groups_Ozero__class_Ozero(X2) != X0
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(cnf_transformation,[],[f3736]) ).
fof(f7530,plain,
spl47_324,
inference(avatar_split_clause,[],[f5772,f7528]) ).
fof(f7528,plain,
( spl47_324
<=> ! [X2,X1] :
( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Ominus__class_Ominus(X2,X1,X1)
| ~ class_Groups_Oab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_324])]) ).
fof(f5772,plain,
! [X2,X1] :
( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Ominus__class_Ominus(X2,X1,X1)
| ~ class_Groups_Oab__group__add(X2) ),
inference(equality_resolution,[],[f4852]) ).
fof(f4852,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Ominus__class_Ominus(X2,X1,X0)
| X0 != X1
| ~ class_Groups_Oab__group__add(X2) ),
inference(cnf_transformation,[],[f3735]) ).
fof(f7526,plain,
spl47_323,
inference(avatar_split_clause,[],[f5662,f7524]) ).
fof(f7524,plain,
( spl47_323
<=> ! [X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_323])]) ).
fof(f5662,plain,
! [X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(equality_resolution,[],[f4286]) ).
fof(f4286,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,X0) = X0
| c_Groups_Ozero__class_Ozero(X1) != X0
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3551]) ).
fof(f7522,plain,
spl47_322,
inference(avatar_split_clause,[],[f5514,f7520]) ).
fof(f5514,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(definition_unfolding,[],[f4108,f4118]) ).
fof(f4108,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X0)),
inference(cnf_transformation,[],[f1232]) ).
fof(f1232,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X0)),
inference(rectify,[],[f136]) ).
fof(f136,axiom,
! [X7] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
fof(f7518,plain,
spl47_321,
inference(avatar_split_clause,[],[f5503,f7515]) ).
fof(f5503,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK31,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(definition_unfolding,[],[f4088,f4118]) ).
fof(f4088,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Nat_OSuc(sK31),
inference(cnf_transformation,[],[f3539]) ).
fof(f3539,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Nat_OSuc(sK31),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f2310,f3538]) ).
fof(f3538,plain,
( ? [X0] : c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Nat_OSuc(X0)
=> c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Nat_OSuc(sK31) ),
introduced(choice_axiom,[]) ).
fof(f2310,plain,
? [X0] : c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Nat_OSuc(X0),
inference(ennf_transformation,[],[f1212]) ).
fof(f1212,plain,
~ ! [X0] : c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Nat_OSuc(X0),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
~ ! [X19] : c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Nat_OSuc(X19),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bn_O_Adegree_Ap_A_061_ASuc_An_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(f7513,plain,
spl47_320,
inference(avatar_split_clause,[],[f5502,f7510]) ).
fof(f7508,plain,
spl47_319,
inference(avatar_split_clause,[],[f4386,f7506]) ).
fof(f4386,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2489]) ).
fof(f2489,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1473]) ).
fof(f1473,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),X0)) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X4),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__refl) ).
fof(f7504,plain,
spl47_318,
inference(avatar_split_clause,[],[f4385,f7502]) ).
fof(f7502,plain,
( spl47_318
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_318])]) ).
fof(f4385,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2488]) ).
fof(f2488,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1472]) ).
fof(f1472,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 ),
inference(rectify,[],[f457]) ).
fof(f457,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Ozero__class_Ozero(X5),X4) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(f7500,plain,
spl47_317,
inference(avatar_split_clause,[],[f4384,f7498]) ).
fof(f7498,plain,
( spl47_317
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_317])]) ).
fof(f4384,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2487]) ).
fof(f2487,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1471]) ).
fof(f1471,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f458]) ).
fof(f458,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(f7496,plain,
spl47_316,
inference(avatar_split_clause,[],[f4383,f7494]) ).
fof(f4383,plain,
! [X0,X1] :
( c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X0) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2486]) ).
fof(f2486,plain,
! [X0,X1] :
( c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X0) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1470]) ).
fof(f1470,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X0) = X0 ),
inference(rectify,[],[f242]) ).
fof(f242,axiom,
! [X8,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Polynomial_Osmult(X5,c_Groups_Oone__class_Oone(X5),X8) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__1__left) ).
fof(f7492,plain,
spl47_315,
inference(avatar_split_clause,[],[f4359,f7490]) ).
fof(f7490,plain,
( spl47_315
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0
| ~ class_Groups_Ocomm__monoid__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_315])]) ).
fof(f4359,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(cnf_transformation,[],[f2465]) ).
fof(f2465,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(ennf_transformation,[],[f1450]) ).
fof(f1450,plain,
! [X0,X1] :
( class_Groups_Ocomm__monoid__add(X1)
=> c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 ),
inference(rectify,[],[f357]) ).
fof(f357,axiom,
! [X4,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Ozero__class_Ozero(X5),X4) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).
fof(f7488,plain,
spl47_314,
inference(avatar_split_clause,[],[f4358,f7486]) ).
fof(f7486,plain,
( spl47_314
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Groups_Ocomm__monoid__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_314])]) ).
fof(f4358,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(cnf_transformation,[],[f2464]) ).
fof(f2464,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(ennf_transformation,[],[f1449]) ).
fof(f1449,plain,
! [X0,X1] :
( class_Groups_Ocomm__monoid__add(X1)
=> c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f354]) ).
fof(f354,axiom,
! [X4,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(f7484,plain,
spl47_313,
inference(avatar_split_clause,[],[f4348,f7482]) ).
fof(f4348,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0
| ~ class_Groups_Omonoid__add(X1) ),
inference(cnf_transformation,[],[f2454]) ).
fof(f2454,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0
| ~ class_Groups_Omonoid__add(X1) ),
inference(ennf_transformation,[],[f1439]) ).
fof(f1439,plain,
! [X0,X1] :
( class_Groups_Omonoid__add(X1)
=> c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 ),
inference(rectify,[],[f358]) ).
fof(f358,axiom,
! [X4,X5] :
( class_Groups_Omonoid__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Ozero__class_Ozero(X5),X4) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(f7480,plain,
spl47_312,
inference(avatar_split_clause,[],[f4347,f7478]) ).
fof(f4347,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Groups_Omonoid__add(X1) ),
inference(cnf_transformation,[],[f2453]) ).
fof(f2453,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Groups_Omonoid__add(X1) ),
inference(ennf_transformation,[],[f1438]) ).
fof(f1438,plain,
! [X0,X1] :
( class_Groups_Omonoid__add(X1)
=> c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f355]) ).
fof(f355,axiom,
! [X4,X5] :
( class_Groups_Omonoid__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(f7476,plain,
spl47_311,
inference(avatar_split_clause,[],[f4332,f7474]) ).
fof(f4332,plain,
! [X0,X1] :
( c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Groups_Ogroup__add(X1) ),
inference(cnf_transformation,[],[f2441]) ).
fof(f2441,plain,
! [X0,X1] :
( c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Groups_Ogroup__add(X1) ),
inference(ennf_transformation,[],[f1426]) ).
fof(f1426,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f798]) ).
fof(f798,axiom,
! [X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ominus__class_Ominus(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__right) ).
fof(f7472,plain,
spl47_310,
inference(avatar_split_clause,[],[f4331,f7470]) ).
fof(f4331,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0
| ~ class_Groups_Ogroup__add(X1) ),
inference(cnf_transformation,[],[f2440]) ).
fof(f2440,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0
| ~ class_Groups_Ogroup__add(X1) ),
inference(ennf_transformation,[],[f1425]) ).
fof(f1425,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0 ),
inference(rectify,[],[f397]) ).
fof(f397,axiom,
! [X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Ouminus__class_Ouminus(X5,X4)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).
fof(f7468,plain,
spl47_309,
inference(avatar_split_clause,[],[f4330,f7466]) ).
fof(f4330,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ominus__class_Ominus(X1,X0,X0)
| ~ class_Groups_Ogroup__add(X1) ),
inference(cnf_transformation,[],[f2439]) ).
fof(f2439,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ominus__class_Ominus(X1,X0,X0)
| ~ class_Groups_Ogroup__add(X1) ),
inference(ennf_transformation,[],[f1424]) ).
fof(f1424,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ominus__class_Ominus(X1,X0,X0) ),
inference(rectify,[],[f799]) ).
fof(f799,axiom,
! [X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Groups_Ominus__class_Ominus(X5,X4,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self) ).
fof(f7463,plain,
spl47_308,
inference(avatar_split_clause,[],[f4327,f7461]) ).
fof(f4327,plain,
! [X0,X1] :
( c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Divides_Osemiring__div(X1) ),
inference(cnf_transformation,[],[f2436]) ).
fof(f2436,plain,
! [X0,X1] :
( c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Divides_Osemiring__div(X1) ),
inference(ennf_transformation,[],[f1421]) ).
fof(f1421,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f990]) ).
fof(f990,axiom,
! [X4,X5] :
( class_Divides_Osemiring__div(X5)
=> c_Divides_Odiv__class_Omod(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__by__0) ).
fof(f7459,plain,
spl47_307,
inference(avatar_split_clause,[],[f4326,f7457]) ).
fof(f4326,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,X0)
| ~ class_Divides_Osemiring__div(X1) ),
inference(cnf_transformation,[],[f2435]) ).
fof(f2435,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,X0)
| ~ class_Divides_Osemiring__div(X1) ),
inference(ennf_transformation,[],[f1420]) ).
fof(f1420,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,X0) ),
inference(rectify,[],[f991]) ).
fof(f991,axiom,
! [X4,X5] :
( class_Divides_Osemiring__div(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Divides_Odiv__class_Omod(X5,X4,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__self) ).
fof(f7455,plain,
spl47_306,
inference(avatar_split_clause,[],[f4284,f7453]) ).
fof(f4284,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(cnf_transformation,[],[f2412]) ).
fof(f2412,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(ennf_transformation,[],[f1398]) ).
fof(f1398,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(X1)
=> c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0 ),
inference(rectify,[],[f629]) ).
fof(f629,axiom,
! [X6,X5] :
( class_Lattices_Oboolean__algebra(X5)
=> c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Ouminus__class_Ouminus(X5,X6)) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__compl) ).
fof(f7451,plain,
spl47_305,
inference(avatar_split_clause,[],[f4272,f7449]) ).
fof(f4272,plain,
! [X0,X1] :
( c_Rings_Oinverse__class_Odivide(X1,X0,c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Rings_Odivision__ring(X1) ),
inference(cnf_transformation,[],[f2399]) ).
fof(f2399,plain,
! [X0,X1] :
( c_Rings_Oinverse__class_Odivide(X1,X0,c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Rings_Odivision__ring(X1) ),
inference(ennf_transformation,[],[f1386]) ).
fof(f1386,plain,
! [X0,X1] :
( class_Rings_Odivision__ring(X1)
=> c_Rings_Oinverse__class_Odivide(X1,X0,c_Groups_Oone__class_Oone(X1)) = X0 ),
inference(rectify,[],[f905]) ).
fof(f905,axiom,
! [X4,X5] :
( class_Rings_Odivision__ring(X5)
=> c_Rings_Oinverse__class_Odivide(X5,X4,c_Groups_Oone__class_Oone(X5)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__1) ).
fof(f7447,plain,
spl47_304,
inference(avatar_split_clause,[],[f4242,f7445]) ).
fof(f7445,plain,
( spl47_304
<=> ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_304])]) ).
fof(f4242,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0) = X1,
inference(cnf_transformation,[],[f1358]) ).
fof(f1358,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0) = X1,
inference(rectify,[],[f766]) ).
fof(f766,axiom,
! [X7,X21] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X7),X7) = X21,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
fof(f7443,plain,
spl47_303,
inference(avatar_split_clause,[],[f4241,f7441]) ).
fof(f4241,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1) = X0,
inference(cnf_transformation,[],[f1357]) ).
fof(f1357,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1) = X0,
inference(rectify,[],[f765]) ).
fof(f765,axiom,
! [X21,X7] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X21),X7) = X21,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
fof(f7439,plain,
spl47_302,
inference(avatar_split_clause,[],[f4240,f7437]) ).
fof(f7435,plain,
spl47_301,
inference(avatar_split_clause,[],[f4239,f7433]) ).
fof(f7431,plain,
spl47_300,
inference(avatar_split_clause,[],[f4219,f7429]) ).
fof(f7429,plain,
( spl47_300
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_300])]) ).
fof(f4219,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(cnf_transformation,[],[f3542]) ).
fof(f3542,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(nnf_transformation,[],[f1341]) ).
fof(f1341,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(rectify,[],[f93]) ).
fof(f93,axiom,
! [X11] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).
fof(f7427,plain,
spl47_299,
inference(avatar_split_clause,[],[f4208,f7425]) ).
fof(f7425,plain,
( spl47_299
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_299])]) ).
fof(f4208,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f2384]) ).
fof(f2384,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(ennf_transformation,[],[f1332]) ).
fof(f1332,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(rectify,[],[f215]) ).
fof(f215,axiom,
! [X7] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X7
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).
fof(f7423,plain,
( spl47_298
| ~ spl47_276
| ~ spl47_282 ),
inference(avatar_split_clause,[],[f7360,f7331,f7307,f7421]) ).
fof(f7421,plain,
( spl47_298
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_298])]) ).
fof(f7307,plain,
( spl47_276
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_276])]) ).
fof(f7360,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl47_276
| ~ spl47_282 ),
inference(resolution,[],[f7332,f7308]) ).
fof(f7308,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
| ~ spl47_276 ),
inference(avatar_component_clause,[],[f7307]) ).
fof(f7419,plain,
spl47_297,
inference(avatar_split_clause,[],[f4170,f7417]) ).
fof(f4170,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Ogroup__add(X0) ),
inference(cnf_transformation,[],[f2346]) ).
fof(f2346,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Ogroup__add(X0) ),
inference(ennf_transformation,[],[f1294]) ).
fof(f1294,plain,
! [X0] :
( class_Groups_Ogroup__add(X0)
=> c_Groups_Ozero__class_Ozero(X0) = c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f410]) ).
fof(f410,axiom,
! [X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__zero) ).
fof(f7415,plain,
spl47_296,
inference(avatar_split_clause,[],[f4129,f7413]) ).
fof(f7413,plain,
( spl47_296
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_296])]) ).
fof(f4129,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0)),
inference(cnf_transformation,[],[f1253]) ).
fof(f1253,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0)),
inference(rectify,[],[f664]) ).
fof(f664,axiom,
! [X21] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).
fof(f7411,plain,
spl47_295,
inference(avatar_split_clause,[],[f4127,f7409]) ).
fof(f4127,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0,
inference(cnf_transformation,[],[f1251]) ).
fof(f1251,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f665]) ).
fof(f665,axiom,
! [X7] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X7) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).
fof(f7407,plain,
spl47_294,
inference(avatar_split_clause,[],[f4126,f7405]) ).
fof(f4126,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0,
inference(cnf_transformation,[],[f1250]) ).
fof(f1250,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0,
inference(rectify,[],[f645]) ).
fof(f645,axiom,
! [X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X26) = X26,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).
fof(f7403,plain,
spl47_293,
inference(avatar_split_clause,[],[f4125,f7401]) ).
fof(f4125,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f1249]) ).
fof(f1249,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(rectify,[],[f667]) ).
fof(f667,axiom,
! [X7] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
fof(f7399,plain,
spl47_292,
inference(avatar_split_clause,[],[f4124,f7397]) ).
fof(f4124,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0,
inference(cnf_transformation,[],[f1248]) ).
fof(f1248,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0,
inference(rectify,[],[f644]) ).
fof(f644,axiom,
! [X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X26,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).
fof(f7395,plain,
spl47_291,
inference(avatar_split_clause,[],[f4123,f7393]) ).
fof(f4123,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0),
inference(cnf_transformation,[],[f1247]) ).
fof(f1247,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0),
inference(rectify,[],[f484]) ).
fof(f484,axiom,
! [X26] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X26),X26),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).
fof(f7391,plain,
( ~ spl47_290
| spl47_289 ),
inference(avatar_split_clause,[],[f4084,f7381,f7388]) ).
fof(f4084,plain,
( sP3
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK29) ),
inference(cnf_transformation,[],[f3535]) ).
fof(f7384,plain,
( spl47_288
| spl47_289 ),
inference(avatar_split_clause,[],[f4083,f7381,f7377]) ).
fof(f4083,plain,
( sP3
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK29) ),
inference(cnf_transformation,[],[f3535]) ).
fof(f7375,plain,
( ~ spl47_287
| spl47_286 ),
inference(avatar_split_clause,[],[f4076,f7367,f7372]) ).
fof(f4076,plain,
( sP1
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK28) ),
inference(cnf_transformation,[],[f3529]) ).
fof(f7370,plain,
( spl47_285
| spl47_286 ),
inference(avatar_split_clause,[],[f4075,f7367,f7363]) ).
fof(f4075,plain,
( sP1
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK28) ),
inference(cnf_transformation,[],[f3529]) ).
fof(f7357,plain,
( ~ spl47_284
| ~ spl47_246
| ~ spl47_280 ),
inference(avatar_split_clause,[],[f7352,f7323,f7173,f7354]) ).
fof(f7354,plain,
( spl47_284
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_284])]) ).
fof(f7352,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl47_246
| ~ spl47_280 ),
inference(superposition,[],[f7324,f7174]) ).
fof(f7337,plain,
spl47_283,
inference(avatar_split_clause,[],[f5847,f7335]) ).
fof(f7335,plain,
( spl47_283
<=> ! [X2,X1] : sP18(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X1,X2,c_Groups_Ozero__class_Ozero(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_283])]) ).
fof(f5847,plain,
! [X2,X1] : sP18(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X1,X2,c_Groups_Ozero__class_Ozero(X2)),
inference(equality_resolution,[],[f5846]) ).
fof(f5846,plain,
! [X2,X0,X1] :
( sP18(X0,X1,X2,c_Groups_Ozero__class_Ozero(X2))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0 ),
inference(equality_resolution,[],[f5190]) ).
fof(f5190,plain,
! [X2,X3,X0,X1] :
( sP18(X0,X1,X2,X3)
| c_Groups_Ozero__class_Ozero(X2) != X3
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0 ),
inference(cnf_transformation,[],[f3842]) ).
fof(f7333,plain,
spl47_282,
inference(avatar_split_clause,[],[f5722,f7331]) ).
fof(f5722,plain,
! [X1] : c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(equality_resolution,[],[f4583]) ).
fof(f4583,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| X0 != X1 ),
inference(cnf_transformation,[],[f3646]) ).
fof(f7329,plain,
spl47_281,
inference(avatar_split_clause,[],[f5513,f7327]) ).
fof(f5513,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(definition_unfolding,[],[f4107,f4118]) ).
fof(f4107,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X0)),
inference(cnf_transformation,[],[f1231]) ).
fof(f1231,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X0)),
inference(rectify,[],[f135]) ).
fof(f135,axiom,
! [X7] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,c_Nat_OSuc(X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).
fof(f7325,plain,
spl47_280,
inference(avatar_split_clause,[],[f5512,f7323]) ).
fof(f5512,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),
inference(definition_unfolding,[],[f4104,f4118]) ).
fof(f4104,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X0),
inference(cnf_transformation,[],[f1228]) ).
fof(f1228,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X0),
inference(rectify,[],[f94]) ).
fof(f94,axiom,
! [X7] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X7),X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(f7321,plain,
spl47_279,
inference(avatar_split_clause,[],[f5506,f7319]) ).
fof(f5506,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(definition_unfolding,[],[f4095,f4118]) ).
fof(f4095,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X0),
inference(cnf_transformation,[],[f1219]) ).
fof(f1219,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X0),
inference(rectify,[],[f29]) ).
fof(f29,axiom,
! [X21] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(f7317,plain,
spl47_278,
inference(avatar_split_clause,[],[f5413,f7315]) ).
fof(f7315,plain,
( spl47_278
<=> ! [X4,X0,X3,X2,X1] :
( sP26(X3,X1,X2,X4,X0)
| ~ class_Fields_Ofield(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_278])]) ).
fof(f5413,plain,
! [X2,X3,X0,X1,X4] :
( sP26(X3,X1,X2,X4,X0)
| ~ class_Fields_Ofield(X4) ),
inference(cnf_transformation,[],[f3517]) ).
fof(f3517,plain,
! [X0,X1,X2,X3,X4] :
( sP26(X3,X1,X2,X4,X0)
| ~ class_Fields_Ofield(X4) ),
inference(definition_folding,[],[f3378,f3516,f3515,f3514]) ).
fof(f3378,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
<=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X0),c_Polynomial_Odegree(X4,X2))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X0
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2 )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2 )
& c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X1),X2),X0) = X3 ) )
| ~ class_Fields_Ofield(X4) ),
inference(flattening,[],[f3377]) ).
fof(f3377,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
<=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X0),c_Polynomial_Odegree(X4,X2))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X0
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2 )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2 )
& c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X1),X2),X0) = X3 ) )
| ~ class_Fields_Ofield(X4) ),
inference(ennf_transformation,[],[f2196]) ).
fof(f2196,plain,
! [X0,X1,X2,X3,X4] :
( class_Fields_Ofield(X4)
=> ( c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) != X2
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X4,X0),c_Polynomial_Odegree(X4,X2))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X0 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X2
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X1 )
& c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),X1),X2),X0) = X3 ) ) ),
inference(rectify,[],[f730]) ).
fof(f730,axiom,
! [X70,X18,X25,X15,X5] :
( class_Fields_Ofield(X5)
=> ( c_Polynomial_Opdivmod__rel(X5,X15,X25,X18,X70)
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) != X25
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5,X70),c_Polynomial_Odegree(X5,X25))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X70 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X25
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X18 )
& c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X18),X25),X70) = X15 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__def) ).
fof(f7313,plain,
spl47_277,
inference(avatar_split_clause,[],[f5054,f7311]) ).
fof(f7311,plain,
( spl47_277
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_277])]) ).
fof(f5054,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f3780]) ).
fof(f7309,plain,
spl47_276,
inference(avatar_split_clause,[],[f4516,f7307]) ).
fof(f4516,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3607]) ).
fof(f7305,plain,
spl47_275,
inference(avatar_split_clause,[],[f4432,f7303]) ).
fof(f7303,plain,
( spl47_275
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_275])]) ).
fof(f4432,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2538]) ).
fof(f2538,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1515]) ).
fof(f1515,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f391]) ).
fof(f391,axiom,
! [X10,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X10)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(f7301,plain,
spl47_274,
inference(avatar_split_clause,[],[f4266,f7299]) ).
fof(f7299,plain,
( spl47_274
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_274])]) ).
fof(f4266,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f1379]) ).
fof(f1379,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f85]) ).
fof(f85,axiom,
! [X7,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X21)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).
fof(f7297,plain,
spl47_273,
inference(avatar_split_clause,[],[f4265,f7295]) ).
fof(f7295,plain,
( spl47_273
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_273])]) ).
fof(f4265,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f1378]) ).
fof(f1378,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(rectify,[],[f468]) ).
fof(f468,axiom,
! [X48,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X48,X26)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X26,X48) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__linear) ).
fof(f7293,plain,
spl47_272,
inference(avatar_split_clause,[],[f4179,f7291]) ).
fof(f7291,plain,
( spl47_272
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Olinordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_272])]) ).
fof(f4179,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(cnf_transformation,[],[f2355]) ).
fof(f2355,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(ennf_transformation,[],[f1303]) ).
fof(f1303,plain,
! [X0] :
( class_Rings_Olinordered__semidom(X0)
=> c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0)) ),
inference(rectify,[],[f142]) ).
fof(f142,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oone__class_Oone(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).
fof(f7289,plain,
spl47_271,
inference(avatar_split_clause,[],[f4178,f7287]) ).
fof(f7287,plain,
( spl47_271
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Olinordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_271])]) ).
fof(f4178,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(cnf_transformation,[],[f2354]) ).
fof(f2354,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(ennf_transformation,[],[f1302]) ).
fof(f1302,plain,
! [X0] :
( class_Rings_Olinordered__semidom(X0)
=> c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oone__class_Oone(X0)) ),
inference(rectify,[],[f250]) ).
fof(f250,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oone__class_Oone(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).
fof(f7285,plain,
spl47_270,
inference(avatar_split_clause,[],[f4177,f7283]) ).
fof(f7283,plain,
( spl47_270
<=> ! [X0] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Olinordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_270])]) ).
fof(f4177,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(cnf_transformation,[],[f2353]) ).
fof(f2353,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(ennf_transformation,[],[f1301]) ).
fof(f1301,plain,
! [X0] :
( class_Rings_Olinordered__semidom(X0)
=> ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f141]) ).
fof(f141,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
fof(f7281,plain,
spl47_269,
inference(avatar_split_clause,[],[f4176,f7279]) ).
fof(f7279,plain,
( spl47_269
<=> ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Olinordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_269])]) ).
fof(f4176,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(cnf_transformation,[],[f2352]) ).
fof(f2352,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(ennf_transformation,[],[f1300]) ).
fof(f1300,plain,
! [X0] :
( class_Rings_Olinordered__semidom(X0)
=> ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f251]) ).
fof(f251,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
fof(f7277,plain,
spl47_268,
inference(avatar_split_clause,[],[f4122,f7275]) ).
fof(f4122,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)),
inference(cnf_transformation,[],[f1246]) ).
fof(f1246,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)),
inference(rectify,[],[f240]) ).
fof(f240,axiom,
! [X6] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Obot__least) ).
fof(f7273,plain,
( ~ spl47_267
| ~ spl47_246
| ~ spl47_261 ),
inference(avatar_split_clause,[],[f7260,f7233,f7173,f7270]) ).
fof(f7270,plain,
( spl47_267
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_267])]) ).
fof(f7260,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ spl47_246
| ~ spl47_261 ),
inference(superposition,[],[f7234,f7174]) ).
fof(f7268,plain,
spl47_266,
inference(avatar_split_clause,[],[f4121,f7266]) ).
fof(f4121,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cnf_transformation,[],[f1245]) ).
fof(f1245,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rectify,[],[f72]) ).
fof(f72,axiom,
! [X6] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Otop__greatest) ).
fof(f7264,plain,
spl47_265,
inference(avatar_split_clause,[],[f4117,f7262]) ).
fof(f4117,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f1241]) ).
fof(f1241,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
inference(rectify,[],[f792]) ).
fof(f792,axiom,
! [X7] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
fof(f7247,plain,
spl47_264,
inference(avatar_split_clause,[],[f5831,f7245]) ).
fof(f7245,plain,
( spl47_264
<=> ! [X1,X3] : sP16(c_Groups_Ozero__class_Ozero(X1),X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_264])]) ).
fof(f5831,plain,
! [X3,X1] : sP16(c_Groups_Ozero__class_Ozero(X1),X1,c_Groups_Ozero__class_Ozero(X1),X3),
inference(equality_resolution,[],[f5830]) ).
fof(f5830,plain,
! [X2,X3,X1] :
( sP16(c_Groups_Ozero__class_Ozero(X1),X1,X2,X3)
| c_Groups_Ozero__class_Ozero(X1) != X2 ),
inference(equality_resolution,[],[f5146]) ).
fof(f5146,plain,
! [X2,X3,X0,X1] :
( sP16(X0,X1,X2,X3)
| c_Groups_Ozero__class_Ozero(X1) != X0
| c_Groups_Ozero__class_Ozero(X1) != X2 ),
inference(cnf_transformation,[],[f3830]) ).
fof(f7243,plain,
spl47_263,
inference(avatar_split_clause,[],[f5823,f7241]) ).
fof(f7241,plain,
( spl47_263
<=> ! [X1,X3] : sP14(c_Groups_Ozero__class_Ozero(X1),X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_263])]) ).
fof(f5823,plain,
! [X3,X1] : sP14(c_Groups_Ozero__class_Ozero(X1),X1,c_Groups_Ozero__class_Ozero(X1),X3),
inference(equality_resolution,[],[f5822]) ).
fof(f5822,plain,
! [X2,X3,X1] :
( sP14(c_Groups_Ozero__class_Ozero(X1),X1,X2,X3)
| c_Groups_Ozero__class_Ozero(X1) != X2 ),
inference(equality_resolution,[],[f5137]) ).
fof(f5137,plain,
! [X2,X3,X0,X1] :
( sP14(X0,X1,X2,X3)
| c_Groups_Ozero__class_Ozero(X1) != X0
| c_Groups_Ozero__class_Ozero(X1) != X2 ),
inference(cnf_transformation,[],[f3825]) ).
fof(f7239,plain,
spl47_262,
inference(avatar_split_clause,[],[f5744,f7237]) ).
fof(f7237,plain,
( spl47_262
<=> ! [X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X1)
| ~ class_Rings_Olinordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_262])]) ).
fof(f5744,plain,
! [X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X1)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(equality_resolution,[],[f4719]) ).
fof(f4719,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X2),X1,X0)
| X0 != X1
| ~ class_Rings_Olinordered__idom(X2) ),
inference(cnf_transformation,[],[f3699]) ).
fof(f7235,plain,
spl47_261,
inference(avatar_split_clause,[],[f5504,f7233]) ).
fof(f5504,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X0,
inference(definition_unfolding,[],[f4089,f4118]) ).
fof(f4089,plain,
! [X0] : c_Nat_OSuc(X0) != X0,
inference(cnf_transformation,[],[f1213]) ).
fof(f1213,plain,
! [X0] : c_Nat_OSuc(X0) != X0,
inference(rectify,[],[f68]) ).
fof(f68,axiom,
! [X7] : c_Nat_OSuc(X7) != X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(f7231,plain,
spl47_260,
inference(avatar_split_clause,[],[f5223,f7229]) ).
fof(f7229,plain,
( spl47_260
<=> ! [X0,X3,X2,X1] :
( sP23(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_260])]) ).
fof(f5223,plain,
! [X2,X3,X0,X1] :
( sP23(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f3513]) ).
fof(f3513,plain,
! [X0,X1,X2,X3] :
( sP23(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(definition_folding,[],[f3130,f3512,f3511]) ).
fof(f3130,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
<=> ( ( c_Orderings_Oord__class_Oless(X3,X0,X2)
& c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X2,X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) ) )
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(ennf_transformation,[],[f2034]) ).
fof(f2034,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
<=> ( ( c_Orderings_Oord__class_Oless(X3,X0,X2)
& c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X2,X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) ) ) ),
inference(rectify,[],[f579]) ).
fof(f579,axiom,
! [X29,X24,X12,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X29),X24))
<=> ( ( c_Orderings_Oord__class_Oless(X5,X29,X12)
& c_Orderings_Oord__class_Oless(X5,X24,c_Groups_Ozero__class_Ozero(X5)) )
| ( c_Orderings_Oord__class_Oless(X5,X12,X29)
& c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X24) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
fof(f7227,plain,
spl47_259,
inference(avatar_split_clause,[],[f5214,f7225]) ).
fof(f7225,plain,
( spl47_259
<=> ! [X0,X3,X2,X1] :
( sP21(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_259])]) ).
fof(f5214,plain,
! [X2,X3,X0,X1] :
( sP21(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f3510]) ).
fof(f3510,plain,
! [X0,X1,X2,X3] :
( sP21(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(definition_folding,[],[f3129,f3509,f3508]) ).
fof(f3129,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> ( ( c_Orderings_Oord__class_Oless(X3,X0,X1)
& c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X1,X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) ) ) )
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(ennf_transformation,[],[f2033]) ).
fof(f2033,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> ( ( c_Orderings_Oord__class_Oless(X3,X0,X1)
& c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X1,X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) ) ) ) ),
inference(rectify,[],[f578]) ).
fof(f578,axiom,
! [X29,X12,X24,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X29))
<=> ( ( c_Orderings_Oord__class_Oless(X5,X29,X12)
& c_Orderings_Oord__class_Oless(X5,X24,c_Groups_Ozero__class_Ozero(X5)) )
| ( c_Orderings_Oord__class_Oless(X5,X12,X29)
& c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X24) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
fof(f7223,plain,
spl47_258,
inference(avatar_split_clause,[],[f5193,f7221]) ).
fof(f7221,plain,
( spl47_258
<=> ! [X0,X3,X2,X1] :
( sP19(X2,X3,X1,X0)
| ~ class_Fields_Ofield(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_258])]) ).
fof(f5193,plain,
! [X2,X3,X0,X1] :
( sP19(X2,X3,X1,X0)
| ~ class_Fields_Ofield(X3) ),
inference(cnf_transformation,[],[f3507]) ).
fof(f3507,plain,
! [X0,X1,X2,X3] :
( sP19(X2,X3,X1,X0)
| ~ class_Fields_Ofield(X3) ),
inference(definition_folding,[],[f3112,f3506,f3505]) ).
fof(f3112,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0))
<=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0))
| c_Groups_Ozero__class_Ozero(X3) = X2 )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X0
| c_Groups_Ozero__class_Ozero(X3) != X2 ) ) )
| ~ class_Fields_Ofield(X3) ),
inference(ennf_transformation,[],[f2024]) ).
fof(f2024,plain,
! [X0,X1,X2,X3] :
( class_Fields_Ofield(X3)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),c_Polynomial_Osmult(X3,X2,X1)),X0))
<=> ( ( c_Groups_Ozero__class_Ozero(X3) != X2
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3)),X1),X0)) )
& ( c_Groups_Ozero__class_Ozero(X3) = X2
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X0 ) ) ) ),
inference(rectify,[],[f80]) ).
fof(f80,axiom,
! [X18,X9,X12,X5] :
( class_Fields_Ofield(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),c_Polynomial_Osmult(X5,X12,X9)),X18))
<=> ( ( c_Groups_Ozero__class_Ozero(X5) != X12
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),X9),X18)) )
& ( c_Groups_Ozero__class_Ozero(X5) = X12
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X18 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd__iff) ).
fof(f7219,plain,
spl47_257,
inference(avatar_split_clause,[],[f5148,f7217]) ).
fof(f7217,plain,
( spl47_257
<=> ! [X0,X3,X2,X1] :
( sP17(X2,X1,X3,X0)
| ~ class_Fields_Ofield__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_257])]) ).
fof(f5148,plain,
! [X2,X3,X0,X1] :
( sP17(X2,X1,X3,X0)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(cnf_transformation,[],[f3504]) ).
fof(f3504,plain,
! [X0,X1,X2,X3] :
( sP17(X2,X1,X3,X0)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(definition_folding,[],[f3067,f3503,f3502]) ).
fof(f3067,plain,
! [X0,X1,X2,X3] :
( ( c_Rings_Oinverse__class_Odivide(X3,X2,X1) = X0
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = X0
| c_Groups_Ozero__class_Ozero(X3) != X1 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1) = X2
| c_Groups_Ozero__class_Ozero(X3) = X1 ) ) )
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(ennf_transformation,[],[f1994]) ).
fof(f1994,plain,
! [X0,X1,X2,X3] :
( class_Fields_Ofield__inverse__zero(X3)
=> ( c_Rings_Oinverse__class_Odivide(X3,X2,X1) = X0
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = X1
=> c_Groups_Ozero__class_Ozero(X3) = X0 )
& ( c_Groups_Ozero__class_Ozero(X3) != X1
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1) = X2 ) ) ) ),
inference(rectify,[],[f946]) ).
fof(f946,axiom,
! [X12,X24,X29,X5] :
( class_Fields_Ofield__inverse__zero(X5)
=> ( c_Rings_Oinverse__class_Odivide(X5,X29,X24) = X12
<=> ( ( c_Groups_Ozero__class_Ozero(X5) = X24
=> c_Groups_Ozero__class_Ozero(X5) = X12 )
& ( c_Groups_Ozero__class_Ozero(X5) != X24
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X24) = X29 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq) ).
fof(f7215,plain,
spl47_256,
inference(avatar_split_clause,[],[f5139,f7213]) ).
fof(f7213,plain,
( spl47_256
<=> ! [X0,X3,X2,X1] :
( sP15(X1,X0,X3,X2)
| ~ class_Fields_Ofield__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_256])]) ).
fof(f5139,plain,
! [X2,X3,X0,X1] :
( sP15(X1,X0,X3,X2)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(cnf_transformation,[],[f3501]) ).
fof(f3501,plain,
! [X0,X1,X2,X3] :
( sP15(X1,X0,X3,X2)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(definition_folding,[],[f3066,f3500,f3499]) ).
fof(f3066,plain,
! [X0,X1,X2,X3] :
( ( c_Rings_Oinverse__class_Odivide(X3,X1,X0) = X2
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Ozero__class_Ozero(X3) != X0 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0) = X1
| c_Groups_Ozero__class_Ozero(X3) = X0 ) ) )
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(ennf_transformation,[],[f1993]) ).
fof(f1993,plain,
! [X0,X1,X2,X3] :
( class_Fields_Ofield__inverse__zero(X3)
=> ( c_Rings_Oinverse__class_Odivide(X3,X1,X0) = X2
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = X0
=> c_Groups_Ozero__class_Ozero(X3) = X2 )
& ( c_Groups_Ozero__class_Ozero(X3) != X0
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0) = X1 ) ) ) ),
inference(rectify,[],[f947]) ).
fof(f947,axiom,
! [X24,X29,X12,X5] :
( class_Fields_Ofield__inverse__zero(X5)
=> ( c_Rings_Oinverse__class_Odivide(X5,X29,X24) = X12
<=> ( ( c_Groups_Ozero__class_Ozero(X5) = X24
=> c_Groups_Ozero__class_Ozero(X5) = X12 )
& ( c_Groups_Ozero__class_Ozero(X5) != X24
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X24) = X29 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq) ).
fof(f7211,plain,
spl47_255,
inference(avatar_split_clause,[],[f4264,f7209]) ).
fof(f7209,plain,
( spl47_255
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(c_fequal(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_255])]) ).
fof(f4264,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(c_fequal(X1,X0)) ),
inference(cnf_transformation,[],[f1377]) ).
fof(f1377,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(c_fequal(X1,X0)) ),
inference(rectify,[],[f1204]) ).
fof(f1204,axiom,
! [X25,X15] :
( X15 = X25
| ~ hBOOL(c_fequal(X15,X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
fof(f7207,plain,
spl47_254,
inference(avatar_split_clause,[],[f4235,f7205]) ).
fof(f7205,plain,
( spl47_254
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_254])]) ).
fof(f4235,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),X1),
inference(cnf_transformation,[],[f1351]) ).
fof(f1351,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),X1),
inference(rectify,[],[f789]) ).
fof(f789,axiom,
! [X7,X21] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X7),X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__self) ).
fof(f7203,plain,
spl47_253,
inference(avatar_split_clause,[],[f4234,f7201]) ).
fof(f4234,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
inference(cnf_transformation,[],[f1350]) ).
fof(f1350,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
inference(rectify,[],[f339]) ).
fof(f339,axiom,
! [X21,X7] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).
fof(f7199,plain,
spl47_252,
inference(avatar_split_clause,[],[f4233,f7197]) ).
fof(f4233,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
inference(cnf_transformation,[],[f1349]) ).
fof(f1349,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
inference(rectify,[],[f338]) ).
fof(f338,axiom,
! [X21,X7] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).
fof(f7195,plain,
spl47_251,
inference(avatar_split_clause,[],[f4232,f7193]) ).
fof(f4232,plain,
! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0),
inference(cnf_transformation,[],[f1348]) ).
fof(f1348,plain,
! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0),
inference(rectify,[],[f326]) ).
fof(f326,axiom,
! [X32,X33] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X32),X32),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(f7191,plain,
spl47_250,
inference(avatar_split_clause,[],[f4231,f7189]) ).
fof(f4231,plain,
! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1),
inference(cnf_transformation,[],[f1347]) ).
fof(f1347,plain,
! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1),
inference(rectify,[],[f327]) ).
fof(f327,axiom,
! [X33,X32] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X33),X32),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).
fof(f7187,plain,
spl47_249,
inference(avatar_split_clause,[],[f4184,f7185]) ).
fof(f7185,plain,
( spl47_249
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0)
| ~ class_Rings_Ozero__neq__one(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_249])]) ).
fof(f4184,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0)
| ~ class_Rings_Ozero__neq__one(X0) ),
inference(cnf_transformation,[],[f2360]) ).
fof(f2360,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0)
| ~ class_Rings_Ozero__neq__one(X0) ),
inference(ennf_transformation,[],[f1308]) ).
fof(f1308,plain,
! [X0] :
( class_Rings_Ozero__neq__one(X0)
=> c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0) ),
inference(rectify,[],[f210]) ).
fof(f210,axiom,
! [X5] :
( class_Rings_Ozero__neq__one(X5)
=> c_Groups_Ozero__class_Ozero(X5) != c_Groups_Oone__class_Oone(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).
fof(f7183,plain,
spl47_248,
inference(avatar_split_clause,[],[f4160,f7181]) ).
fof(f7181,plain,
( spl47_248
<=> ! [X0] :
( ~ c_Polynomial_Opos__poly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_248])]) ).
fof(f4160,plain,
! [X0] :
( ~ c_Polynomial_Opos__poly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2336]) ).
fof(f2336,plain,
! [X0] :
( ~ c_Polynomial_Opos__poly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1284]) ).
fof(f1284,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> ~ c_Polynomial_Opos__poly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
inference(rectify,[],[f589]) ).
fof(f589,axiom,
! [X5] :
( class_Rings_Olinordered__idom(X5)
=> ~ c_Polynomial_Opos__poly(X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__pos__poly__0) ).
fof(f7179,plain,
spl47_247,
inference(avatar_split_clause,[],[f4116,f7177]) ).
fof(f4116,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X0)),
inference(cnf_transformation,[],[f1240]) ).
fof(f1240,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X0)),
inference(rectify,[],[f37]) ).
fof(f37,axiom,
! [X6] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__refl) ).
fof(f7175,plain,
spl47_246,
inference(avatar_split_clause,[],[f4115,f7173]) ).
fof(f4115,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
inference(cnf_transformation,[],[f1239]) ).
fof(f1239,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
inference(rectify,[],[f310]) ).
fof(f310,axiom,
! [X7] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(f7171,plain,
spl47_245,
inference(avatar_split_clause,[],[f4114,f7169]) ).
fof(f7167,plain,
spl47_244,
inference(avatar_split_clause,[],[f4113,f7165]) ).
fof(f7165,plain,
( spl47_244
<=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_244])]) ).
fof(f4113,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) = X0,
inference(cnf_transformation,[],[f1237]) ).
fof(f1237,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) = X0,
inference(rectify,[],[f482]) ).
fof(f482,axiom,
! [X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X26) = X26,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0) ).
fof(f7163,plain,
spl47_243,
inference(avatar_split_clause,[],[f4112,f7161]) ).
fof(f7161,plain,
( spl47_243
<=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_243])]) ).
fof(f4112,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
inference(cnf_transformation,[],[f1236]) ).
fof(f1236,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
inference(rectify,[],[f483]) ).
fof(f483,axiom,
! [X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X26,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0__right) ).
fof(f7159,plain,
spl47_242,
inference(avatar_split_clause,[],[f4111,f7157]) ).
fof(f7157,plain,
( spl47_242
<=> ! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_242])]) ).
fof(f4111,plain,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f1235]) ).
fof(f1235,plain,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f793]) ).
fof(f793,axiom,
! [X21] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X21,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
fof(f7155,plain,
spl47_241,
inference(avatar_split_clause,[],[f4110,f7153]) ).
fof(f7153,plain,
( spl47_241
<=> ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl47_241])]) ).
fof(f4110,plain,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = X0,
inference(cnf_transformation,[],[f1234]) ).
fof(f1234,plain,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = X0,
inference(rectify,[],[f648]) ).
fof(f648,axiom,
! [X26] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X26)) = X26,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zminus) ).
fof(f7151,plain,
spl47_240,
inference(avatar_split_clause,[],[f4109,f7149]) ).
fof(f4109,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0),
inference(cnf_transformation,[],[f1233]) ).
fof(f1233,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0),
inference(rectify,[],[f794]) ).
fof(f794,axiom,
! [X21] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
fof(f7147,plain,
spl47_239,
inference(avatar_split_clause,[],[f4069,f7144]) ).
fof(f7144,plain,
( spl47_239
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_239])]) ).
fof(f4069,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f497]) ).
fof(f497,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__0) ).
fof(f7142,plain,
spl47_238,
inference(avatar_split_clause,[],[f5990,f7139]) ).
fof(f7139,plain,
( spl47_238
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_238])]) ).
fof(f5990,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f5733,f5658]) ).
fof(f5733,plain,
! [X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f4607]) ).
fof(f4607,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f3662]) ).
fof(f7137,plain,
spl47_237,
inference(avatar_split_clause,[],[f5871,f7135]) ).
fof(f7135,plain,
( spl47_237
<=> ! [X2,X1] : sP24(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_237])]) ).
fof(f5871,plain,
! [X2,X1] : sP24(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1,X2),
inference(equality_resolution,[],[f5410]) ).
fof(f5410,plain,
! [X2,X0,X1] :
( sP24(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X0 ),
inference(cnf_transformation,[],[f3887]) ).
fof(f7133,plain,
spl47_236,
inference(avatar_split_clause,[],[f5870,f7131]) ).
fof(f7131,plain,
( spl47_236
<=> ! [X0,X1] : sP24(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_236])]) ).
fof(f5870,plain,
! [X0,X1] : sP24(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),
inference(equality_resolution,[],[f5411]) ).
fof(f5411,plain,
! [X2,X0,X1] :
( sP24(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X2 ),
inference(cnf_transformation,[],[f3887]) ).
fof(f7129,plain,
spl47_235,
inference(avatar_split_clause,[],[f5788,f7127]) ).
fof(f7127,plain,
( spl47_235
<=> ! [X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X1)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_235])]) ).
fof(f5788,plain,
! [X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X1)
| ~ class_Orderings_Oorder(X2) ),
inference(equality_resolution,[],[f4946]) ).
fof(f4946,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| X0 != X1
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f3751]) ).
fof(f3751,plain,
! [X0,X1,X2] :
( ( ( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
& ( ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
| X0 != X1 ) )
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f3750]) ).
fof(f3750,plain,
! [X0,X1,X2] :
( ( ( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
& ( ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
| X0 != X1 ) )
| ~ class_Orderings_Oorder(X2) ),
inference(nnf_transformation,[],[f2930]) ).
fof(f2930,plain,
! [X0,X1,X2] :
( ( X0 = X1
<=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) )
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f1859]) ).
fof(f1859,plain,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( X0 = X1
<=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ) ),
inference(rectify,[],[f296]) ).
fof(f296,axiom,
! [X25,X15,X5] :
( class_Orderings_Oorder(X5)
=> ( X15 = X25
<=> ( c_Orderings_Oord__class_Oless__eq(X5,X25,X15)
& c_Orderings_Oord__class_Oless__eq(X5,X15,X25) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(f7125,plain,
spl47_234,
inference(avatar_split_clause,[],[f5785,f7123]) ).
fof(f7123,plain,
( spl47_234
<=> ! [X2,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_234])]) ).
fof(f5785,plain,
! [X2,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
| ~ class_Orderings_Oorder(X2) ),
inference(equality_resolution,[],[f4941]) ).
fof(f4941,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f2923]) ).
fof(f2923,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f2922]) ).
fof(f2922,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f1855]) ).
fof(f1855,plain,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X0)
=> X0 != X1 ) ),
inference(rectify,[],[f159]) ).
fof(f159,axiom,
! [X10,X6,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X6,X10)
=> X6 != X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(f7121,plain,
spl47_233,
inference(avatar_split_clause,[],[f5753,f7119]) ).
fof(f7119,plain,
( spl47_233
<=> ! [X2,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_233])]) ).
fof(f5753,plain,
! [X2,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(equality_resolution,[],[f4790]) ).
fof(f4790,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f3714]) ).
fof(f3714,plain,
! [X0,X1,X2] :
( ( ( X0 != X1
| ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
& ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
& ( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| X0 = X1 ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(flattening,[],[f3713]) ).
fof(f3713,plain,
! [X0,X1,X2] :
( ( ( X0 != X1
| ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
& ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
& ( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| X0 = X1 ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(nnf_transformation,[],[f2765]) ).
fof(f2765,plain,
! [X0,X1,X2] :
( ( X0 != X1
<=> ( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f1741]) ).
fof(f1741,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( X0 != X1
<=> ( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless(X2,X1,X0) ) ) ),
inference(rectify,[],[f168]) ).
fof(f168,axiom,
! [X25,X15,X5] :
( class_Orderings_Olinorder(X5)
=> ( X15 != X25
<=> ( c_Orderings_Oord__class_Oless(X5,X25,X15)
| c_Orderings_Oord__class_Oless(X5,X15,X25) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(f7117,plain,
spl47_232,
inference(avatar_split_clause,[],[f4686,f7115]) ).
fof(f7115,plain,
( spl47_232
<=> ! [X2,X0,X1] :
( sP10(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_232])]) ).
fof(f4686,plain,
! [X2,X0,X1] :
( sP10(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f3492]) ).
fof(f3492,plain,
! [X0,X1,X2] :
( sP10(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(definition_folding,[],[f2654,f3491,f3490]) ).
fof(f2654,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) )
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(ennf_transformation,[],[f1670]) ).
fof(f1670,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) ) ),
inference(rectify,[],[f549]) ).
fof(f549,axiom,
! [X29,X12,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X29),c_Groups_Ozero__class_Ozero(X5))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X29)
& c_Orderings_Oord__class_Oless__eq(X5,X12,c_Groups_Ozero__class_Ozero(X5)) )
| ( c_Orderings_Oord__class_Oless__eq(X5,X29,c_Groups_Ozero__class_Ozero(X5))
& c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X12) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
fof(f7113,plain,
spl47_231,
inference(avatar_split_clause,[],[f4677,f7111]) ).
fof(f7111,plain,
( spl47_231
<=> ! [X2,X0,X1] :
( sP8(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_231])]) ).
fof(f4677,plain,
! [X2,X0,X1] :
( sP8(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f3489]) ).
fof(f3489,plain,
! [X0,X1,X2] :
( sP8(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(definition_folding,[],[f2653,f3488,f3487]) ).
fof(f2653,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) )
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(ennf_transformation,[],[f1669]) ).
fof(f1669,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) ) ),
inference(rectify,[],[f548]) ).
fof(f548,axiom,
! [X29,X12,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X12),X29))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X5,X29,c_Groups_Ozero__class_Ozero(X5))
& c_Orderings_Oord__class_Oless__eq(X5,X12,c_Groups_Ozero__class_Ozero(X5)) )
| ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X29)
& c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X12) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
fof(f7109,plain,
spl47_230,
inference(avatar_split_clause,[],[f4406,f7107]) ).
fof(f7107,plain,
( spl47_230
<=> ! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_230])]) ).
fof(f4406,plain,
! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ),
inference(cnf_transformation,[],[f2509]) ).
fof(f2509,plain,
! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ),
inference(ennf_transformation,[],[f1492]) ).
fof(f1492,plain,
! [X0,X1] :
( class_Groups_Ominus(X1)
=> class_Groups_Ominus(tc_fun(X0,X1)) ),
inference(rectify,[],[f1005]) ).
fof(f1005,axiom,
! [X87,X86] :
( class_Groups_Ominus(X86)
=> class_Groups_Ominus(tc_fun(X87,X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
fof(f7105,plain,
spl47_229,
inference(avatar_split_clause,[],[f4405,f7103]) ).
fof(f7103,plain,
( spl47_229
<=> ! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_229])]) ).
fof(f4405,plain,
! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(cnf_transformation,[],[f2508]) ).
fof(f2508,plain,
! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(ennf_transformation,[],[f1491]) ).
fof(f1491,plain,
! [X0,X1] :
( class_Orderings_Oorder(X1)
=> class_Orderings_Oorder(tc_fun(X0,X1)) ),
inference(rectify,[],[f1002]) ).
fof(f1002,axiom,
! [X87,X86] :
( class_Orderings_Oorder(X86)
=> class_Orderings_Oorder(tc_fun(X87,X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(f7101,plain,
spl47_228,
inference(avatar_split_clause,[],[f4404,f7099]) ).
fof(f7099,plain,
( spl47_228
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_228])]) ).
fof(f4404,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f2507]) ).
fof(f2507,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f1490]) ).
fof(f1490,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> c_Orderings_Oord__class_Oless__eq(X1,X0,X0) ),
inference(rectify,[],[f123]) ).
fof(f123,axiom,
! [X6,X5] :
( class_Orderings_Opreorder(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,X6,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).
fof(f7097,plain,
spl47_227,
inference(avatar_split_clause,[],[f4403,f7095]) ).
fof(f7095,plain,
( spl47_227
<=> ! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_227])]) ).
fof(f4403,plain,
! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f2506]) ).
fof(f2506,plain,
! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f1489]) ).
fof(f1489,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> class_Orderings_Opreorder(tc_fun(X0,X1)) ),
inference(rectify,[],[f1001]) ).
fof(f1001,axiom,
! [X87,X86] :
( class_Orderings_Opreorder(X86)
=> class_Orderings_Opreorder(tc_fun(X87,X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(f7093,plain,
spl47_226,
inference(avatar_split_clause,[],[f4402,f7091]) ).
fof(f7091,plain,
( spl47_226
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_226])]) ).
fof(f4402,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f2505]) ).
fof(f2505,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f1488]) ).
fof(f1488,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> ~ c_Orderings_Oord__class_Oless(X1,X0,X0) ),
inference(rectify,[],[f169]) ).
fof(f169,axiom,
! [X6,X5] :
( class_Orderings_Opreorder(X5)
=> ~ c_Orderings_Oord__class_Oless(X5,X6,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(f7089,plain,
spl47_225,
inference(avatar_split_clause,[],[f4401,f7087]) ).
fof(f7087,plain,
( spl47_225
<=> ! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_225])]) ).
fof(f4401,plain,
! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ),
inference(cnf_transformation,[],[f2504]) ).
fof(f2504,plain,
! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ),
inference(ennf_transformation,[],[f1487]) ).
fof(f1487,plain,
! [X0,X1] :
( class_Orderings_Oord(X1)
=> class_Orderings_Oord(tc_fun(X0,X1)) ),
inference(rectify,[],[f1003]) ).
fof(f1003,axiom,
! [X87,X86] :
( class_Orderings_Oord(X86)
=> class_Orderings_Oord(tc_fun(X87,X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(f7085,plain,
spl47_224,
inference(avatar_split_clause,[],[f4400,f7083]) ).
fof(f7083,plain,
( spl47_224
<=> ! [X0,X1] :
( class_Groups_Ouminus(tc_fun(X0,X1))
| ~ class_Groups_Ouminus(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_224])]) ).
fof(f4400,plain,
! [X0,X1] :
( class_Groups_Ouminus(tc_fun(X0,X1))
| ~ class_Groups_Ouminus(X1) ),
inference(cnf_transformation,[],[f2503]) ).
fof(f2503,plain,
! [X0,X1] :
( class_Groups_Ouminus(tc_fun(X0,X1))
| ~ class_Groups_Ouminus(X1) ),
inference(ennf_transformation,[],[f1486]) ).
fof(f1486,plain,
! [X0,X1] :
( class_Groups_Ouminus(X1)
=> class_Groups_Ouminus(tc_fun(X0,X1)) ),
inference(rectify,[],[f1004]) ).
fof(f1004,axiom,
! [X87,X86] :
( class_Groups_Ouminus(X86)
=> class_Groups_Ouminus(tc_fun(X87,X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).
fof(f7081,plain,
spl47_223,
inference(avatar_split_clause,[],[f4283,f7079]) ).
fof(f7079,plain,
( spl47_223
<=> ! [X0,X1] :
( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_223])]) ).
fof(f4283,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(cnf_transformation,[],[f2411]) ).
fof(f2411,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(ennf_transformation,[],[f1397]) ).
fof(f1397,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(X1)
=> class_Lattices_Oboolean__algebra(tc_fun(X0,X1)) ),
inference(rectify,[],[f1000]) ).
fof(f1000,axiom,
! [X87,X86] :
( class_Lattices_Oboolean__algebra(X86)
=> class_Lattices_Oboolean__algebra(tc_fun(X87,X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
fof(f7077,plain,
spl47_222,
inference(avatar_split_clause,[],[f4068,f7074]) ).
fof(f4068,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f481]) ).
fof(f481,axiom,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__less__1) ).
fof(f7072,plain,
spl47_221,
inference(avatar_split_clause,[],[f4066,f7069]) ).
fof(f7069,plain,
( spl47_221
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_221])]) ).
fof(f4066,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f709]) ).
fof(f709,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(f7067,plain,
~ spl47_220,
inference(avatar_split_clause,[],[f4063,f7064]) ).
fof(f4063,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dp) ).
fof(f7062,plain,
( spl47_145
| spl47_219
| spl47_153 ),
inference(avatar_split_clause,[],[f3913,f6789,f7059,f6756]) ).
fof(f3913,plain,
( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| sP0 ),
inference(cnf_transformation,[],[f3523]) ).
fof(f7057,plain,
spl47_218,
inference(avatar_split_clause,[],[f5960,f7054]) ).
fof(f7054,plain,
( spl47_218
<=> sP6(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_218])]) ).
fof(f5960,plain,
sP6(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f5959,f4114]) ).
fof(f5959,plain,
sP6(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(forward_demodulation,[],[f5721,f4240]) ).
fof(f5721,plain,
sP6(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(equality_resolution,[],[f5720]) ).
fof(f5720,plain,
! [X1] :
( sP6(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1 ),
inference(equality_resolution,[],[f5603]) ).
fof(f5603,plain,
! [X0,X1] :
( sP6(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1 ),
inference(definition_unfolding,[],[f4571,f4118]) ).
fof(f4571,plain,
! [X0,X1] :
( sP6(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(cnf_transformation,[],[f3640]) ).
fof(f7052,plain,
spl47_217,
inference(avatar_split_clause,[],[f5958,f7049]) ).
fof(f7049,plain,
( spl47_217
<=> sP6(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_217])]) ).
fof(f5958,plain,
sP6(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_demodulation,[],[f5957,f4114]) ).
fof(f5957,plain,
sP6(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_demodulation,[],[f5719,f4240]) ).
fof(f5719,plain,
sP6(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f5718]) ).
fof(f5718,plain,
! [X1] :
( sP6(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(equality_resolution,[],[f5602]) ).
fof(f5602,plain,
! [X0,X1] :
( sP6(X0,X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(definition_unfolding,[],[f4572,f4118]) ).
fof(f4572,plain,
! [X0,X1] :
( sP6(X0,X1)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f3640]) ).
fof(f7047,plain,
spl47_216,
inference(avatar_split_clause,[],[f5944,f7044]) ).
fof(f7044,plain,
( spl47_216
<=> sP5(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_216])]) ).
fof(f5944,plain,
sP5(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f5943,f4114]) ).
fof(f5943,plain,
sP5(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(forward_demodulation,[],[f5717,f4240]) ).
fof(f5717,plain,
sP5(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(equality_resolution,[],[f5716]) ).
fof(f5716,plain,
! [X1] :
( sP5(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1 ),
inference(equality_resolution,[],[f5596]) ).
fof(f5596,plain,
! [X0,X1] :
( sP5(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1 ),
inference(definition_unfolding,[],[f4563,f4118]) ).
fof(f4563,plain,
! [X0,X1] :
( sP5(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(cnf_transformation,[],[f3637]) ).
fof(f7042,plain,
spl47_215,
inference(avatar_split_clause,[],[f5942,f7039]) ).
fof(f7039,plain,
( spl47_215
<=> sP5(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_215])]) ).
fof(f5942,plain,
sP5(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_demodulation,[],[f5941,f4114]) ).
fof(f5941,plain,
sP5(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_demodulation,[],[f5715,f4240]) ).
fof(f5715,plain,
sP5(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f5714]) ).
fof(f5714,plain,
! [X1] :
( sP5(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(equality_resolution,[],[f5595]) ).
fof(f5595,plain,
! [X0,X1] :
( sP5(X0,X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(definition_unfolding,[],[f4564,f4118]) ).
fof(f4564,plain,
! [X0,X1] :
( sP5(X0,X1)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f3637]) ).
fof(f7037,plain,
spl47_214,
inference(avatar_split_clause,[],[f4205,f7035]) ).
fof(f4205,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2381]) ).
fof(f2381,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1329]) ).
fof(f1329,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1175]) ).
fof(f1175,axiom,
! [X86] :
( class_Rings_Ocomm__semiring__1(X86)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(f7033,plain,
spl47_213,
inference(avatar_split_clause,[],[f4204,f7031]) ).
fof(f7031,plain,
( spl47_213
<=> ! [X0] :
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_213])]) ).
fof(f4204,plain,
! [X0] :
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2380]) ).
fof(f2380,plain,
! [X0] :
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1328]) ).
fof(f1328,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1184]) ).
fof(f1184,axiom,
! [X86] :
( class_Rings_Ocomm__semiring__1(X86)
=> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).
fof(f7029,plain,
spl47_212,
inference(avatar_split_clause,[],[f4203,f7027]) ).
fof(f7027,plain,
( spl47_212
<=> ! [X0] :
( class_Power_Opower(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_212])]) ).
fof(f4203,plain,
! [X0] :
( class_Power_Opower(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2379]) ).
fof(f2379,plain,
! [X0] :
( class_Power_Opower(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1327]) ).
fof(f1327,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Power_Opower(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1198]) ).
fof(f1198,axiom,
! [X86] :
( class_Rings_Ocomm__semiring__1(X86)
=> class_Power_Opower(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).
fof(f7025,plain,
spl47_211,
inference(avatar_split_clause,[],[f4202,f7023]) ).
fof(f7023,plain,
( spl47_211
<=> ! [X0] :
( class_Rings_Odvd(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_211])]) ).
fof(f4202,plain,
! [X0] :
( class_Rings_Odvd(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2378]) ).
fof(f2378,plain,
! [X0] :
( class_Rings_Odvd(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1326]) ).
fof(f1326,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Rings_Odvd(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1203]) ).
fof(f1203,axiom,
! [X86] :
( class_Rings_Ocomm__semiring__1(X86)
=> class_Rings_Odvd(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Odvd) ).
fof(f7021,plain,
spl47_210,
inference(avatar_split_clause,[],[f4201,f7019]) ).
fof(f7019,plain,
( spl47_210
<=> ! [X0] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_210])]) ).
fof(f4201,plain,
! [X0] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2377]) ).
fof(f2377,plain,
! [X0] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1325]) ).
fof(f1325,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1180]) ).
fof(f1180,axiom,
! [X86] :
( class_Rings_Ocomm__semiring__1(X86)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
fof(f7017,plain,
spl47_209,
inference(avatar_split_clause,[],[f4200,f7015]) ).
fof(f7015,plain,
( spl47_209
<=> ! [X0] :
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_209])]) ).
fof(f4200,plain,
! [X0] :
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2376]) ).
fof(f2376,plain,
! [X0] :
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1324]) ).
fof(f1324,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1168]) ).
fof(f1168,axiom,
! [X86] :
( class_Rings_Ocomm__semiring__1(X86)
=> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).
fof(f7013,plain,
spl47_208,
inference(avatar_split_clause,[],[f4199,f7011]) ).
fof(f7011,plain,
( spl47_208
<=> ! [X0] :
( class_Groups_Oone(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_208])]) ).
fof(f4199,plain,
! [X0] :
( class_Groups_Oone(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2375]) ).
fof(f2375,plain,
! [X0] :
( class_Groups_Oone(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1323]) ).
fof(f1323,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Groups_Oone(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1202]) ).
fof(f1202,axiom,
! [X86] :
( class_Rings_Ocomm__semiring__1(X86)
=> class_Groups_Oone(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).
fof(f7009,plain,
spl47_207,
inference(avatar_split_clause,[],[f4198,f7007]) ).
fof(f7007,plain,
( spl47_207
<=> ! [X0] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_207])]) ).
fof(f4198,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2374]) ).
fof(f2374,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1322]) ).
fof(f1322,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1176]) ).
fof(f1176,axiom,
! [X86] :
( class_Rings_Ocomm__semiring__0(X86)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
fof(f7005,plain,
spl47_206,
inference(avatar_split_clause,[],[f4197,f7003]) ).
fof(f7003,plain,
( spl47_206
<=> ! [X0] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_206])]) ).
fof(f4197,plain,
! [X0] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2373]) ).
fof(f2373,plain,
! [X0] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1321]) ).
fof(f1321,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1189]) ).
fof(f1189,axiom,
! [X86] :
( class_Rings_Ocomm__semiring__0(X86)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).
fof(f7001,plain,
spl47_205,
inference(avatar_split_clause,[],[f4196,f6999]) ).
fof(f6999,plain,
( spl47_205
<=> ! [X0] :
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_205])]) ).
fof(f4196,plain,
! [X0] :
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2372]) ).
fof(f2372,plain,
! [X0] :
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1320]) ).
fof(f1320,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1187]) ).
fof(f1187,axiom,
! [X86] :
( class_Rings_Ocomm__semiring__0(X86)
=> class_Rings_Osemiring__0(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).
fof(f6997,plain,
spl47_204,
inference(avatar_split_clause,[],[f4195,f6995]) ).
fof(f6995,plain,
( spl47_204
<=> ! [X0] :
( class_Rings_Osemiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_204])]) ).
fof(f4195,plain,
! [X0] :
( class_Rings_Osemiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2371]) ).
fof(f2371,plain,
! [X0] :
( class_Rings_Osemiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1319]) ).
fof(f1319,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Rings_Osemiring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1193]) ).
fof(f1193,axiom,
! [X86] :
( class_Rings_Ocomm__semiring__0(X86)
=> class_Rings_Osemiring(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).
fof(f6993,plain,
spl47_203,
inference(avatar_split_clause,[],[f4194,f6991]) ).
fof(f6991,plain,
( spl47_203
<=> ! [X0] :
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_203])]) ).
fof(f4194,plain,
! [X0] :
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2370]) ).
fof(f2370,plain,
! [X0] :
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1318]) ).
fof(f1318,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1178]) ).
fof(f1178,axiom,
! [X86] :
( class_Rings_Ocomm__semiring__0(X86)
=> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).
fof(f6989,plain,
spl47_202,
inference(avatar_split_clause,[],[f4193,f6987]) ).
fof(f6987,plain,
( spl47_202
<=> ! [X0] :
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_202])]) ).
fof(f4193,plain,
! [X0] :
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2369]) ).
fof(f2369,plain,
! [X0] :
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1317]) ).
fof(f1317,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1167]) ).
fof(f1167,axiom,
! [X86] :
( class_Rings_Ocomm__semiring__0(X86)
=> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).
fof(f6985,plain,
spl47_201,
inference(avatar_split_clause,[],[f4190,f6983]) ).
fof(f6983,plain,
( spl47_201
<=> ! [X0] :
( class_Groups_Ozero(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_201])]) ).
fof(f4190,plain,
! [X0] :
( class_Groups_Ozero(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f2366]) ).
fof(f2366,plain,
! [X0] :
( class_Groups_Ozero(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ozero(X0) ),
inference(ennf_transformation,[],[f1314]) ).
fof(f1314,plain,
! [X0] :
( class_Groups_Ozero(X0)
=> class_Groups_Ozero(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1199]) ).
fof(f1199,axiom,
! [X86] :
( class_Groups_Ozero(X86)
=> class_Groups_Ozero(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).
fof(f6981,plain,
spl47_200,
inference(avatar_split_clause,[],[f4189,f6979]) ).
fof(f6979,plain,
( spl47_200
<=> ! [X0] :
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_200])]) ).
fof(f4189,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2365]) ).
fof(f2365,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(ennf_transformation,[],[f1313]) ).
fof(f1313,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(X0)
=> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1172]) ).
fof(f1172,axiom,
! [X86] :
( class_Groups_Ocomm__monoid__add(X86)
=> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).
fof(f6977,plain,
spl47_199,
inference(avatar_split_clause,[],[f4188,f6975]) ).
fof(f6975,plain,
( spl47_199
<=> ! [X0] :
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_199])]) ).
fof(f4188,plain,
! [X0] :
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2364]) ).
fof(f2364,plain,
! [X0] :
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(ennf_transformation,[],[f1312]) ).
fof(f1312,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(X0)
=> class_Groups_Omonoid__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1186]) ).
fof(f1186,axiom,
! [X86] :
( class_Groups_Ocomm__monoid__add(X86)
=> class_Groups_Omonoid__add(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).
fof(f6973,plain,
spl47_198,
inference(avatar_split_clause,[],[f4187,f6971]) ).
fof(f6971,plain,
( spl47_198
<=> ! [X0] :
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_198])]) ).
fof(f4187,plain,
! [X0] :
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2363]) ).
fof(f2363,plain,
! [X0] :
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(ennf_transformation,[],[f1311]) ).
fof(f1311,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(X0)
=> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1169]) ).
fof(f1169,axiom,
! [X86] :
( class_Groups_Ocomm__monoid__add(X86)
=> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).
fof(f6969,plain,
spl47_197,
inference(avatar_split_clause,[],[f4183,f6967]) ).
fof(f6967,plain,
( spl47_197
<=> ! [X0] :
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_197])]) ).
fof(f4183,plain,
! [X0] :
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2359]) ).
fof(f2359,plain,
! [X0] :
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(ennf_transformation,[],[f1307]) ).
fof(f1307,plain,
! [X0] :
( class_Groups_Ocancel__comm__monoid__add(X0)
=> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1164]) ).
fof(f1164,axiom,
! [X86] :
( class_Groups_Ocancel__comm__monoid__add(X86)
=> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).
fof(f6965,plain,
spl47_196,
inference(avatar_split_clause,[],[f4182,f6963]) ).
fof(f6963,plain,
( spl47_196
<=> ! [X0] :
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_196])]) ).
fof(f4182,plain,
! [X0] :
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2358]) ).
fof(f2358,plain,
! [X0] :
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(ennf_transformation,[],[f1306]) ).
fof(f1306,plain,
! [X0] :
( class_Groups_Ocancel__comm__monoid__add(X0)
=> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f996]) ).
fof(f996,axiom,
! [X86] :
( class_Groups_Ocancel__comm__monoid__add(X86)
=> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).
fof(f6961,plain,
spl47_195,
inference(avatar_split_clause,[],[f4181,f6959]) ).
fof(f6959,plain,
( spl47_195
<=> ! [X0] :
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_195])]) ).
fof(f4181,plain,
! [X0] :
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2357]) ).
fof(f2357,plain,
! [X0] :
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(ennf_transformation,[],[f1305]) ).
fof(f1305,plain,
! [X0] :
( class_Groups_Ocancel__comm__monoid__add(X0)
=> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1156]) ).
fof(f1156,axiom,
! [X86] :
( class_Groups_Ocancel__comm__monoid__add(X86)
=> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).
fof(f6957,plain,
spl47_194,
inference(avatar_split_clause,[],[f4174,f6955]) ).
fof(f6955,plain,
( spl47_194
<=> ! [X0] :
( class_Groups_Ominus(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_194])]) ).
fof(f4174,plain,
! [X0] :
( class_Groups_Ominus(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f2350]) ).
fof(f2350,plain,
! [X0] :
( class_Groups_Ominus(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(ennf_transformation,[],[f1298]) ).
fof(f1298,plain,
! [X0] :
( class_Groups_Oab__group__add(X0)
=> class_Groups_Ominus(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1197]) ).
fof(f1197,axiom,
! [X86] :
( class_Groups_Oab__group__add(X86)
=> class_Groups_Ominus(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ominus) ).
fof(f6953,plain,
spl47_193,
inference(avatar_split_clause,[],[f4173,f6951]) ).
fof(f6951,plain,
( spl47_193
<=> ! [X0] :
( class_Groups_Ouminus(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_193])]) ).
fof(f4173,plain,
! [X0] :
( class_Groups_Ouminus(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f2349]) ).
fof(f2349,plain,
! [X0] :
( class_Groups_Ouminus(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(ennf_transformation,[],[f1297]) ).
fof(f1297,plain,
! [X0] :
( class_Groups_Oab__group__add(X0)
=> class_Groups_Ouminus(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1195]) ).
fof(f1195,axiom,
! [X86] :
( class_Groups_Oab__group__add(X86)
=> class_Groups_Ouminus(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ouminus) ).
fof(f6949,plain,
spl47_192,
inference(avatar_split_clause,[],[f4172,f6947]) ).
fof(f6947,plain,
( spl47_192
<=> ! [X0] :
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_192])]) ).
fof(f4172,plain,
! [X0] :
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f2348]) ).
fof(f2348,plain,
! [X0] :
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(ennf_transformation,[],[f1296]) ).
fof(f1296,plain,
! [X0] :
( class_Groups_Oab__group__add(X0)
=> class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1179]) ).
fof(f1179,axiom,
! [X86] :
( class_Groups_Oab__group__add(X86)
=> class_Groups_Oab__group__add(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).
fof(f6945,plain,
spl47_191,
inference(avatar_split_clause,[],[f4171,f6943]) ).
fof(f6943,plain,
( spl47_191
<=> ! [X0] :
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_191])]) ).
fof(f4171,plain,
! [X0] :
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f2347]) ).
fof(f2347,plain,
! [X0] :
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(ennf_transformation,[],[f1295]) ).
fof(f1295,plain,
! [X0] :
( class_Groups_Oab__group__add(X0)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1188]) ).
fof(f1188,axiom,
! [X86] :
( class_Groups_Oab__group__add(X86)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
fof(f6941,plain,
spl47_190,
inference(avatar_split_clause,[],[f4169,f6939]) ).
fof(f6939,plain,
( spl47_190
<=> ! [X0] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_190])]) ).
fof(f4169,plain,
! [X0] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f2345]) ).
fof(f2345,plain,
! [X0] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(ennf_transformation,[],[f1293]) ).
fof(f1293,plain,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1147]) ).
fof(f1147,axiom,
! [X86] :
( class_Rings_Oidom(X86)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f6937,plain,
spl47_189,
inference(avatar_split_clause,[],[f4168,f6935]) ).
fof(f6935,plain,
( spl47_189
<=> ! [X0] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_189])]) ).
fof(f4168,plain,
! [X0] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f2344]) ).
fof(f2344,plain,
! [X0] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(ennf_transformation,[],[f1292]) ).
fof(f1292,plain,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1171]) ).
fof(f1171,axiom,
! [X86] :
( class_Rings_Oidom(X86)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
fof(f6933,plain,
spl47_188,
inference(avatar_split_clause,[],[f4167,f6931]) ).
fof(f6931,plain,
( spl47_188
<=> ! [X0] :
( class_Rings_Oidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_188])]) ).
fof(f4167,plain,
! [X0] :
( class_Rings_Oidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f2343]) ).
fof(f2343,plain,
! [X0] :
( class_Rings_Oidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(ennf_transformation,[],[f1291]) ).
fof(f1291,plain,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Rings_Oidom(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1201]) ).
fof(f1201,axiom,
! [X86] :
( class_Rings_Oidom(X86)
=> class_Rings_Oidom(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).
fof(f6929,plain,
spl47_187,
inference(avatar_split_clause,[],[f4166,f6927]) ).
fof(f6927,plain,
( spl47_187
<=> ! [X0] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_187])]) ).
fof(f4166,plain,
! [X0] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f2342]) ).
fof(f2342,plain,
! [X0] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(ennf_transformation,[],[f1290]) ).
fof(f1290,plain,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1157]) ).
fof(f1157,axiom,
! [X86] :
( class_Rings_Oidom(X86)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).
fof(f6925,plain,
spl47_186,
inference(avatar_split_clause,[],[f4165,f6923]) ).
fof(f6923,plain,
( spl47_186
<=> ! [X0] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_186])]) ).
fof(f4165,plain,
! [X0] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f2341]) ).
fof(f2341,plain,
! [X0] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(ennf_transformation,[],[f1289]) ).
fof(f1289,plain,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1160]) ).
fof(f1160,axiom,
! [X86] :
( class_Rings_Oidom(X86)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).
fof(f6921,plain,
spl47_185,
inference(avatar_split_clause,[],[f4164,f6919]) ).
fof(f6919,plain,
( spl47_185
<=> ! [X0] :
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_185])]) ).
fof(f4164,plain,
! [X0] :
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(cnf_transformation,[],[f2340]) ).
fof(f2340,plain,
! [X0] :
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(ennf_transformation,[],[f1288]) ).
fof(f1288,plain,
! [X0] :
( class_Rings_Ocomm__ring__1(X0)
=> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1185]) ).
fof(f1185,axiom,
! [X86] :
( class_Rings_Ocomm__ring__1(X86)
=> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).
fof(f6917,plain,
spl47_184,
inference(avatar_split_clause,[],[f4163,f6915]) ).
fof(f6915,plain,
( spl47_184
<=> ! [X0] :
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_184])]) ).
fof(f4163,plain,
! [X0] :
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ),
inference(cnf_transformation,[],[f2339]) ).
fof(f2339,plain,
! [X0] :
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ),
inference(ennf_transformation,[],[f1287]) ).
fof(f1287,plain,
! [X0] :
( class_Rings_Ocomm__ring(X0)
=> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1190]) ).
fof(f1190,axiom,
! [X86] :
( class_Rings_Ocomm__ring(X86)
=> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).
fof(f6913,plain,
spl47_183,
inference(avatar_split_clause,[],[f4162,f6911]) ).
fof(f6911,plain,
( spl47_183
<=> ! [X0] :
( class_Rings_Oring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_183])]) ).
fof(f4162,plain,
! [X0] :
( class_Rings_Oring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ),
inference(cnf_transformation,[],[f2338]) ).
fof(f2338,plain,
! [X0] :
( class_Rings_Oring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ),
inference(ennf_transformation,[],[f1286]) ).
fof(f1286,plain,
! [X0] :
( class_Rings_Ocomm__ring(X0)
=> class_Rings_Oring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1200]) ).
fof(f1200,axiom,
! [X86] :
( class_Rings_Ocomm__ring(X86)
=> class_Rings_Oring(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).
fof(f6909,plain,
spl47_182,
inference(avatar_split_clause,[],[f4161,f6907]) ).
fof(f6907,plain,
( spl47_182
<=> ! [X0] :
( class_Rings_Oring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_182])]) ).
fof(f4161,plain,
! [X0] :
( class_Rings_Oring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(cnf_transformation,[],[f2337]) ).
fof(f2337,plain,
! [X0] :
( class_Rings_Oring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(ennf_transformation,[],[f1285]) ).
fof(f1285,plain,
! [X0] :
( class_Rings_Ocomm__ring__1(X0)
=> class_Rings_Oring__1(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1196]) ).
fof(f1196,axiom,
! [X86] :
( class_Rings_Ocomm__ring__1(X86)
=> class_Rings_Oring__1(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).
fof(f6905,plain,
spl47_181,
inference(avatar_split_clause,[],[f4159,f6903]) ).
fof(f6903,plain,
( spl47_181
<=> ! [X0] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_181])]) ).
fof(f4159,plain,
! [X0] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2335]) ).
fof(f2335,plain,
! [X0] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1283]) ).
fof(f1283,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Orderings_Oorder(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1191]) ).
fof(f1191,axiom,
! [X86] :
( class_Rings_Olinordered__idom(X86)
=> class_Orderings_Oorder(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oorder) ).
fof(f6901,plain,
spl47_180,
inference(avatar_split_clause,[],[f4158,f6899]) ).
fof(f6899,plain,
( spl47_180
<=> ! [X0] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_180])]) ).
fof(f4158,plain,
! [X0] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2334]) ).
fof(f2334,plain,
! [X0] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1282]) ).
fof(f1282,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Orderings_Opreorder(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1182]) ).
fof(f1182,axiom,
! [X86] :
( class_Rings_Olinordered__idom(X86)
=> class_Orderings_Opreorder(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(f6897,plain,
spl47_179,
inference(avatar_split_clause,[],[f4157,f6895]) ).
fof(f6895,plain,
( spl47_179
<=> ! [X0] :
( class_Orderings_Oord(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_179])]) ).
fof(f4157,plain,
! [X0] :
( class_Orderings_Oord(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2333]) ).
fof(f2333,plain,
! [X0] :
( class_Orderings_Oord(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1281]) ).
fof(f1281,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Orderings_Oord(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1194]) ).
fof(f1194,axiom,
! [X86] :
( class_Rings_Olinordered__idom(X86)
=> class_Orderings_Oord(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).
fof(f6893,plain,
spl47_178,
inference(avatar_split_clause,[],[f4156,f6891]) ).
fof(f6891,plain,
( spl47_178
<=> ! [X0] :
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_178])]) ).
fof(f4156,plain,
! [X0] :
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2332]) ).
fof(f2332,plain,
! [X0] :
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1280]) ).
fof(f1280,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1166]) ).
fof(f1166,axiom,
! [X86] :
( class_Rings_Olinordered__idom(X86)
=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).
fof(f6889,plain,
spl47_177,
inference(avatar_split_clause,[],[f4155,f6887]) ).
fof(f6887,plain,
( spl47_177
<=> ! [X0] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_177])]) ).
fof(f4155,plain,
! [X0] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2331]) ).
fof(f2331,plain,
! [X0] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1279]) ).
fof(f1279,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Orderings_Olinorder(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1183]) ).
fof(f1183,axiom,
! [X86] :
( class_Rings_Olinordered__idom(X86)
=> class_Orderings_Olinorder(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(f6885,plain,
spl47_176,
inference(avatar_split_clause,[],[f4154,f6883]) ).
fof(f6883,plain,
( spl47_176
<=> ! [X0] :
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_176])]) ).
fof(f4154,plain,
! [X0] :
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2330]) ).
fof(f2330,plain,
! [X0] :
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1278]) ).
fof(f1278,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1152]) ).
fof(f1152,axiom,
! [X86] :
( class_Rings_Olinordered__idom(X86)
=> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).
fof(f6881,plain,
spl47_175,
inference(avatar_split_clause,[],[f4153,f6879]) ).
fof(f6879,plain,
( spl47_175
<=> ! [X0] :
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_175])]) ).
fof(f4153,plain,
! [X0] :
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2329]) ).
fof(f2329,plain,
! [X0] :
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1277]) ).
fof(f1277,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1154]) ).
fof(f1154,axiom,
! [X86] :
( class_Rings_Olinordered__idom(X86)
=> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).
fof(f6877,plain,
spl47_174,
inference(avatar_split_clause,[],[f4152,f6875]) ).
fof(f6875,plain,
( spl47_174
<=> ! [X0] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_174])]) ).
fof(f4152,plain,
! [X0] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2328]) ).
fof(f2328,plain,
! [X0] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1276]) ).
fof(f1276,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1149]) ).
fof(f1149,axiom,
! [X86] :
( class_Rings_Olinordered__idom(X86)
=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f6873,plain,
spl47_173,
inference(avatar_split_clause,[],[f4151,f6871]) ).
fof(f6871,plain,
( spl47_173
<=> ! [X0] :
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_173])]) ).
fof(f4151,plain,
! [X0] :
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2327]) ).
fof(f2327,plain,
! [X0] :
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1275]) ).
fof(f1275,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1158]) ).
fof(f1158,axiom,
! [X86] :
( class_Rings_Olinordered__idom(X86)
=> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).
fof(f6869,plain,
spl47_172,
inference(avatar_split_clause,[],[f4150,f6867]) ).
fof(f6867,plain,
( spl47_172
<=> ! [X0] :
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_172])]) ).
fof(f4150,plain,
! [X0] :
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2326]) ).
fof(f2326,plain,
! [X0] :
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1274]) ).
fof(f1274,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1148]) ).
fof(f1148,axiom,
! [X86] :
( class_Rings_Olinordered__idom(X86)
=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f6865,plain,
spl47_171,
inference(avatar_split_clause,[],[f4149,f6863]) ).
fof(f6863,plain,
( spl47_171
<=> ! [X0] :
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_171])]) ).
fof(f4149,plain,
! [X0] :
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2325]) ).
fof(f2325,plain,
! [X0] :
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1273]) ).
fof(f1273,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1170]) ).
fof(f1170,axiom,
! [X86] :
( class_Rings_Olinordered__idom(X86)
=> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).
fof(f6861,plain,
spl47_170,
inference(avatar_split_clause,[],[f4148,f6859]) ).
fof(f6859,plain,
( spl47_170
<=> ! [X0] :
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_170])]) ).
fof(f4148,plain,
! [X0] :
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2324]) ).
fof(f2324,plain,
! [X0] :
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1272]) ).
fof(f1272,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1153]) ).
fof(f1153,axiom,
! [X86] :
( class_Rings_Olinordered__idom(X86)
=> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).
fof(f6857,plain,
spl47_169,
inference(avatar_split_clause,[],[f4147,f6855]) ).
fof(f6855,plain,
( spl47_169
<=> ! [X0] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_169])]) ).
fof(f4147,plain,
! [X0] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2323]) ).
fof(f2323,plain,
! [X0] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1271]) ).
fof(f1271,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Int_Oring__char__0(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1192]) ).
fof(f1192,axiom,
! [X86] :
( class_Rings_Olinordered__idom(X86)
=> class_Int_Oring__char__0(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).
fof(f6853,plain,
spl47_168,
inference(avatar_split_clause,[],[f4146,f6851]) ).
fof(f6851,plain,
( spl47_168
<=> ! [X0] :
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_168])]) ).
fof(f4146,plain,
! [X0] :
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2322]) ).
fof(f2322,plain,
! [X0] :
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1270]) ).
fof(f1270,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1165]) ).
fof(f1165,axiom,
! [X86] :
( class_Rings_Olinordered__idom(X86)
=> class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).
fof(f6849,plain,
spl47_167,
inference(avatar_split_clause,[],[f4145,f6847]) ).
fof(f6847,plain,
( spl47_167
<=> ! [X0] :
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_167])]) ).
fof(f4145,plain,
! [X0] :
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2321]) ).
fof(f2321,plain,
! [X0] :
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1269]) ).
fof(f1269,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1150]) ).
fof(f1150,axiom,
! [X86] :
( class_Rings_Olinordered__idom(X86)
=> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).
fof(f6845,plain,
spl47_166,
inference(avatar_split_clause,[],[f4144,f6843]) ).
fof(f6843,plain,
( spl47_166
<=> ! [X0] :
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_166])]) ).
fof(f4144,plain,
! [X0] :
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2320]) ).
fof(f2320,plain,
! [X0] :
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1268]) ).
fof(f1268,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1161]) ).
fof(f1161,axiom,
! [X86] :
( class_Rings_Olinordered__idom(X86)
=> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).
fof(f6841,plain,
spl47_165,
inference(avatar_split_clause,[],[f4143,f6839]) ).
fof(f6839,plain,
( spl47_165
<=> ! [X0] :
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_165])]) ).
fof(f4143,plain,
! [X0] :
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2319]) ).
fof(f2319,plain,
! [X0] :
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1267]) ).
fof(f1267,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1174]) ).
fof(f1174,axiom,
! [X86] :
( class_Rings_Olinordered__idom(X86)
=> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).
fof(f6837,plain,
spl47_164,
inference(avatar_split_clause,[],[f4142,f6835]) ).
fof(f6835,plain,
( spl47_164
<=> ! [X0] :
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_164])]) ).
fof(f4142,plain,
! [X0] :
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2318]) ).
fof(f2318,plain,
! [X0] :
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1266]) ).
fof(f1266,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1163]) ).
fof(f1163,axiom,
! [X86] :
( class_Rings_Olinordered__idom(X86)
=> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).
fof(f6833,plain,
spl47_163,
inference(avatar_split_clause,[],[f4141,f6831]) ).
fof(f6831,plain,
( spl47_163
<=> ! [X0] :
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_163])]) ).
fof(f4141,plain,
! [X0] :
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2317]) ).
fof(f2317,plain,
! [X0] :
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1265]) ).
fof(f1265,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1159]) ).
fof(f1159,axiom,
! [X86] :
( class_Rings_Olinordered__idom(X86)
=> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).
fof(f6829,plain,
spl47_162,
inference(avatar_split_clause,[],[f4140,f6827]) ).
fof(f6827,plain,
( spl47_162
<=> ! [X0] :
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_162])]) ).
fof(f4140,plain,
! [X0] :
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2316]) ).
fof(f2316,plain,
! [X0] :
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1264]) ).
fof(f1264,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1155]) ).
fof(f1155,axiom,
! [X86] :
( class_Rings_Olinordered__idom(X86)
=> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).
fof(f6825,plain,
spl47_161,
inference(avatar_split_clause,[],[f4139,f6823]) ).
fof(f6823,plain,
( spl47_161
<=> ! [X0] :
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_161])]) ).
fof(f4139,plain,
! [X0] :
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2315]) ).
fof(f2315,plain,
! [X0] :
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1263]) ).
fof(f1263,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1181]) ).
fof(f1181,axiom,
! [X86] :
( class_Rings_Olinordered__idom(X86)
=> class_Rings_Oordered__ring(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).
fof(f6821,plain,
spl47_160,
inference(avatar_split_clause,[],[f4138,f6819]) ).
fof(f6819,plain,
( spl47_160
<=> ! [X0] :
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_160])]) ).
fof(f4138,plain,
! [X0] :
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2314]) ).
fof(f2314,plain,
! [X0] :
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1262]) ).
fof(f1262,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1173]) ).
fof(f1173,axiom,
! [X86] :
( class_Rings_Olinordered__idom(X86)
=> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).
fof(f6817,plain,
spl47_159,
inference(avatar_split_clause,[],[f4137,f6815]) ).
fof(f6815,plain,
( spl47_159
<=> ! [X0] :
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_159])]) ).
fof(f4137,plain,
! [X0] :
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2313]) ).
fof(f2313,plain,
! [X0] :
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1261]) ).
fof(f1261,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1151]) ).
fof(f1151,axiom,
! [X86] :
( class_Rings_Olinordered__idom(X86)
=> class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).
fof(f6813,plain,
spl47_158,
inference(avatar_split_clause,[],[f4136,f6811]) ).
fof(f6811,plain,
( spl47_158
<=> ! [X0] :
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_158])]) ).
fof(f4136,plain,
! [X0] :
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2312]) ).
fof(f2312,plain,
! [X0] :
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1260]) ).
fof(f1260,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1162]) ).
fof(f1162,axiom,
! [X86] :
( class_Rings_Olinordered__idom(X86)
=> class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).
fof(f6809,plain,
spl47_157,
inference(avatar_split_clause,[],[f4135,f6807]) ).
fof(f4135,plain,
! [X0] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0))
| ~ class_Fields_Ofield(X0) ),
inference(cnf_transformation,[],[f2311]) ).
fof(f2311,plain,
! [X0] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0))
| ~ class_Fields_Ofield(X0) ),
inference(ennf_transformation,[],[f1259]) ).
fof(f1259,plain,
! [X0] :
( class_Fields_Ofield(X0)
=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1177]) ).
fof(f1177,axiom,
! [X86] :
( class_Fields_Ofield(X86)
=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Osemiring__div) ).
fof(f6805,plain,
spl47_156,
inference(avatar_split_clause,[],[f4105,f6803]) ).
fof(f4105,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f1229]) ).
fof(f1229,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
inference(rectify,[],[f81]) ).
fof(f81,axiom,
! [X7] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).
fof(f6801,plain,
spl47_155,
inference(avatar_split_clause,[],[f4101,f6799]) ).
fof(f4101,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f1225]) ).
fof(f1225,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rectify,[],[f133]) ).
fof(f133,axiom,
! [X7] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).
fof(f6797,plain,
~ spl47_154,
inference(avatar_split_clause,[],[f4062,f6794]) ).
fof(f6794,plain,
( spl47_154
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_154])]) ).
fof(f4062,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(cnf_transformation,[],[f479]) ).
fof(f479,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
fof(f6792,plain,
~ spl47_153,
inference(avatar_split_clause,[],[f4061,f6789]) ).
fof(f4061,plain,
v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pe) ).
fof(f6787,plain,
spl47_152,
inference(avatar_split_clause,[],[f5703,f6785]) ).
fof(f5703,plain,
! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(equality_resolution,[],[f4517]) ).
fof(f4517,plain,
! [X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3607]) ).
fof(f6783,plain,
spl47_151,
inference(avatar_split_clause,[],[f5660,f6781]) ).
fof(f6781,plain,
( spl47_151
<=> ! [X1] : hBOOL(c_fequal(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_151])]) ).
fof(f5660,plain,
! [X1] : hBOOL(c_fequal(X1,X1)),
inference(equality_resolution,[],[f4263]) ).
fof(f4263,plain,
! [X0,X1] :
( hBOOL(c_fequal(X1,X0))
| X0 != X1 ),
inference(cnf_transformation,[],[f1376]) ).
fof(f1376,plain,
! [X0,X1] :
( hBOOL(c_fequal(X1,X0))
| X0 != X1 ),
inference(rectify,[],[f1205]) ).
fof(f1205,axiom,
! [X25,X15] :
( hBOOL(c_fequal(X15,X25))
| X15 != X25 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
fof(f6779,plain,
spl47_150,
inference(avatar_split_clause,[],[f4094,f6777]) ).
fof(f4094,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0),
inference(cnf_transformation,[],[f1218]) ).
fof(f1218,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0),
inference(rectify,[],[f86]) ).
fof(f86,axiom,
! [X7] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).
fof(f6775,plain,
spl47_149,
inference(avatar_split_clause,[],[f4093,f6773]) ).
fof(f4093,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f1217]) ).
fof(f1217,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0),
inference(rectify,[],[f467]) ).
fof(f467,axiom,
! [X48] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X48,X48),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__refl) ).
fof(f6771,plain,
spl47_148,
inference(avatar_split_clause,[],[f4091,f6769]) ).
fof(f4091,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0),
inference(cnf_transformation,[],[f1215]) ).
fof(f1215,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0),
inference(rectify,[],[f173]) ).
fof(f173,axiom,
! [X7] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(f6767,plain,
( ~ spl47_145
| ~ spl47_146
| ~ spl47_147 ),
inference(avatar_split_clause,[],[f5889,f6764,f6760,f6756]) ).
fof(f6760,plain,
( spl47_146
<=> v_p = v_q ),
introduced(avatar_definition,[new_symbols(naming,[spl47_146])]) ).
fof(f6764,plain,
( spl47_147
<=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q ),
introduced(avatar_definition,[new_symbols(naming,[spl47_147])]) ).
fof(f5889,plain,
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
| v_p != v_q
| ~ sP0 ),
inference(inner_rewriting,[],[f3916]) ).
fof(f3916,plain,
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
| v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ sP0 ),
inference(cnf_transformation,[],[f3523]) ).
fof(f6754,plain,
spl47_144,
inference(avatar_split_clause,[],[f4060,f6751]) ).
fof(f6751,plain,
( spl47_144
<=> class_Groups_Ominus(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_144])]) ).
fof(f4060,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(cnf_transformation,[],[f1096]) ).
fof(f1096,axiom,
class_Groups_Ominus(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
fof(f6749,plain,
spl47_143,
inference(avatar_split_clause,[],[f4059,f6746]) ).
fof(f6746,plain,
( spl47_143
<=> class_Groups_Ominus(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_143])]) ).
fof(f4059,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(cnf_transformation,[],[f1056]) ).
fof(f1056,axiom,
class_Groups_Ominus(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).
fof(f6744,plain,
spl47_142,
inference(avatar_split_clause,[],[f4058,f6741]) ).
fof(f6741,plain,
( spl47_142
<=> class_Groups_Ominus(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_142])]) ).
fof(f4058,plain,
class_Groups_Ominus(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1139]) ).
fof(f1139,axiom,
class_Groups_Ominus(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ominus) ).
fof(f6739,plain,
spl47_141,
inference(avatar_split_clause,[],[f4057,f6736]) ).
fof(f6736,plain,
( spl47_141
<=> class_Groups_Ominus(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_141])]) ).
fof(f4057,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(cnf_transformation,[],[f1106]) ).
fof(f1106,axiom,
class_Groups_Ominus(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
fof(f6734,plain,
spl47_140,
inference(avatar_split_clause,[],[f4056,f6731]) ).
fof(f6731,plain,
( spl47_140
<=> class_Orderings_Oorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_140])]) ).
fof(f4056,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f1093]) ).
fof(f1093,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(f6729,plain,
spl47_139,
inference(avatar_split_clause,[],[f4055,f6726]) ).
fof(f6726,plain,
( spl47_139
<=> class_Orderings_Oorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_139])]) ).
fof(f4055,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(cnf_transformation,[],[f1050]) ).
fof(f1050,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
fof(f6724,plain,
spl47_138,
inference(avatar_split_clause,[],[f4054,f6721]) ).
fof(f6721,plain,
( spl47_138
<=> class_Orderings_Oorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_138])]) ).
fof(f4054,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f1103]) ).
fof(f1103,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(f6719,plain,
spl47_137,
inference(avatar_split_clause,[],[f4053,f6716]) ).
fof(f6716,plain,
( spl47_137
<=> class_Orderings_Opreorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_137])]) ).
fof(f4053,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f1087]) ).
fof(f1087,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(f6714,plain,
spl47_136,
inference(avatar_split_clause,[],[f4052,f6711]) ).
fof(f6711,plain,
( spl47_136
<=> class_Orderings_Opreorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_136])]) ).
fof(f4052,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(cnf_transformation,[],[f1041]) ).
fof(f1041,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
fof(f6709,plain,
spl47_135,
inference(avatar_split_clause,[],[f4051,f6706]) ).
fof(f6706,plain,
( spl47_135
<=> class_Orderings_Opreorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_135])]) ).
fof(f4051,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f1102]) ).
fof(f1102,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(f6704,plain,
spl47_134,
inference(avatar_split_clause,[],[f4050,f6701]) ).
fof(f4050,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(cnf_transformation,[],[f1095]) ).
fof(f1095,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(f6699,plain,
spl47_133,
inference(avatar_split_clause,[],[f4049,f6696]) ).
fof(f4049,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(cnf_transformation,[],[f1053]) ).
fof(f1053,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
fof(f6694,plain,
spl47_132,
inference(avatar_split_clause,[],[f4048,f6691]) ).
fof(f6691,plain,
( spl47_132
<=> class_Orderings_Oord(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_132])]) ).
fof(f4048,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(cnf_transformation,[],[f1104]) ).
fof(f1104,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(f6689,plain,
spl47_131,
inference(avatar_split_clause,[],[f4047,f6686]) ).
fof(f6686,plain,
( spl47_131
<=> class_Groups_Ouminus(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_131])]) ).
fof(f4047,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(cnf_transformation,[],[f1054]) ).
fof(f1054,axiom,
class_Groups_Ouminus(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).
fof(f6684,plain,
spl47_130,
inference(avatar_split_clause,[],[f4046,f6681]) ).
fof(f6681,plain,
( spl47_130
<=> class_Groups_Ouminus(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_130])]) ).
fof(f4046,plain,
class_Groups_Ouminus(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1137]) ).
fof(f1137,axiom,
class_Groups_Ouminus(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ouminus) ).
fof(f6679,plain,
spl47_129,
inference(avatar_split_clause,[],[f4045,f6676]) ).
fof(f6676,plain,
( spl47_129
<=> class_Groups_Ouminus(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_129])]) ).
fof(f4045,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(cnf_transformation,[],[f1105]) ).
fof(f1105,axiom,
class_Groups_Ouminus(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).
fof(f6674,plain,
spl47_128,
inference(avatar_split_clause,[],[f4044,f6671]) ).
fof(f4044,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(cnf_transformation,[],[f1082]) ).
fof(f1082,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(f6669,plain,
spl47_127,
inference(avatar_split_clause,[],[f4043,f6666]) ).
fof(f4043,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f1034]) ).
fof(f1034,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(f6664,plain,
spl47_126,
inference(avatar_split_clause,[],[f4042,f6661]) ).
fof(f4042,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1121]) ).
fof(f1121,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(f6659,plain,
spl47_125,
inference(avatar_split_clause,[],[f4041,f6656]) ).
fof(f6656,plain,
( spl47_125
<=> class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_125])]) ).
fof(f4041,plain,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f1083]) ).
fof(f1083,axiom,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).
fof(f6654,plain,
spl47_124,
inference(avatar_split_clause,[],[f4040,f6651]) ).
fof(f6651,plain,
( spl47_124
<=> class_Rings_Ocomm__semiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_124])]) ).
fof(f4040,plain,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
inference(cnf_transformation,[],[f1035]) ).
fof(f1035,axiom,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).
fof(f6649,plain,
spl47_123,
inference(avatar_split_clause,[],[f4039,f6646]) ).
fof(f6646,plain,
( spl47_123
<=> class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_123])]) ).
fof(f4039,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1122]) ).
fof(f1122,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(f6644,plain,
spl47_122,
inference(avatar_split_clause,[],[f4038,f6641]) ).
fof(f4038,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f1098]) ).
fof(f1098,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
fof(f6639,plain,
spl47_121,
inference(avatar_split_clause,[],[f4037,f6636]) ).
fof(f4037,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(cnf_transformation,[],[f1058]) ).
fof(f1058,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
fof(f6634,plain,
spl47_120,
inference(avatar_split_clause,[],[f4036,f6631]) ).
fof(f4036,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1142]) ).
fof(f1142,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(f6629,plain,
spl47_119,
inference(avatar_split_clause,[],[f4035,f6626]) ).
fof(f6626,plain,
( spl47_119
<=> class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_119])]) ).
fof(f4035,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1081]) ).
fof(f1081,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(f6624,plain,
spl47_118,
inference(avatar_split_clause,[],[f4034,f6621]) ).
fof(f6621,plain,
( spl47_118
<=> class_Groups_Ocomm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_118])]) ).
fof(f4034,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1031]) ).
fof(f1031,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(f6619,plain,
spl47_117,
inference(avatar_split_clause,[],[f4033,f6616]) ).
fof(f6616,plain,
( spl47_117
<=> class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_117])]) ).
fof(f4033,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1120]) ).
fof(f1120,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
fof(f6614,plain,
spl47_116,
inference(avatar_split_clause,[],[f4032,f6611]) ).
fof(f6611,plain,
( spl47_116
<=> class_Groups_Omonoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_116])]) ).
fof(f4032,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f1089]) ).
fof(f1089,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
fof(f6609,plain,
spl47_115,
inference(avatar_split_clause,[],[f4031,f6606]) ).
fof(f6606,plain,
( spl47_115
<=> class_Groups_Omonoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_115])]) ).
fof(f4031,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f1043]) ).
fof(f1043,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(f6604,plain,
spl47_114,
inference(avatar_split_clause,[],[f4030,f6601]) ).
fof(f6601,plain,
( spl47_114
<=> class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_114])]) ).
fof(f4030,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1128]) ).
fof(f1128,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
fof(f6599,plain,
spl47_113,
inference(avatar_split_clause,[],[f4029,f6596]) ).
fof(f6596,plain,
( spl47_113
<=> class_Power_Opower(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_113])]) ).
fof(f4029,plain,
class_Power_Opower(tc_Nat_Onat),
inference(cnf_transformation,[],[f1097]) ).
fof(f1097,axiom,
class_Power_Opower(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
fof(f6594,plain,
spl47_112,
inference(avatar_split_clause,[],[f4028,f6591]) ).
fof(f6591,plain,
( spl47_112
<=> class_Power_Opower(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_112])]) ).
fof(f4028,plain,
class_Power_Opower(tc_Int_Oint),
inference(cnf_transformation,[],[f1057]) ).
fof(f1057,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
fof(f6589,plain,
spl47_111,
inference(avatar_split_clause,[],[f4027,f6586]) ).
fof(f6586,plain,
( spl47_111
<=> class_Power_Opower(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_111])]) ).
fof(f4027,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1141]) ).
fof(f1141,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).
fof(f6584,plain,
spl47_110,
inference(avatar_split_clause,[],[f4026,f6581]) ).
fof(f6581,plain,
( spl47_110
<=> class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_110])]) ).
fof(f4026,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1073]) ).
fof(f1073,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(f6579,plain,
spl47_109,
inference(avatar_split_clause,[],[f4025,f6576]) ).
fof(f6576,plain,
( spl47_109
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_109])]) ).
fof(f4025,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(cnf_transformation,[],[f1063]) ).
fof(f1063,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f6574,plain,
spl47_108,
inference(avatar_split_clause,[],[f4024,f6571]) ).
fof(f6571,plain,
( spl47_108
<=> class_Rings_Odvd(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_108])]) ).
fof(f4024,plain,
class_Rings_Odvd(tc_Nat_Onat),
inference(cnf_transformation,[],[f1100]) ).
fof(f1100,axiom,
class_Rings_Odvd(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).
fof(f6569,plain,
spl47_107,
inference(avatar_split_clause,[],[f4023,f6566]) ).
fof(f6566,plain,
( spl47_107
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_107])]) ).
fof(f4023,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(cnf_transformation,[],[f1006]) ).
fof(f1006,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f6564,plain,
spl47_106,
inference(avatar_split_clause,[],[f4022,f6561]) ).
fof(f6561,plain,
( spl47_106
<=> class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_106])]) ).
fof(f4022,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1023]) ).
fof(f1023,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
fof(f6559,plain,
spl47_105,
inference(avatar_split_clause,[],[f4021,f6556]) ).
fof(f6556,plain,
( spl47_105
<=> class_Rings_Odvd(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_105])]) ).
fof(f4021,plain,
class_Rings_Odvd(tc_Int_Oint),
inference(cnf_transformation,[],[f1062]) ).
fof(f1062,axiom,
class_Rings_Odvd(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).
fof(f6554,plain,
spl47_104,
inference(avatar_split_clause,[],[f4020,f6551]) ).
fof(f6551,plain,
( spl47_104
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_104])]) ).
fof(f4020,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1107]) ).
fof(f1107,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f6549,plain,
spl47_103,
inference(avatar_split_clause,[],[f4019,f6546]) ).
fof(f6546,plain,
( spl47_103
<=> class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_103])]) ).
fof(f4019,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1114]) ).
fof(f1114,axiom,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).
fof(f6544,plain,
spl47_102,
inference(avatar_split_clause,[],[f4018,f6541]) ).
fof(f6541,plain,
( spl47_102
<=> class_Rings_Odvd(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_102])]) ).
fof(f4018,plain,
class_Rings_Odvd(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1146]) ).
fof(f1146,axiom,
class_Rings_Odvd(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odvd) ).
fof(f6539,plain,
spl47_101,
inference(avatar_split_clause,[],[f4017,f6536]) ).
fof(f6536,plain,
( spl47_101
<=> class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_101])]) ).
fof(f4017,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f998]) ).
fof(f998,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).
fof(f6534,plain,
spl47_100,
inference(avatar_split_clause,[],[f4016,f6531]) ).
fof(f6531,plain,
( spl47_100
<=> class_Rings_Ozero__neq__one(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_100])]) ).
fof(f4016,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(cnf_transformation,[],[f1086]) ).
fof(f1086,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(f6529,plain,
spl47_99,
inference(avatar_split_clause,[],[f4015,f6526]) ).
fof(f6526,plain,
( spl47_99
<=> class_Rings_Omult__zero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_99])]) ).
fof(f4015,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(cnf_transformation,[],[f1092]) ).
fof(f1092,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
fof(f6524,plain,
spl47_98,
inference(avatar_split_clause,[],[f4014,f6521]) ).
fof(f6521,plain,
( spl47_98
<=> class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_98])]) ).
fof(f4014,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f1077]) ).
fof(f1077,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
fof(f6519,plain,
spl47_97,
inference(avatar_split_clause,[],[f4013,f6516]) ).
fof(f6516,plain,
( spl47_97
<=> class_Rings_Ono__zero__divisors(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_97])]) ).
fof(f4013,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(cnf_transformation,[],[f1080]) ).
fof(f1080,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
fof(f6514,plain,
spl47_96,
inference(avatar_split_clause,[],[f4012,f6511]) ).
fof(f6511,plain,
( spl47_96
<=> class_Rings_Osemiring__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_96])]) ).
fof(f4012,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f1091]) ).
fof(f1091,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(f6509,plain,
spl47_95,
inference(avatar_split_clause,[],[f4011,f6506]) ).
fof(f6506,plain,
( spl47_95
<=> class_Rings_Ono__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_95])]) ).
fof(f4011,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f1030]) ).
fof(f1030,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
fof(f6504,plain,
spl47_94,
inference(avatar_split_clause,[],[f4010,f6501]) ).
fof(f6501,plain,
( spl47_94
<=> class_Rings_Ozero__neq__one(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_94])]) ).
fof(f4010,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(cnf_transformation,[],[f1039]) ).
fof(f1039,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(f6499,plain,
spl47_93,
inference(avatar_split_clause,[],[f4009,f6496]) ).
fof(f6496,plain,
( spl47_93
<=> class_Rings_Osemiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_93])]) ).
fof(f4009,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(cnf_transformation,[],[f1046]) ).
fof(f1046,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
fof(f6494,plain,
spl47_92,
inference(avatar_split_clause,[],[f4008,f6491]) ).
fof(f6491,plain,
( spl47_92
<=> class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_92])]) ).
fof(f4008,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f1027]) ).
fof(f1027,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
fof(f6489,plain,
spl47_91,
inference(avatar_split_clause,[],[f4007,f6486]) ).
fof(f4007,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(cnf_transformation,[],[f1048]) ).
fof(f1048,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
fof(f6484,plain,
spl47_90,
inference(avatar_split_clause,[],[f4006,f6481]) ).
fof(f6481,plain,
( spl47_90
<=> class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_90])]) ).
fof(f4006,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f999]) ).
fof(f999,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).
fof(f6479,plain,
spl47_89,
inference(avatar_split_clause,[],[f4005,f6476]) ).
fof(f6476,plain,
( spl47_89
<=> class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_89])]) ).
fof(f4005,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1119]) ).
fof(f1119,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
fof(f6474,plain,
spl47_88,
inference(avatar_split_clause,[],[f4004,f6471]) ).
fof(f6471,plain,
( spl47_88
<=> class_Rings_Omult__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_88])]) ).
fof(f4004,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1133]) ).
fof(f1133,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).
fof(f6469,plain,
spl47_87,
inference(avatar_split_clause,[],[f4003,f6466]) ).
fof(f6466,plain,
( spl47_87
<=> class_Rings_Osemiring__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_87])]) ).
fof(f4003,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1131]) ).
fof(f1131,axiom,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).
fof(f6464,plain,
spl47_86,
inference(avatar_split_clause,[],[f4002,f6461]) ).
fof(f6461,plain,
( spl47_86
<=> class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_86])]) ).
fof(f4002,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1117]) ).
fof(f1117,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
fof(f6459,plain,
spl47_85,
inference(avatar_split_clause,[],[f4001,f6456]) ).
fof(f6456,plain,
( spl47_85
<=> class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_85])]) ).
fof(f4001,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1127]) ).
fof(f1127,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
fof(f6454,plain,
spl47_84,
inference(avatar_split_clause,[],[f4000,f6451]) ).
fof(f6451,plain,
( spl47_84
<=> class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_84])]) ).
fof(f4000,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f997]) ).
fof(f997,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).
fof(f6449,plain,
spl47_83,
inference(avatar_split_clause,[],[f3999,f6446]) ).
fof(f6446,plain,
( spl47_83
<=> class_Groups_Omonoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_83])]) ).
fof(f3999,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1090]) ).
fof(f1090,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(f6444,plain,
spl47_82,
inference(avatar_split_clause,[],[f3998,f6441]) ).
fof(f6441,plain,
( spl47_82
<=> class_Groups_Omonoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_82])]) ).
fof(f3998,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1045]) ).
fof(f1045,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
fof(f6439,plain,
spl47_81,
inference(avatar_split_clause,[],[f3997,f6436]) ).
fof(f3997,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1130]) ).
fof(f1130,axiom,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).
fof(f6434,plain,
spl47_80,
inference(avatar_split_clause,[],[f3996,f6431]) ).
fof(f6431,plain,
( spl47_80
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_80])]) ).
fof(f3996,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1070]) ).
fof(f1070,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(f6429,plain,
spl47_79,
inference(avatar_split_clause,[],[f3995,f6426]) ).
fof(f6426,plain,
( spl47_79
<=> class_Rings_Osemiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_79])]) ).
fof(f3995,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1094]) ).
fof(f1094,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
fof(f6424,plain,
spl47_78,
inference(avatar_split_clause,[],[f3994,f6421]) ).
fof(f6421,plain,
( spl47_78
<=> class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_78])]) ).
fof(f3994,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1078]) ).
fof(f1078,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(f6419,plain,
spl47_77,
inference(avatar_split_clause,[],[f3993,f6416]) ).
fof(f6416,plain,
( spl47_77
<=> class_Rings_Ocomm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_77])]) ).
fof(f3993,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1085]) ).
fof(f1085,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
fof(f6414,plain,
spl47_76,
inference(avatar_split_clause,[],[f3992,f6411]) ).
fof(f6411,plain,
( spl47_76
<=> class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_76])]) ).
fof(f3992,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f1076]) ).
fof(f1076,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
fof(f6409,plain,
spl47_75,
inference(avatar_split_clause,[],[f3991,f6406]) ).
fof(f6406,plain,
( spl47_75
<=> class_Groups_Oone(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_75])]) ).
fof(f3991,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(cnf_transformation,[],[f1099]) ).
fof(f1099,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
fof(f6404,plain,
spl47_74,
inference(avatar_split_clause,[],[f3990,f6401]) ).
fof(f6401,plain,
( spl47_74
<=> class_Rings_Osemiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_74])]) ).
fof(f3990,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1052]) ).
fof(f1052,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
fof(f6399,plain,
spl47_73,
inference(avatar_split_clause,[],[f3989,f6396]) ).
fof(f6396,plain,
( spl47_73
<=> class_Rings_Ocomm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_73])]) ).
fof(f3989,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1037]) ).
fof(f1037,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
fof(f6394,plain,
spl47_72,
inference(avatar_split_clause,[],[f3988,f6391]) ).
fof(f6391,plain,
( spl47_72
<=> class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_72])]) ).
fof(f3988,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1028]) ).
fof(f1028,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
fof(f6389,plain,
spl47_71,
inference(avatar_split_clause,[],[f3987,f6386]) ).
fof(f6386,plain,
( spl47_71
<=> class_Groups_Oone(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_71])]) ).
fof(f3987,plain,
class_Groups_Oone(tc_Int_Oint),
inference(cnf_transformation,[],[f1061]) ).
fof(f1061,axiom,
class_Groups_Oone(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
fof(f6384,plain,
spl47_70,
inference(avatar_split_clause,[],[f3986,f6381]) ).
fof(f6381,plain,
( spl47_70
<=> class_Groups_Oab__semigroup__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_70])]) ).
fof(f3986,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f1026]) ).
fof(f1026,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
fof(f6379,plain,
spl47_69,
inference(avatar_split_clause,[],[f3985,f6376]) ).
fof(f6376,plain,
( spl47_69
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_69])]) ).
fof(f3985,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1015]) ).
fof(f1015,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
fof(f6374,plain,
spl47_68,
inference(avatar_split_clause,[],[f3984,f6371]) ).
fof(f6371,plain,
( spl47_68
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_68])]) ).
fof(f3984,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1110]) ).
fof(f1110,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).
fof(f6369,plain,
spl47_67,
inference(avatar_split_clause,[],[f3983,f6366]) ).
fof(f6366,plain,
( spl47_67
<=> class_Rings_Osemiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_67])]) ).
fof(f3983,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1136]) ).
fof(f1136,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).
fof(f6364,plain,
spl47_66,
inference(avatar_split_clause,[],[f3982,f6361]) ).
fof(f6361,plain,
( spl47_66
<=> class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_66])]) ).
fof(f3982,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1116]) ).
fof(f1116,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
fof(f6359,plain,
spl47_65,
inference(avatar_split_clause,[],[f3981,f6356]) ).
fof(f6356,plain,
( spl47_65
<=> class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_65])]) ).
fof(f3981,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1118]) ).
fof(f1118,axiom,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).
fof(f6354,plain,
spl47_64,
inference(avatar_split_clause,[],[f3980,f6351]) ).
fof(f6351,plain,
( spl47_64
<=> class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_64])]) ).
fof(f3980,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1125]) ).
fof(f1125,axiom,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).
fof(f6349,plain,
spl47_63,
inference(avatar_split_clause,[],[f3979,f6346]) ).
fof(f6346,plain,
( spl47_63
<=> class_Groups_Oone(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_63])]) ).
fof(f3979,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1145]) ).
fof(f1145,axiom,
class_Groups_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).
fof(f6344,plain,
spl47_62,
inference(avatar_split_clause,[],[f3978,f6341]) ).
fof(f6341,plain,
( spl47_62
<=> class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_62])]) ).
fof(f3978,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(cnf_transformation,[],[f1075]) ).
fof(f1075,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(f6339,plain,
spl47_61,
inference(avatar_split_clause,[],[f3977,f6336]) ).
fof(f6336,plain,
( spl47_61
<=> class_Rings_Olinordered__semidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_61])]) ).
fof(f3977,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(cnf_transformation,[],[f1025]) ).
fof(f1025,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
fof(f6334,plain,
spl47_60,
inference(avatar_split_clause,[],[f3976,f6331]) ).
fof(f6331,plain,
( spl47_60
<=> class_Groups_Oab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_60])]) ).
fof(f3976,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1038]) ).
fof(f1038,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
fof(f6329,plain,
spl47_59,
inference(avatar_split_clause,[],[f3975,f6326]) ).
fof(f6326,plain,
( spl47_59
<=> class_Groups_Oab__group__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_59])]) ).
fof(f3975,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1126]) ).
fof(f1126,axiom,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).
fof(f6324,plain,
spl47_58,
inference(avatar_split_clause,[],[f3974,f6321]) ).
fof(f3974,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1047]) ).
fof(f1047,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
fof(f6319,plain,
spl47_57,
inference(avatar_split_clause,[],[f3973,f6316]) ).
fof(f6316,plain,
( spl47_57
<=> class_Rings_Oidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_57])]) ).
fof(f3973,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(cnf_transformation,[],[f1060]) ).
fof(f1060,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
fof(f6314,plain,
spl47_56,
inference(avatar_split_clause,[],[f3972,f6311]) ).
fof(f3972,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1144]) ).
fof(f1144,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
fof(f6309,plain,
spl47_55,
inference(avatar_split_clause,[],[f3971,f6306]) ).
fof(f3971,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1132]) ).
fof(f1132,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(f6304,plain,
spl47_54,
inference(avatar_split_clause,[],[f3970,f6301]) ).
fof(f6301,plain,
( spl47_54
<=> class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_54])]) ).
fof(f3970,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f1067]) ).
fof(f1067,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
fof(f6299,plain,
spl47_53,
inference(avatar_split_clause,[],[f3969,f6296]) ).
fof(f6296,plain,
( spl47_53
<=> class_Orderings_Olinorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_53])]) ).
fof(f3969,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f1088]) ).
fof(f1088,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(f6294,plain,
spl47_52,
inference(avatar_split_clause,[],[f3968,f6291]) ).
fof(f6291,plain,
( spl47_52
<=> class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_52])]) ).
fof(f3968,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f1011]) ).
fof(f1011,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
fof(f6289,plain,
spl47_51,
inference(avatar_split_clause,[],[f3967,f6286]) ).
fof(f3967,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(cnf_transformation,[],[f1042]) ).
fof(f1042,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
fof(f6284,plain,
spl47_50,
inference(avatar_split_clause,[],[f3966,f6281]) ).
fof(f6281,plain,
( spl47_50
<=> class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_50])]) ).
fof(f3966,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1069]) ).
fof(f1069,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(f6279,plain,
spl47_49,
inference(avatar_split_clause,[],[f3965,f6276]) ).
fof(f6276,plain,
( spl47_49
<=> class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_49])]) ).
fof(f3965,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1013]) ).
fof(f1013,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
fof(f6274,plain,
spl47_48,
inference(avatar_split_clause,[],[f3964,f6271]) ).
fof(f6271,plain,
( spl47_48
<=> class_Rings_Ocomm__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_48])]) ).
fof(f3964,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f1049]) ).
fof(f1049,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
fof(f6269,plain,
spl47_47,
inference(avatar_split_clause,[],[f3963,f6266]) ).
fof(f6266,plain,
( spl47_47
<=> class_Rings_Ocomm__ring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_47])]) ).
fof(f3963,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f1044]) ).
fof(f1044,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
fof(f6264,plain,
spl47_46,
inference(avatar_split_clause,[],[f3962,f6261]) ).
fof(f6261,plain,
( spl47_46
<=> class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_46])]) ).
fof(f3962,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1129]) ).
fof(f1129,axiom,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).
fof(f6259,plain,
spl47_45,
inference(avatar_split_clause,[],[f3961,f6256]) ).
fof(f6256,plain,
( spl47_45
<=> class_Rings_Ocomm__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_45])]) ).
fof(f3961,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1134]) ).
fof(f1134,axiom,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).
fof(f6254,plain,
spl47_44,
inference(avatar_split_clause,[],[f3960,f6251]) ).
fof(f6251,plain,
( spl47_44
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_44])]) ).
fof(f3960,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(cnf_transformation,[],[f1065]) ).
fof(f1065,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f6249,plain,
spl47_43,
inference(avatar_split_clause,[],[f3959,f6246]) ).
fof(f6246,plain,
( spl47_43
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_43])]) ).
fof(f3959,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(cnf_transformation,[],[f1008]) ).
fof(f1008,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f6244,plain,
spl47_42,
inference(avatar_split_clause,[],[f3958,f6241]) ).
fof(f3958,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(cnf_transformation,[],[f1084]) ).
fof(f1084,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).
fof(f6239,plain,
spl47_41,
inference(avatar_split_clause,[],[f3957,f6236]) ).
fof(f3957,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(cnf_transformation,[],[f1036]) ).
fof(f1036,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).
fof(f6234,plain,
spl47_40,
inference(avatar_split_clause,[],[f3956,f6231]) ).
fof(f6231,plain,
( spl47_40
<=> class_Rings_Oring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_40])]) ).
fof(f3956,plain,
class_Rings_Oring(tc_Int_Oint),
inference(cnf_transformation,[],[f1059]) ).
fof(f1059,axiom,
class_Rings_Oring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
fof(f6229,plain,
spl47_39,
inference(avatar_split_clause,[],[f3955,f6226]) ).
fof(f6226,plain,
( spl47_39
<=> class_Rings_Oring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_39])]) ).
fof(f3955,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1143]) ).
fof(f1143,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).
fof(f6224,plain,
spl47_38,
inference(avatar_split_clause,[],[f3954,f6221]) ).
fof(f6221,plain,
( spl47_38
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_38])]) ).
fof(f3954,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1064]) ).
fof(f1064,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f6219,plain,
spl47_37,
inference(avatar_split_clause,[],[f3953,f6216]) ).
fof(f6216,plain,
( spl47_37
<=> class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_37])]) ).
fof(f3953,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1071]) ).
fof(f1071,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
fof(f6214,plain,
spl47_36,
inference(avatar_split_clause,[],[f3952,f6211]) ).
fof(f6211,plain,
( spl47_36
<=> class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_36])]) ).
fof(f3952,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1017]) ).
fof(f1017,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
fof(f6209,plain,
spl47_35,
inference(avatar_split_clause,[],[f3951,f6206]) ).
fof(f6206,plain,
( spl47_35
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_35])]) ).
fof(f3951,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1007]) ).
fof(f1007,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f6204,plain,
spl47_34,
inference(avatar_split_clause,[],[f3950,f6201]) ).
fof(f6201,plain,
( spl47_34
<=> class_Rings_Oordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_34])]) ).
fof(f3950,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1079]) ).
fof(f1079,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
fof(f6199,plain,
spl47_33,
inference(avatar_split_clause,[],[f3949,f6196]) ).
fof(f6196,plain,
( spl47_33
<=> class_Rings_Oordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_33])]) ).
fof(f3949,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1029]) ).
fof(f1029,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
fof(f6194,plain,
spl47_32,
inference(avatar_split_clause,[],[f3948,f6191]) ).
fof(f6191,plain,
( spl47_32
<=> class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_32])]) ).
fof(f3948,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1068]) ).
fof(f1068,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(f6189,plain,
spl47_31,
inference(avatar_split_clause,[],[f3947,f6186]) ).
fof(f6186,plain,
( spl47_31
<=> class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_31])]) ).
fof(f3947,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1012]) ).
fof(f1012,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
fof(f6184,plain,
spl47_30,
inference(avatar_split_clause,[],[f3946,f6181]) ).
fof(f6181,plain,
( spl47_30
<=> class_Rings_Olinordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_30])]) ).
fof(f3946,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1074]) ).
fof(f1074,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
fof(f6179,plain,
spl47_29,
inference(avatar_split_clause,[],[f3945,f6176]) ).
fof(f6176,plain,
( spl47_29
<=> class_Rings_Oring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_29])]) ).
fof(f3945,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f1055]) ).
fof(f1055,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
fof(f6174,plain,
spl47_28,
inference(avatar_split_clause,[],[f3944,f6171]) ).
fof(f6171,plain,
( spl47_28
<=> class_Rings_Olinordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_28])]) ).
fof(f3944,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1024]) ).
fof(f1024,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
fof(f6169,plain,
spl47_27,
inference(avatar_split_clause,[],[f3943,f6166]) ).
fof(f6166,plain,
( spl47_27
<=> class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_27])]) ).
fof(f3943,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f1016]) ).
fof(f1016,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
fof(f6164,plain,
spl47_26,
inference(avatar_split_clause,[],[f3942,f6161]) ).
fof(f6161,plain,
( spl47_26
<=> class_Int_Oring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_26])]) ).
fof(f3942,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(cnf_transformation,[],[f1051]) ).
fof(f1051,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
fof(f6159,plain,
spl47_25,
inference(avatar_split_clause,[],[f3941,f6156]) ).
fof(f6156,plain,
( spl47_25
<=> class_Rings_Oring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_25])]) ).
fof(f3941,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1138]) ).
fof(f1138,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).
fof(f6154,plain,
spl47_24,
inference(avatar_split_clause,[],[f3940,f6151]) ).
fof(f6151,plain,
( spl47_24
<=> class_Int_Oring__char__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_24])]) ).
fof(f3940,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1135]) ).
fof(f1135,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(f6149,plain,
spl47_23,
inference(avatar_split_clause,[],[f3939,f6146]) ).
fof(f6146,plain,
( spl47_23
<=> class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_23])]) ).
fof(f3939,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1111]) ).
fof(f1111,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).
fof(f6144,plain,
spl47_22,
inference(avatar_split_clause,[],[f3938,f6141]) ).
fof(f6141,plain,
( spl47_22
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_22])]) ).
fof(f3938,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f1066]) ).
fof(f1066,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
fof(f6139,plain,
spl47_21,
inference(avatar_split_clause,[],[f3937,f6136]) ).
fof(f6136,plain,
( spl47_21
<=> class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_21])]) ).
fof(f3937,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1072]) ).
fof(f1072,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
fof(f6134,plain,
spl47_20,
inference(avatar_split_clause,[],[f3936,f6131]) ).
fof(f6131,plain,
( spl47_20
<=> class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_20])]) ).
fof(f3936,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f1019]) ).
fof(f1019,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
fof(f6129,plain,
spl47_19,
inference(avatar_split_clause,[],[f3935,f6126]) ).
fof(f6126,plain,
( spl47_19
<=> class_Rings_Oordered__comm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_19])]) ).
fof(f3935,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1020]) ).
fof(f1020,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
fof(f6124,plain,
spl47_18,
inference(avatar_split_clause,[],[f3934,f6121]) ).
fof(f6121,plain,
( spl47_18
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_18])]) ).
fof(f3934,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f1009]) ).
fof(f1009,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
fof(f6119,plain,
spl47_17,
inference(avatar_split_clause,[],[f3933,f6116]) ).
fof(f6116,plain,
( spl47_17
<=> class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_17])]) ).
fof(f3933,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1113]) ).
fof(f1113,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).
fof(f6114,plain,
spl47_16,
inference(avatar_split_clause,[],[f3932,f6111]) ).
fof(f6111,plain,
( spl47_16
<=> class_Rings_Olinordered__idom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_16])]) ).
fof(f3932,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(cnf_transformation,[],[f1033]) ).
fof(f1033,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
fof(f6109,plain,
spl47_15,
inference(avatar_split_clause,[],[f3931,f6106]) ).
fof(f6106,plain,
( spl47_15
<=> class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_15])]) ).
fof(f3931,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1022]) ).
fof(f1022,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
fof(f6104,plain,
spl47_14,
inference(avatar_split_clause,[],[f3930,f6101]) ).
fof(f6101,plain,
( spl47_14
<=> class_Rings_Olinordered__ring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_14])]) ).
fof(f3930,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f1018]) ).
fof(f1018,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
fof(f6099,plain,
spl47_13,
inference(avatar_split_clause,[],[f3929,f6096]) ).
fof(f6096,plain,
( spl47_13
<=> class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_13])]) ).
fof(f3929,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1014]) ).
fof(f1014,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
fof(f6094,plain,
spl47_12,
inference(avatar_split_clause,[],[f3928,f6091]) ).
fof(f6091,plain,
( spl47_12
<=> class_Rings_Oordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_12])]) ).
fof(f3928,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f1040]) ).
fof(f1040,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
fof(f6089,plain,
spl47_11,
inference(avatar_split_clause,[],[f3927,f6086]) ).
fof(f3927,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(cnf_transformation,[],[f1101]) ).
fof(f1101,axiom,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).
fof(f6084,plain,
spl47_10,
inference(avatar_split_clause,[],[f3926,f6081]) ).
fof(f6081,plain,
( spl47_10
<=> class_Rings_Olinordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_10])]) ).
fof(f3926,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f1032]) ).
fof(f1032,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
fof(f6079,plain,
spl47_9,
inference(avatar_split_clause,[],[f3925,f6076]) ).
fof(f6076,plain,
( spl47_9
<=> class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_9])]) ).
fof(f3925,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f1010]) ).
fof(f1010,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
fof(f6074,plain,
spl47_8,
inference(avatar_split_clause,[],[f3924,f6071]) ).
fof(f6071,plain,
( spl47_8
<=> class_Rings_Olinordered__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_8])]) ).
fof(f3924,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f1021]) ).
fof(f1021,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
fof(f6069,plain,
spl47_7,
inference(avatar_split_clause,[],[f3923,f6066]) ).
fof(f3923,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1140]) ).
fof(f1140,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
fof(f6064,plain,
spl47_6,
inference(avatar_split_clause,[],[f3922,f6061]) ).
fof(f6061,plain,
( spl47_6
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_6])]) ).
fof(f3922,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1109]) ).
fof(f1109,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(f6059,plain,
spl47_5,
inference(avatar_split_clause,[],[f3921,f6056]) ).
fof(f3921,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1124]) ).
fof(f1124,axiom,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).
fof(f6054,plain,
spl47_4,
inference(avatar_split_clause,[],[f3920,f6051]) ).
fof(f6051,plain,
( spl47_4
<=> class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_4])]) ).
fof(f3920,plain,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1115]) ).
fof(f1115,axiom,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).
fof(f6049,plain,
spl47_3,
inference(avatar_split_clause,[],[f3919,f6046]) ).
fof(f3919,plain,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1112]) ).
fof(f1112,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
fof(f6044,plain,
spl47_2,
inference(avatar_split_clause,[],[f3918,f6041]) ).
fof(f3918,plain,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1108]) ).
fof(f1108,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).
fof(f6039,plain,
spl47_1,
inference(avatar_split_clause,[],[f3917,f6036]) ).
fof(f6036,plain,
( spl47_1
<=> class_RealVector_Oreal__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl47_1])]) ).
fof(f3917,plain,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1123]) ).
fof(f1123,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__field) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SWW287+1 : TPTP v8.1.2. Released v5.2.0.
% 0.02/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri May 3 19:38:38 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.34 % (13850)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.42 % (13853)WARNING: value z3 for option sas not known
% 0.17/0.42 % (13852)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.17/0.42 % (13855)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)
% 0.17/0.42 % (13854)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.17/0.42 % (13853)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)
% 0.17/0.42 % (13856)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)
% 0.17/0.42 % (13857)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)
% 0.17/0.42 % (13851)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 2.29/0.74 TRYING [1]
% 2.65/0.77 TRYING [2]
% 6.82/1.45 TRYING [1]
% 8.07/1.54 TRYING [3]
% 8.07/1.56 TRYING [2]
% 9.83/1.80 TRYING [1]
% 10.08/1.85 TRYING [2]
% 14.27/2.44 TRYING [3]
% 14.85/2.53 % (13855)First to succeed.
% 15.32/2.66 % (13855)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-13850"
% 15.91/2.66 % (13855)Refutation found. Thanks to Tanya!
% 15.91/2.66 % SZS status Theorem for theBenchmark
% 15.91/2.66 % SZS output start Proof for theBenchmark
% See solution above
% 15.98/2.73 % (13855)------------------------------
% 15.98/2.73 % (13855)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 15.98/2.73 % (13855)Termination reason: Refutation
% 15.98/2.73
% 15.98/2.73 % (13855)Memory used [KB]: 22228
% 15.98/2.73 % (13855)Time elapsed: 2.239 s
% 15.98/2.73 % (13855)Instructions burned: 4411 (million)
% 15.98/2.73 % (13850)Success in time 2.391 s
%------------------------------------------------------------------------------