TSTP Solution File: SWW215+1 by Vampire-SAT---4.9
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.9
% Problem : SWW215+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d SAT
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:48:34 EDT 2024
% Result : Theorem 2.32s 0.82s
% Output : Refutation 2.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1688
% Syntax : Number of formulae : 4765 (1566 unt; 0 def)
% Number of atoms : 11590 (1864 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 10400 (3575 ~;3640 |; 994 &)
% (1231 <=>; 960 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 1054 (1052 usr; 922 prp; 0-5 aty)
% Number of functors : 85 ( 85 usr; 21 con; 0-3 aty)
% Number of variables : 7218 (7042 !; 176 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16868,plain,
$false,
inference(avatar_sat_refutation,[],[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,f6759,f6764,f6769,f6774,f6779,f6784,f6789,f6794,f6799,f6804,f6809,f6814,f6819,f6824,f6829,f6834,f6839,f6844,f6849,f6854,f6859,f6864,f6869,f6874,f6879,f6884,f6889,f6894,f6899,f6904,f6909,f6914,f6919,f6924,f6929,f6934,f6939,f6944,f6949,f6954,f6959,f6964,f6969,f6974,f6979,f6984,f6989,f6994,f6999,f7004,f7009,f7014,f7019,f7024,f7029,f7034,f7039,f7044,f7049,f7054,f7059,f7064,f7069,f7074,f7079,f7084,f7089,f7094,f7099,f7104,f7109,f7114,f7119,f7124,f7129,f7134,f7139,f7144,f7149,f7154,f7159,f7164,f7169,f7174,f7179,f7184,f7189,f7194,f7199,f7204,f7209,f7214,f7219,f7224,f7229,f7234,f7239,f7244,f7249,f7254,f7259,f7264,f7269,f7274,f7279,f7284,f7288,f7292,f7296,f7300,f7304,f7309,f7314,f7319,f7324,f7329,f7334,f7339,f7344,f7349,f7354,f7358,f7362,f7366,f7370,f7374,f7378,f7382,f7386,f7390,f7394,f7398,f7402,f7406,f7410,f7414,f7418,f7422,f7426,f7430,f7434,f7438,f7442,f7446,f7450,f7454,f7458,f7462,f7466,f7470,f7474,f7478,f7482,f7486,f7490,f7494,f7498,f7502,f7506,f7510,f7514,f7518,f7522,f7526,f7530,f7534,f7538,f7542,f7546,f7550,f7554,f7558,f7562,f7566,f7570,f7574,f7578,f7582,f7586,f7590,f7594,f7598,f7602,f7606,f7610,f7615,f7620,f7625,f7630,f7634,f7638,f7643,f7648,f7653,f7658,f7663,f7668,f7673,f7677,f7681,f7685,f7689,f7693,f7697,f7701,f7705,f7709,f7713,f7717,f7721,f7725,f7729,f7733,f7737,f7741,f7745,f7749,f7753,f7758,f7763,f7768,f7773,f7779,f7784,f7789,f7794,f7798,f7802,f7806,f7810,f7814,f7818,f7822,f7826,f7830,f7834,f7838,f7842,f7846,f7850,f7854,f7858,f7862,f7866,f7870,f7874,f7878,f7882,f7886,f7890,f7894,f7898,f7902,f7906,f7910,f7915,f7919,f7923,f7932,f7945,f7960,f7965,f7969,f7973,f7977,f7981,f7985,f7989,f7993,f7997,f8001,f8005,f8009,f8013,f8017,f8021,f8025,f8029,f8033,f8037,f8041,f8045,f8084,f8089,f8094,f8098,f8102,f8106,f8110,f8114,f8118,f8122,f8126,f8130,f8134,f8138,f8142,f8146,f8150,f8154,f8158,f8163,f8167,f8171,f8175,f8179,f8183,f8187,f8191,f8195,f8199,f8203,f8208,f8212,f8216,f8220,f8224,f8228,f8232,f8236,f8240,f8244,f8248,f8253,f8257,f8261,f8265,f8269,f8273,f8277,f8281,f8285,f8289,f8293,f8298,f8302,f8306,f8310,f8315,f8327,f8386,f8402,f8439,f8478,f8504,f8508,f8512,f8516,f8520,f8525,f8529,f8533,f8537,f8541,f8545,f8549,f8553,f8557,f8561,f8565,f8570,f8574,f8578,f8582,f8586,f8590,f8594,f8598,f8602,f8606,f8610,f8615,f8619,f8623,f8627,f8631,f8635,f8639,f8643,f8647,f8651,f8655,f8660,f8664,f8668,f8672,f8676,f8680,f8684,f8688,f8692,f8696,f8700,f8704,f8904,f9137,f9141,f9145,f9151,f9155,f9159,f9163,f9167,f9171,f9175,f9179,f9183,f9187,f9193,f9197,f9201,f9205,f9209,f9213,f9217,f9221,f9225,f9229,f9235,f9239,f9243,f9247,f9251,f9255,f9259,f9263,f9267,f9271,f9277,f9281,f9285,f9289,f9293,f9297,f9301,f9305,f9309,f9313,f9319,f9323,f9327,f9331,f9335,f9339,f9343,f9347,f9351,f9355,f9361,f9365,f9369,f9373,f9377,f9381,f9385,f9389,f9393,f9397,f9403,f9407,f9411,f9415,f9419,f9423,f9427,f9431,f9435,f9439,f9445,f9449,f9453,f9457,f9461,f9465,f9469,f9473,f9477,f9481,f9487,f9491,f9593,f9896,f10149,f10228,f10275,f10279,f10283,f10288,f10292,f10296,f10300,f10304,f10308,f10312,f10316,f10320,f10324,f10328,f10333,f10337,f10341,f10345,f10349,f10353,f10357,f10361,f10365,f10369,f10373,f10377,f10381,f10385,f10389,f10393,f10397,f10401,f10405,f10409,f10413,f10417,f10422,f10426,f10430,f10434,f10438,f10442,f10446,f10450,f10454,f10458,f10462,f10467,f10471,f10475,f10479,f10483,f10487,f10491,f10495,f10499,f10503,f10507,f10512,f10516,f10520,f10524,f10528,f10532,f10536,f10540,f10544,f10548,f10553,f10558,f10562,f10566,f10570,f10574,f10578,f10582,f10587,f10591,f10624,f10676,f10837,f10910,f11075,f11190,f11311,f11315,f11320,f11324,f11328,f11332,f11336,f11340,f11344,f11348,f11352,f11356,f11360,f11371,f11375,f11379,f11383,f11387,f11391,f11395,f11399,f11403,f11407,f11412,f11416,f11420,f11424,f11428,f11432,f11436,f11440,f11444,f11448,f11452,f11464,f11468,f11472,f11476,f11480,f11484,f11488,f11492,f11496,f11500,f11505,f11509,f11513,f11517,f11523,f11534,f11539,f11740,f12177,f12528,f12532,f12536,f12540,f12544,f12548,f12552,f12556,f12565,f12569,f12573,f12577,f12581,f12585,f12589,f12593,f12597,f12601,f12605,f12609,f12613,f12617,f12621,f12625,f12629,f12633,f12637,f12641,f12645,f12649,f12653,f12657,f12661,f12665,f12669,f12673,f12677,f12681,f12685,f12690,f12694,f12698,f12702,f12706,f12710,f12714,f12718,f12722,f12726,f12730,f12734,f12738,f12742,f12746,f12750,f12754,f12758,f12762,f12766,f12770,f12775,f12779,f12783,f12787,f12791,f12795,f12799,f12803,f12807,f12811,f12815,f12824,f12828,f12832,f12836,f12840,f12844,f12848,f12852,f12856,f12860,f12864,f12868,f12872,f12876,f12880,f12884,f12888,f12892,f12896,f12900,f12904,f12924,f12928,f12932,f12936,f12940,f12944,f12948,f12952,f12956,f12960,f12964,f13076,f13561,f13740,f14433,f15252,f15256,f15260,f15264,f15268,f15272,f15276,f15280,f15284,f15288,f15292,f15296,f15300,f15338,f15342,f15346,f15350,f15354,f15358,f15362,f15366,f15370,f15374,f15392,f15396,f15400,f15404,f15408,f15412,f15416,f15420,f15424,f15428,f15432,f15436,f15440,f15444,f15448,f15452,f15456,f15460,f15464,f15468,f15472,f15518,f15522,f15526,f15530,f15534,f15538,f15542,f15546,f15550,f15554,f15558,f15562,f15566,f15570,f15574,f15578,f15582,f15586,f15590,f15594,f15598,f15636,f15640,f15644,f15648,f15652,f15656,f15740,f16180,f16631,f16867]) ).
fof(f16867,plain,
( ~ spl107_107
| ~ spl107_229
| ~ spl107_492
| ~ spl107_920 ),
inference(avatar_split_clause,[],[f16540,f16177,f8629,f7311,f6706]) ).
fof(f6706,plain,
( spl107_107
<=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_107])]) ).
fof(f7311,plain,
( spl107_229
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_229])]) ).
fof(f8629,plain,
( spl107_492
<=> ! [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,[spl107_492])]) ).
fof(f16177,plain,
( spl107_920
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),v_da____) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_920])]) ).
fof(f16540,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ spl107_492
| ~ spl107_920 ),
inference(resolution,[],[f16179,f8630]) ).
fof(f8630,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl107_492 ),
inference(avatar_component_clause,[],[f8629]) ).
fof(f16179,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),v_da____)
| ~ spl107_920 ),
inference(avatar_component_clause,[],[f16177]) ).
fof(f16631,plain,
( spl107_921
| ~ spl107_392
| ~ spl107_920 ),
inference(avatar_split_clause,[],[f16539,f16177,f8019,f16628]) ).
fof(f16628,plain,
( spl107_921
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),v_da____) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_921])]) ).
fof(f8019,plain,
( spl107_392
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_392])]) ).
fof(f16539,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),v_da____)
| ~ spl107_392
| ~ spl107_920 ),
inference(resolution,[],[f16179,f8020]) ).
fof(f8020,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) )
| ~ spl107_392 ),
inference(avatar_component_clause,[],[f8019]) ).
fof(f16180,plain,
( spl107_920
| ~ spl107_400
| ~ spl107_919 ),
inference(avatar_split_clause,[],[f15939,f15738,f8086,f16177]) ).
fof(f8086,plain,
( spl107_400
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),v_da____) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_400])]) ).
fof(f15738,plain,
( spl107_919
<=> ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),X0)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_919])]) ).
fof(f15939,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),v_da____)
| ~ spl107_400
| ~ spl107_919 ),
inference(resolution,[],[f15739,f8088]) ).
fof(f8088,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),v_da____)
| ~ spl107_400 ),
inference(avatar_component_clause,[],[f8086]) ).
fof(f15739,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),X0)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) )
| ~ spl107_919 ),
inference(avatar_component_clause,[],[f15738]) ).
fof(f15740,plain,
( ~ spl107_207
| spl107_919
| ~ spl107_399
| ~ spl107_832 ),
inference(avatar_split_clause,[],[f14647,f12922,f8081,f15738,f7206]) ).
fof(f7206,plain,
( spl107_207
<=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_207])]) ).
fof(f8081,plain,
( spl107_399
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_399])]) ).
fof(f12922,plain,
( spl107_832
<=> ! [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,[spl107_832])]) ).
fof(f14647,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),X0)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
| ~ spl107_399
| ~ spl107_832 ),
inference(resolution,[],[f12923,f8083]) ).
fof(f8083,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))
| ~ spl107_399 ),
inference(avatar_component_clause,[],[f8081]) ).
fof(f12923,plain,
( ! [X2,X3,X0,X1] :
( ~ 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)
| ~ class_Orderings_Opreorder(X3) )
| ~ spl107_832 ),
inference(avatar_component_clause,[],[f12922]) ).
fof(f15656,plain,
spl107_918,
inference(avatar_split_clause,[],[f6152,f15654]) ).
fof(f15654,plain,
( spl107_918
<=> ! [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,[spl107_918])]) ).
fof(f6152,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,[],[f4894,f4893]) ).
fof(f4893,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,[],[f1693]) ).
fof(f1693,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,[],[f516]) ).
fof(f516,axiom,
! [X13,X14,X15] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X15,X14),X13) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4894,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,[],[f1694]) ).
fof(f1694,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,[],[f485]) ).
fof(f485,axiom,
! [X13,X14,X15] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X15,X14),X13) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X15,X13),X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15652,plain,
spl107_917,
inference(avatar_split_clause,[],[f5827,f15650]) ).
fof(f15650,plain,
( spl107_917
<=> ! [X4,X0,X3,X2,X1] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X4),X3,X2) = X0
| ~ c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
| ~ class_Fields_Ofield(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_917])]) ).
fof(f5827,plain,
! [X2,X3,X0,X1,X4] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X4),X3,X2) = X0
| ~ c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
| ~ class_Fields_Ofield(X4) ),
inference(cnf_transformation,[],[f3474]) ).
fof(f3474,plain,
! [X0,X1,X2,X3,X4] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X4),X3,X2) = X0
| ~ c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
| ~ class_Fields_Ofield(X4) ),
inference(flattening,[],[f3473]) ).
fof(f3473,plain,
! [X0,X1,X2,X3,X4] :
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X4),X3,X2) = X0
| ~ c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
| ~ class_Fields_Ofield(X4) ),
inference(ennf_transformation,[],[f2248]) ).
fof(f2248,plain,
! [X0,X1,X2,X3,X4] :
( class_Fields_Ofield(X4)
=> ( c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X4),X3,X2) = X0 ) ),
inference(rectify,[],[f783]) ).
fof(f783,axiom,
! [X25,X57,X21,X6,X3] :
( class_Fields_Ofield(X3)
=> ( c_Polynomial_Opdivmod__rel(X3,X6,X21,X57,X25)
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X3),X6,X21) = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15648,plain,
spl107_916,
inference(avatar_split_clause,[],[f5826,f15646]) ).
fof(f15646,plain,
( spl107_916
<=> ! [X4,X0,X3,X2,X1] :
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X4),X3,X2) = X1
| ~ c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
| ~ class_Fields_Ofield(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_916])]) ).
fof(f5826,plain,
! [X2,X3,X0,X1,X4] :
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X4),X3,X2) = X1
| ~ c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
| ~ class_Fields_Ofield(X4) ),
inference(cnf_transformation,[],[f3472]) ).
fof(f3472,plain,
! [X0,X1,X2,X3,X4] :
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X4),X3,X2) = X1
| ~ c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
| ~ class_Fields_Ofield(X4) ),
inference(flattening,[],[f3471]) ).
fof(f3471,plain,
! [X0,X1,X2,X3,X4] :
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X4),X3,X2) = X1
| ~ c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
| ~ class_Fields_Ofield(X4) ),
inference(ennf_transformation,[],[f2247]) ).
fof(f2247,plain,
! [X0,X1,X2,X3,X4] :
( class_Fields_Ofield(X4)
=> ( c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
=> c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X4),X3,X2) = X1 ) ),
inference(rectify,[],[f763]) ).
fof(f763,axiom,
! [X25,X57,X21,X6,X3] :
( class_Fields_Ofield(X3)
=> ( c_Polynomial_Opdivmod__rel(X3,X6,X21,X57,X25)
=> c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X3),X6,X21) = X57 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15644,plain,
spl107_915,
inference(avatar_split_clause,[],[f5769,f15642]) ).
fof(f15642,plain,
( spl107_915
<=> ! [X0,X3,X2,X1] :
( c_Rings_Odvd__class_Odvd(X3,X1,X0)
| ~ 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,[spl107_915])]) ).
fof(f5769,plain,
! [X2,X3,X0,X1] :
( c_Rings_Odvd__class_Odvd(X3,X1,X0)
| ~ 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,[],[f3389]) ).
fof(f3389,plain,
! [X0,X1,X2,X3] :
( c_Rings_Odvd__class_Odvd(X3,X1,X0)
| ~ 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,[],[f3388]) ).
fof(f3388,plain,
! [X0,X1,X2,X3] :
( c_Rings_Odvd__class_Odvd(X3,X1,X0)
| ~ 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,[],[f2203]) ).
fof(f2203,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
=> c_Rings_Odvd__class_Odvd(X3,X1,X0) ) ),
inference(rectify,[],[f824]) ).
fof(f824,axiom,
! [X22,X4,X5,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),X4),X22)
=> c_Rings_Odvd__class_Odvd(X3,X4,X22) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15640,plain,
spl107_914,
inference(avatar_split_clause,[],[f5768,f15638]) ).
fof(f15638,plain,
( spl107_914
<=> ! [X0,X3,X2,X1] :
( c_Rings_Odvd__class_Odvd(X3,X2,X0)
| ~ 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,[spl107_914])]) ).
fof(f5768,plain,
! [X2,X3,X0,X1] :
( c_Rings_Odvd__class_Odvd(X3,X2,X0)
| ~ 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,[],[f3387]) ).
fof(f3387,plain,
! [X0,X1,X2,X3] :
( c_Rings_Odvd__class_Odvd(X3,X2,X0)
| ~ 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,[],[f3386]) ).
fof(f3386,plain,
! [X0,X1,X2,X3] :
( c_Rings_Odvd__class_Odvd(X3,X2,X0)
| ~ 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,[],[f2202]) ).
fof(f2202,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
=> c_Rings_Odvd__class_Odvd(X3,X2,X0) ) ),
inference(rectify,[],[f823]) ).
fof(f823,axiom,
! [X22,X4,X5,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),X4),X22)
=> c_Rings_Odvd__class_Odvd(X3,X5,X22) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15636,plain,
spl107_913,
inference(avatar_split_clause,[],[f5764,f15634]) ).
fof(f15634,plain,
( spl107_913
<=> ! [X0,X3,X2,X1] :
( c_Rings_Odvd__class_Odvd(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_913])]) ).
fof(f5764,plain,
! [X2,X3,X0,X1] :
( c_Rings_Odvd__class_Odvd(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3379]) ).
fof(f3379,plain,
! [X0,X1,X2,X3] :
( c_Rings_Odvd__class_Odvd(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(flattening,[],[f3378]) ).
fof(f3378,plain,
! [X0,X1,X2,X3] :
( c_Rings_Odvd__class_Odvd(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2198]) ).
fof(f2198,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X2,X1)
=> c_Rings_Odvd__class_Odvd(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ) ),
inference(rectify,[],[f819]) ).
fof(f819,axiom,
! [X22,X4,X5,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X5,X4)
=> c_Rings_Odvd__class_Odvd(X3,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X4),X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15598,plain,
spl107_912,
inference(avatar_split_clause,[],[f5763,f15596]) ).
fof(f15596,plain,
( spl107_912
<=> ! [X0,X3,X2,X1] :
( c_Rings_Odvd__class_Odvd(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_912])]) ).
fof(f5763,plain,
! [X2,X3,X0,X1] :
( c_Rings_Odvd__class_Odvd(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3377]) ).
fof(f3377,plain,
! [X0,X1,X2,X3] :
( c_Rings_Odvd__class_Odvd(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(flattening,[],[f3376]) ).
fof(f3376,plain,
! [X0,X1,X2,X3] :
( c_Rings_Odvd__class_Odvd(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2197]) ).
fof(f2197,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X2,X1)
=> c_Rings_Odvd__class_Odvd(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ) ),
inference(rectify,[],[f820]) ).
fof(f820,axiom,
! [X4,X22,X5,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X5,X22)
=> c_Rings_Odvd__class_Odvd(X3,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X4),X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15594,plain,
spl107_911,
inference(avatar_split_clause,[],[f5624,f15592]) ).
fof(f15592,plain,
( spl107_911
<=> ! [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)
| ~ sP46(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_911])]) ).
fof(f5624,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)
| ~ sP46(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4047]) ).
fof(f4047,plain,
! [X0,X1,X2,X3] :
( ( sP46(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) )
| ~ sP46(X0,X1,X2,X3) ) ),
inference(rectify,[],[f4046]) ).
fof(f4046,plain,
! [X2,X0,X3,X1] :
( ( sP46(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) )
| ~ sP46(X2,X0,X3,X1) ) ),
inference(flattening,[],[f4045]) ).
fof(f4045,plain,
! [X2,X0,X3,X1] :
( ( sP46(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) )
| ~ sP46(X2,X0,X3,X1) ) ),
inference(nnf_transformation,[],[f3642]) ).
fof(f3642,plain,
! [X2,X0,X3,X1] :
( sP46(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,[sP46])]) ).
fof(f15590,plain,
spl107_910,
inference(avatar_split_clause,[],[f5615,f15588]) ).
fof(f15588,plain,
( spl107_910
<=> ! [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)
| ~ sP44(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_910])]) ).
fof(f5615,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)
| ~ sP44(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4042]) ).
fof(f4042,plain,
! [X0,X1,X2,X3] :
( ( sP44(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) )
| ~ sP44(X0,X1,X2,X3) ) ),
inference(rectify,[],[f4041]) ).
fof(f4041,plain,
! [X1,X0,X3,X2] :
( ( sP44(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) )
| ~ sP44(X1,X0,X3,X2) ) ),
inference(flattening,[],[f4040]) ).
fof(f4040,plain,
! [X1,X0,X3,X2] :
( ( sP44(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) )
| ~ sP44(X1,X0,X3,X2) ) ),
inference(nnf_transformation,[],[f3639]) ).
fof(f3639,plain,
! [X1,X0,X3,X2] :
( sP44(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,[sP44])]) ).
fof(f15586,plain,
spl107_909,
inference(avatar_split_clause,[],[f5599,f15584]) ).
fof(f15584,plain,
( spl107_909
<=> ! [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,[spl107_909])]) ).
fof(f5599,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,[],[f4033]) ).
fof(f4033,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,[],[f4032]) ).
fof(f4032,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,[],[f3182]) ).
fof(f3182,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,[],[f2073]) ).
fof(f2073,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,[],[f643]) ).
fof(f643,axiom,
! [X31,X59,X20,X3] :
( class_Fields_Ofield(X3)
=> ( c_Polynomial_Opdivmod__rel(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X20,X59,X31)
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X31
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X59 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15582,plain,
spl107_908,
inference(avatar_split_clause,[],[f5598,f15580]) ).
fof(f15580,plain,
( spl107_908
<=> ! [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,[spl107_908])]) ).
fof(f5598,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,[],[f4033]) ).
fof(f15578,plain,
spl107_907,
inference(avatar_split_clause,[],[f5595,f15576]) ).
fof(f15576,plain,
( spl107_907
<=> ! [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,[spl107_907])]) ).
fof(f5595,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,[],[f4031]) ).
fof(f4031,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,[],[f4030]) ).
fof(f4030,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,[],[f3181]) ).
fof(f3181,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,[],[f2072]) ).
fof(f2072,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,[],[f642]) ).
fof(f642,axiom,
! [X31,X59,X16,X3] :
( class_Fields_Ofield(X3)
=> ( c_Polynomial_Opdivmod__rel(X3,X16,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X59,X31)
<=> ( X16 = X31
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X59 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15574,plain,
spl107_906,
inference(avatar_split_clause,[],[f5513,f15572]) ).
fof(f15572,plain,
( spl107_906
<=> ! [X0,X3,X2,X1] :
( sP37(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_906])]) ).
fof(f5513,plain,
! [X2,X3,X0,X1] :
( sP37(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(cnf_transformation,[],[f4009]) ).
fof(f4009,plain,
! [X0,X1,X2,X3] :
( ( sP37(X0,X1,X2,X3)
| ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
& ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) )
| ( ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2),X3)
& c_Orderings_Oord__class_Oless(X1,X2,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,X2,c_Groups_Ozero__class_Ozero(X1)) )
& ( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ) )
| ~ sP37(X0,X1,X2,X3) ) ),
inference(rectify,[],[f4008]) ).
fof(f4008,plain,
! [X0,X3,X1,X2] :
( ( sP37(X0,X3,X1,X2)
| ( ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
& ~ c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
| ( ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),X2)
& c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) ) )
& ( ( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
& ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),X2)
| ~ c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) ) )
| ~ sP37(X0,X3,X1,X2) ) ),
inference(flattening,[],[f4007]) ).
fof(f4007,plain,
! [X0,X3,X1,X2] :
( ( sP37(X0,X3,X1,X2)
| ( ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
& ~ c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
| ( ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),X2)
& c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) ) )
& ( ( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
& ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),X2)
| ~ c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) ) )
| ~ sP37(X0,X3,X1,X2) ) ),
inference(nnf_transformation,[],[f3629]) ).
fof(f3629,plain,
! [X0,X3,X1,X2] :
( sP37(X0,X3,X1,X2)
<=> ( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
& ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),X2)
| ~ c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP37])]) ).
fof(f15570,plain,
spl107_905,
inference(avatar_split_clause,[],[f5510,f15568]) ).
fof(f15568,plain,
( spl107_905
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ sP37(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_905])]) ).
fof(f5510,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ sP37(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4009]) ).
fof(f15566,plain,
spl107_904,
inference(avatar_split_clause,[],[f5507,f15564]) ).
fof(f15564,plain,
( spl107_904
<=> ! [X0,X3,X2,X1] :
( sP38(X0,X1,X2,X3)
| ~ sP37(X3,X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_904])]) ).
fof(f5507,plain,
! [X2,X3,X0,X1] :
( sP38(X0,X1,X2,X3)
| ~ sP37(X3,X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1) ),
inference(cnf_transformation,[],[f4006]) ).
fof(f4006,plain,
! [X0,X1,X2,X3] :
( ( sP38(X0,X1,X2,X3)
| ( ~ sP37(X3,X2,X1,X0)
& ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1) )
| ( ~ c_Orderings_Oord__class_Oless(X2,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1))
& c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) )
& ( ( ( sP37(X3,X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1) )
& ( c_Orderings_Oord__class_Oless(X2,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) )
| ~ sP38(X0,X1,X2,X3) ) ),
inference(rectify,[],[f4005]) ).
fof(f4005,plain,
! [X2,X1,X3,X0] :
( ( sP38(X2,X1,X3,X0)
| ( ~ sP37(X0,X3,X1,X2)
& ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) )
| ( ~ c_Orderings_Oord__class_Oless(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) )
& ( ( ( sP37(X0,X3,X1,X2)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) )
& ( c_Orderings_Oord__class_Oless(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) )
| ~ sP38(X2,X1,X3,X0) ) ),
inference(flattening,[],[f4004]) ).
fof(f4004,plain,
! [X2,X1,X3,X0] :
( ( sP38(X2,X1,X3,X0)
| ( ~ sP37(X0,X3,X1,X2)
& ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) )
| ( ~ c_Orderings_Oord__class_Oless(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) )
& ( ( ( sP37(X0,X3,X1,X2)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) )
& ( c_Orderings_Oord__class_Oless(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) )
| ~ sP38(X2,X1,X3,X0) ) ),
inference(nnf_transformation,[],[f3630]) ).
fof(f3630,plain,
! [X2,X1,X3,X0] :
( sP38(X2,X1,X3,X0)
<=> ( ( sP37(X0,X3,X1,X2)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) )
& ( c_Orderings_Oord__class_Oless(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP38])]) ).
fof(f15562,plain,
spl107_903,
inference(avatar_split_clause,[],[f5504,f15560]) ).
fof(f15560,plain,
( spl107_903
<=> ! [X0,X3,X2,X1] :
( sP37(X3,X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ sP38(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_903])]) ).
fof(f5504,plain,
! [X2,X3,X0,X1] :
( sP37(X3,X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ sP38(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4006]) ).
fof(f15558,plain,
( spl107_902
| ~ spl107_315
| ~ spl107_544
| ~ spl107_881 ),
inference(avatar_split_clause,[],[f15505,f15430,f9269,f7675,f15556]) ).
fof(f15556,plain,
( spl107_902
<=> ! [X0] :
( 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,X0,c_RComplete_Onatfloor(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_902])]) ).
fof(f7675,plain,
( spl107_315
<=> ! [X0] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl107_315])]) ).
fof(f9269,plain,
( spl107_544
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_544])]) ).
fof(f15430,plain,
( spl107_881
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatceiling(X0))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_881])]) ).
fof(f15505,plain,
( ! [X0] :
( 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,X0,c_RComplete_Onatfloor(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))) )
| ~ spl107_315
| ~ spl107_544
| ~ spl107_881 ),
inference(forward_demodulation,[],[f15481,f7676]) ).
fof(f7676,plain,
( ! [X0] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X0)) = X0
| ~ spl107_315 ),
inference(avatar_component_clause,[],[f7675]) ).
fof(f15481,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X0)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_RComplete_Onatfloor(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))) )
| ~ spl107_544
| ~ spl107_881 ),
inference(resolution,[],[f15431,f9270]) ).
fof(f9270,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X0)) )
| ~ spl107_544 ),
inference(avatar_component_clause,[],[f9269]) ).
fof(f15431,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatceiling(X0)) )
| ~ spl107_881 ),
inference(avatar_component_clause,[],[f15430]) ).
fof(f15554,plain,
spl107_901,
inference(avatar_split_clause,[],[f5498,f15552]) ).
fof(f15552,plain,
( spl107_901
<=> ! [X0,X3,X2,X1] :
( sP34(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_901])]) ).
fof(f5498,plain,
! [X2,X3,X0,X1] :
( sP34(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f4001]) ).
fof(f4001,plain,
! [X0,X1,X2,X3] :
( ( sP34(X0,X1,X2,X3)
| ( ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
& ~ c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0)) )
| ( ~ c_Orderings_Oord__class_Oless(X0,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2))
& c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0)) ) )
& ( ( ( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0)) )
& ( c_Orderings_Oord__class_Oless(X0,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2))
| ~ c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0)) ) )
| ~ sP34(X0,X1,X2,X3) ) ),
inference(rectify,[],[f4000]) ).
fof(f4000,plain,
! [X3,X2,X0,X1] :
( ( sP34(X3,X2,X0,X1)
| ( ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
& ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3)) )
| ( ~ c_Orderings_Oord__class_Oless(X3,X1,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,c_Groups_Ozero__class_Ozero(X3))
| c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3)) )
& ( c_Orderings_Oord__class_Oless(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3)) ) )
| ~ sP34(X3,X2,X0,X1) ) ),
inference(flattening,[],[f3999]) ).
fof(f3999,plain,
! [X3,X2,X0,X1] :
( ( sP34(X3,X2,X0,X1)
| ( ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
& ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3)) )
| ( ~ c_Orderings_Oord__class_Oless(X3,X1,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,c_Groups_Ozero__class_Ozero(X3))
| c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3)) )
& ( c_Orderings_Oord__class_Oless(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3)) ) )
| ~ sP34(X3,X2,X0,X1) ) ),
inference(nnf_transformation,[],[f3625]) ).
fof(f3625,plain,
! [X3,X2,X0,X1] :
( sP34(X3,X2,X0,X1)
<=> ( ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3)) )
& ( c_Orderings_Oord__class_Oless(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP34])]) ).
fof(f15550,plain,
spl107_900,
inference(avatar_split_clause,[],[f5495,f15548]) ).
fof(f15548,plain,
( spl107_900
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| ~ sP34(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_900])]) ).
fof(f5495,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| ~ sP34(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4001]) ).
fof(f15546,plain,
spl107_899,
inference(avatar_split_clause,[],[f5492,f15544]) ).
fof(f15544,plain,
( spl107_899
<=> ! [X0,X3,X2,X1] :
( sP35(X0,X1,X2,X3)
| ~ sP34(X3,X2,X1,X0)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_899])]) ).
fof(f5492,plain,
! [X2,X3,X0,X1] :
( sP35(X0,X1,X2,X3)
| ~ sP34(X3,X2,X1,X0)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ),
inference(cnf_transformation,[],[f3998]) ).
fof(f3998,plain,
! [X0,X1,X2,X3] :
( ( sP35(X0,X1,X2,X3)
| ( ~ sP34(X3,X2,X1,X0)
& ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) )
| ( ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) )
& ( ( ( sP34(X3,X2,X1,X0)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) )
& ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) )
| ~ sP35(X0,X1,X2,X3) ) ),
inference(rectify,[],[f3997]) ).
fof(f3997,plain,
! [X1,X0,X2,X3] :
( ( sP35(X1,X0,X2,X3)
| ( ~ sP34(X3,X2,X0,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),X1)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0) ) )
& ( ( ( sP34(X3,X2,X0,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),X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0) ) )
| ~ sP35(X1,X0,X2,X3) ) ),
inference(flattening,[],[f3996]) ).
fof(f3996,plain,
! [X1,X0,X2,X3] :
( ( sP35(X1,X0,X2,X3)
| ( ~ sP34(X3,X2,X0,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),X1)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0) ) )
& ( ( ( sP34(X3,X2,X0,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),X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0) ) )
| ~ sP35(X1,X0,X2,X3) ) ),
inference(nnf_transformation,[],[f3626]) ).
fof(f3626,plain,
! [X1,X0,X2,X3] :
( sP35(X1,X0,X2,X3)
<=> ( ( sP34(X3,X2,X0,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),X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP35])]) ).
fof(f15542,plain,
spl107_898,
inference(avatar_split_clause,[],[f5489,f15540]) ).
fof(f15540,plain,
( spl107_898
<=> ! [X0,X3,X2,X1] :
( sP34(X3,X2,X1,X0)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| ~ sP35(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_898])]) ).
fof(f5489,plain,
! [X2,X3,X0,X1] :
( sP34(X3,X2,X1,X0)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| ~ sP35(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3998]) ).
fof(f15538,plain,
spl107_897,
inference(avatar_split_clause,[],[f5483,f15536]) ).
fof(f15536,plain,
( spl107_897
<=> ! [X0,X3,X2,X1] :
( sP31(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_897])]) ).
fof(f5483,plain,
! [X2,X3,X0,X1] :
( sP31(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(cnf_transformation,[],[f3993]) ).
fof(f3993,plain,
! [X0,X1,X2,X3] :
( ( sP31(X0,X1,X2,X3)
| ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
& ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2),X3)
& c_Orderings_Oord__class_Oless(X1,X2,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(X1,X2,c_Groups_Ozero__class_Ozero(X1)) )
& ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ) )
| ~ sP31(X0,X1,X2,X3) ) ),
inference(rectify,[],[f3992]) ).
fof(f3992,plain,
! [X0,X3,X1,X2] :
( ( sP31(X0,X3,X1,X2)
| ( ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
& ~ c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),X2)
& c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
& ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),X2)
| ~ c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) ) )
| ~ sP31(X0,X3,X1,X2) ) ),
inference(flattening,[],[f3991]) ).
fof(f3991,plain,
! [X0,X3,X1,X2] :
( ( sP31(X0,X3,X1,X2)
| ( ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
& ~ c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),X2)
& c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
& ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),X2)
| ~ c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) ) )
| ~ sP31(X0,X3,X1,X2) ) ),
inference(nnf_transformation,[],[f3621]) ).
fof(f3621,plain,
! [X0,X3,X1,X2] :
( sP31(X0,X3,X1,X2)
<=> ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
& ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),X2)
| ~ c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP31])]) ).
fof(f15534,plain,
spl107_896,
inference(avatar_split_clause,[],[f5480,f15532]) ).
fof(f15532,plain,
( spl107_896
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ sP31(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_896])]) ).
fof(f5480,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ sP31(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3993]) ).
fof(f15530,plain,
spl107_895,
inference(avatar_split_clause,[],[f5477,f15528]) ).
fof(f15528,plain,
( spl107_895
<=> ! [X0,X3,X2,X1] :
( sP32(X0,X1,X2,X3)
| ~ sP31(X3,X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_895])]) ).
fof(f5477,plain,
! [X2,X3,X0,X1] :
( sP32(X0,X1,X2,X3)
| ~ sP31(X3,X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1) ),
inference(cnf_transformation,[],[f3990]) ).
fof(f3990,plain,
! [X0,X1,X2,X3] :
( ( sP32(X0,X1,X2,X3)
| ( ~ sP31(X3,X2,X1,X0)
& ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1) )
| ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1))
& c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) )
& ( ( ( sP31(X3,X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1) )
& ( c_Orderings_Oord__class_Oless__eq(X2,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) )
| ~ sP32(X0,X1,X2,X3) ) ),
inference(rectify,[],[f3989]) ).
fof(f3989,plain,
! [X2,X1,X3,X0] :
( ( sP32(X2,X1,X3,X0)
| ( ~ sP31(X0,X3,X1,X2)
& ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) )
| ( ~ c_Orderings_Oord__class_Oless__eq(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) )
& ( ( ( sP31(X0,X3,X1,X2)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) )
& ( c_Orderings_Oord__class_Oless__eq(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) )
| ~ sP32(X2,X1,X3,X0) ) ),
inference(flattening,[],[f3988]) ).
fof(f3988,plain,
! [X2,X1,X3,X0] :
( ( sP32(X2,X1,X3,X0)
| ( ~ sP31(X0,X3,X1,X2)
& ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) )
| ( ~ c_Orderings_Oord__class_Oless__eq(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) )
& ( ( ( sP31(X0,X3,X1,X2)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) )
& ( c_Orderings_Oord__class_Oless__eq(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) )
| ~ sP32(X2,X1,X3,X0) ) ),
inference(nnf_transformation,[],[f3622]) ).
fof(f3622,plain,
! [X2,X1,X3,X0] :
( sP32(X2,X1,X3,X0)
<=> ( ( sP31(X0,X3,X1,X2)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) )
& ( c_Orderings_Oord__class_Oless__eq(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP32])]) ).
fof(f15526,plain,
spl107_894,
inference(avatar_split_clause,[],[f5474,f15524]) ).
fof(f15524,plain,
( spl107_894
<=> ! [X0,X3,X2,X1] :
( sP31(X3,X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ sP32(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_894])]) ).
fof(f5474,plain,
! [X2,X3,X0,X1] :
( sP31(X3,X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ sP32(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3990]) ).
fof(f15522,plain,
spl107_893,
inference(avatar_split_clause,[],[f5468,f15520]) ).
fof(f15520,plain,
( spl107_893
<=> ! [X0,X3,X2,X1] :
( sP28(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_893])]) ).
fof(f5468,plain,
! [X2,X3,X0,X1] :
( sP28(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3985]) ).
fof(f3985,plain,
! [X0,X1,X2,X3] :
( ( sP28(X0,X1,X2,X3)
| ( ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
& ~ c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(X0,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2))
& c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0)) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0)) )
& ( c_Orderings_Oord__class_Oless__eq(X0,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2))
| ~ c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0)) ) )
| ~ sP28(X0,X1,X2,X3) ) ),
inference(rectify,[],[f3984]) ).
fof(f3984,plain,
! [X3,X2,X0,X1] :
( ( sP28(X3,X2,X0,X1)
| ( ~ c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3))
& ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(X3,X1,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__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3)) )
& ( c_Orderings_Oord__class_Oless__eq(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3)) ) )
| ~ sP28(X3,X2,X0,X1) ) ),
inference(flattening,[],[f3983]) ).
fof(f3983,plain,
! [X3,X2,X0,X1] :
( ( sP28(X3,X2,X0,X1)
| ( ~ c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3))
& ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(X3,X1,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__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3)) )
& ( c_Orderings_Oord__class_Oless__eq(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3)) ) )
| ~ sP28(X3,X2,X0,X1) ) ),
inference(nnf_transformation,[],[f3617]) ).
fof(f3617,plain,
! [X3,X2,X0,X1] :
( sP28(X3,X2,X0,X1)
<=> ( ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3)) )
& ( c_Orderings_Oord__class_Oless__eq(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP28])]) ).
fof(f15518,plain,
spl107_892,
inference(avatar_split_clause,[],[f5465,f15516]) ).
fof(f15516,plain,
( spl107_892
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| ~ sP28(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_892])]) ).
fof(f5465,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| ~ sP28(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3985]) ).
fof(f15472,plain,
spl107_891,
inference(avatar_split_clause,[],[f5462,f15470]) ).
fof(f15470,plain,
( spl107_891
<=> ! [X0,X3,X2,X1] :
( sP29(X0,X1,X2,X3)
| ~ sP28(X3,X2,X1,X0)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_891])]) ).
fof(f5462,plain,
! [X2,X3,X0,X1] :
( sP29(X0,X1,X2,X3)
| ~ sP28(X3,X2,X1,X0)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ),
inference(cnf_transformation,[],[f3982]) ).
fof(f3982,plain,
! [X0,X1,X2,X3] :
( ( sP29(X0,X1,X2,X3)
| ( ~ sP28(X3,X2,X1,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),X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) )
& ( ( ( sP28(X3,X2,X1,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),X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) )
| ~ sP29(X0,X1,X2,X3) ) ),
inference(rectify,[],[f3981]) ).
fof(f3981,plain,
! [X1,X0,X2,X3] :
( ( sP29(X1,X0,X2,X3)
| ( ~ sP28(X3,X2,X0,X1)
& ~ c_Orderings_Oord__class_Oless(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),X1)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0) ) )
& ( ( ( sP28(X3,X2,X0,X1)
| c_Orderings_Oord__class_Oless(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),X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0) ) )
| ~ sP29(X1,X0,X2,X3) ) ),
inference(flattening,[],[f3980]) ).
fof(f3980,plain,
! [X1,X0,X2,X3] :
( ( sP29(X1,X0,X2,X3)
| ( ~ sP28(X3,X2,X0,X1)
& ~ c_Orderings_Oord__class_Oless(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),X1)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0) ) )
& ( ( ( sP28(X3,X2,X0,X1)
| c_Orderings_Oord__class_Oless(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),X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0) ) )
| ~ sP29(X1,X0,X2,X3) ) ),
inference(nnf_transformation,[],[f3618]) ).
fof(f3618,plain,
! [X1,X0,X2,X3] :
( sP29(X1,X0,X2,X3)
<=> ( ( sP28(X3,X2,X0,X1)
| c_Orderings_Oord__class_Oless(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),X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP29])]) ).
fof(f15468,plain,
spl107_890,
inference(avatar_split_clause,[],[f5459,f15466]) ).
fof(f15466,plain,
( spl107_890
<=> ! [X0,X3,X2,X1] :
( sP28(X3,X2,X1,X0)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| ~ sP29(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_890])]) ).
fof(f5459,plain,
! [X2,X3,X0,X1] :
( sP28(X3,X2,X1,X0)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1)
| ~ sP29(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3982]) ).
fof(f15464,plain,
spl107_889,
inference(avatar_split_clause,[],[f5405,f15462]) ).
fof(f15462,plain,
( spl107_889
<=> ! [X2,X0,X1] :
( sP27(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK96(X0,X1,X2)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_889])]) ).
fof(f5405,plain,
! [X2,X0,X1] :
( sP27(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK96(X0,X1,X2)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(cnf_transformation,[],[f3950]) ).
fof(f3950,plain,
! [X0,X1,X2] :
( ( sP27(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK96(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK96(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) ) )
| ~ sP27(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK96])],[f3948,f3949]) ).
fof(f3949,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(X0,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) = X1 )
=> ( ~ hBOOL(hAPP(X0,sK96(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK96(X0,X1,X2)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f3948,plain,
! [X0,X1,X2] :
( ( sP27(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) ) )
| ~ sP27(X0,X1,X2) ) ),
inference(rectify,[],[f3947]) ).
fof(f3947,plain,
! [X2,X1,X0] :
( ( sP27(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) ) )
| ~ sP27(X2,X1,X0) ) ),
inference(flattening,[],[f3946]) ).
fof(f3946,plain,
! [X2,X1,X0] :
( ( sP27(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) ) )
| ~ sP27(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f3615]) ).
fof(f3615,plain,
! [X2,X1,X0] :
( sP27(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,[sP27])]) ).
fof(f15460,plain,
spl107_888,
inference(avatar_split_clause,[],[f5397,f15458]) ).
fof(f15458,plain,
( spl107_888
<=> ! [X2,X0,X1] :
( sP26(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK95(X0,X1,X2)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_888])]) ).
fof(f5397,plain,
! [X2,X0,X1] :
( sP26(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK95(X0,X1,X2)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(cnf_transformation,[],[f3944]) ).
fof(f3944,plain,
! [X0,X1,X2] :
( ( sP26(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK95(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK95(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) ) )
| ~ sP26(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK95])],[f3942,f3943]) ).
fof(f3943,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(X0,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) = X1 )
=> ( ~ hBOOL(hAPP(X0,sK95(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK95(X0,X1,X2)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f3942,plain,
! [X0,X1,X2] :
( ( sP26(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) ) )
| ~ sP26(X0,X1,X2) ) ),
inference(rectify,[],[f3941]) ).
fof(f3941,plain,
! [X2,X1,X0] :
( ( sP26(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) ) )
| ~ sP26(X2,X1,X0) ) ),
inference(flattening,[],[f3940]) ).
fof(f3940,plain,
! [X2,X1,X0] :
( ( sP26(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) ) )
| ~ sP26(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f3613]) ).
fof(f3613,plain,
! [X2,X1,X0] :
( sP26(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,[sP26])]) ).
fof(f15456,plain,
spl107_887,
inference(avatar_split_clause,[],[f5392,f15454]) ).
fof(f15454,plain,
( spl107_887
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)))
| ~ sP25(X2,X1,X0)
| ~ hBOOL(hAPP(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_887])]) ).
fof(f5392,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)))
| ~ sP25(X2,X1,X0)
| ~ hBOOL(hAPP(X2,X1)) ),
inference(cnf_transformation,[],[f3939]) ).
fof(f3939,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)))
| ~ sP25(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,X1))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) )
& ( ( sP25(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0))) ) ),
inference(flattening,[],[f3938]) ).
fof(f3938,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)))
| ~ sP25(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,X1))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) )
& ( ( sP25(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0))) ) ),
inference(nnf_transformation,[],[f3612]) ).
fof(f3612,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)))
<=> ( sP25(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
inference(definition_folding,[],[f3079,f3611]) ).
fof(f3611,plain,
! [X2,X1,X0] :
( sP25(X2,X1,X0)
<=> ( ! [X3,X4] :
( hBOOL(hAPP(X2,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X4) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X0) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP25])]) ).
fof(f3079,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)))
<=> ( ( ! [X3,X4] :
( hBOOL(hAPP(X2,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X4) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X0) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
inference(flattening,[],[f3078]) ).
fof(f3078,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)))
<=> ( ( ! [X3,X4] :
( hBOOL(hAPP(X2,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X4) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X0) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
inference(ennf_transformation,[],[f1991]) ).
fof(f1991,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)))
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
=> ! [X3,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X0)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X4) = X1
=> hBOOL(hAPP(X2,X4)) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
=> hBOOL(hAPP(X2,X1)) ) ) ),
inference(rectify,[],[f778]) ).
fof(f778,axiom,
! [X63,X65,X70] :
( hBOOL(hAPP(X70,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X65,X63)))
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X63
=> ! [X80,X81] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X81,X63)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X63),X80),X81) = X65
=> hBOOL(hAPP(X70,X81)) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X63
=> hBOOL(hAPP(X70,X65)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15452,plain,
spl107_886,
inference(avatar_split_clause,[],[f5391,f15450]) ).
fof(f15450,plain,
( spl107_886
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)))
| ~ sP25(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_886])]) ).
fof(f5391,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)))
| ~ sP25(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f3939]) ).
fof(f15448,plain,
spl107_885,
inference(avatar_split_clause,[],[f5363,f15446]) ).
fof(f15446,plain,
( spl107_885
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
| ~ sP21(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_885])]) ).
fof(f5363,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
| ~ sP21(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f3919]) ).
fof(f3919,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
| ~ sP21(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) )
& ( ( sP21(X2,X1,X0)
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0))) ) ),
inference(flattening,[],[f3918]) ).
fof(f3918,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
| ~ sP21(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) )
& ( ( sP21(X2,X1,X0)
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0))) ) ),
inference(nnf_transformation,[],[f3606]) ).
fof(f3606,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
<=> ( sP21(X2,X1,X0)
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
inference(definition_folding,[],[f3075,f3605]) ).
fof(f3605,plain,
! [X2,X1,X0] :
( sP21(X2,X1,X0)
<=> ( ! [X3,X4] :
( hBOOL(hAPP(X2,X3))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X4) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X0) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP21])]) ).
fof(f3075,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
<=> ( ( ! [X3,X4] :
( hBOOL(hAPP(X2,X3))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X4) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X0) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
inference(flattening,[],[f3074]) ).
fof(f3074,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
<=> ( ( ! [X3,X4] :
( hBOOL(hAPP(X2,X3))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X4) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X0) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
inference(ennf_transformation,[],[f1989]) ).
fof(f1989,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
=> ! [X3,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X0)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X4) = X1
=> hBOOL(hAPP(X2,X3)) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
=> hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
inference(rectify,[],[f698]) ).
fof(f698,axiom,
! [X63,X65,X70] :
( hBOOL(hAPP(X70,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X65,X63)))
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X63
=> ! [X80,X81] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X81,X63)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X63),X80),X81) = X65
=> hBOOL(hAPP(X70,X80)) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X63
=> hBOOL(hAPP(X70,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15444,plain,
spl107_884,
inference(avatar_split_clause,[],[f5303,f15442]) ).
fof(f15442,plain,
( spl107_884
<=> ! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X0)
| ~ 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,[spl107_884])]) ).
fof(f5303,plain,
! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0)) ),
inference(cnf_transformation,[],[f3038]) ).
fof(f3038,plain,
! [X0,X1,X2] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0)) ),
inference(flattening,[],[f3037]) ).
fof(f3037,plain,
! [X0,X1,X2] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0)) ),
inference(ennf_transformation,[],[f1968]) ).
fof(f1968,plain,
! [X0,X1,X2] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0))
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X0)
=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1) ) ),
inference(rectify,[],[f956]) ).
fof(f956,axiom,
! [X41,X42,X13] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X13,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X42,X41))
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X13,X41)
=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X13,X42) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15440,plain,
spl107_883,
inference(avatar_split_clause,[],[f5302,f15438]) ).
fof(f15438,plain,
( spl107_883
<=> ! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_883])]) ).
fof(f5302,plain,
! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)) ),
inference(cnf_transformation,[],[f3036]) ).
fof(f3036,plain,
! [X0,X1,X2] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)) ),
inference(flattening,[],[f3035]) ).
fof(f3035,plain,
! [X0,X1,X2] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)) ),
inference(ennf_transformation,[],[f1967]) ).
fof(f1967,plain,
! [X0,X1,X2] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X0)
=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1) ) ),
inference(rectify,[],[f948]) ).
fof(f948,axiom,
! [X41,X42,X13] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X13,c_Divides_Odiv__class_Omod(tc_Int_Oint,X42,X41))
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X13,X41)
=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X13,X42) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15436,plain,
spl107_882,
inference(avatar_split_clause,[],[f5216,f15434]) ).
fof(f15434,plain,
( spl107_882
<=> ! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_882])]) ).
fof(f5216,plain,
! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2961]) ).
fof(f2961,plain,
! [X0,X1,X2] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(flattening,[],[f2960]) ).
fof(f2960,plain,
! [X0,X1,X2] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1912]) ).
fof(f1912,plain,
! [X0,X1,X2] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ) ),
inference(rectify,[],[f826]) ).
fof(f826,axiom,
! [X41,X42,X13] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X42)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X41)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X42,X41)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15432,plain,
( spl107_881
| ~ spl107_388
| ~ spl107_850 ),
inference(avatar_split_clause,[],[f15376,f15258,f8003,f15430]) ).
fof(f8003,plain,
( spl107_388
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_388])]) ).
fof(f15258,plain,
( spl107_850
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatceiling(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_850])]) ).
fof(f15376,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatceiling(X0))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))) )
| ~ spl107_388
| ~ spl107_850 ),
inference(resolution,[],[f15259,f8004]) ).
fof(f8004,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) )
| ~ spl107_388 ),
inference(avatar_component_clause,[],[f8003]) ).
fof(f15259,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatceiling(X0)) )
| ~ spl107_850 ),
inference(avatar_component_clause,[],[f15258]) ).
fof(f15428,plain,
spl107_880,
inference(avatar_split_clause,[],[f5213,f15426]) ).
fof(f15426,plain,
( spl107_880
<=> ! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_880])]) ).
fof(f5213,plain,
! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1) ),
inference(cnf_transformation,[],[f2955]) ).
fof(f2955,plain,
! [X0,X1,X2] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1) ),
inference(flattening,[],[f2954]) ).
fof(f2954,plain,
! [X0,X1,X2] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1) ),
inference(ennf_transformation,[],[f1909]) ).
fof(f1909,plain,
! [X0,X1,X2] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X0)
=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)) ) ),
inference(rectify,[],[f949]) ).
fof(f949,axiom,
! [X41,X42,X87] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X87,X42)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X87,X41)
=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X87,c_Divides_Odiv__class_Omod(tc_Int_Oint,X42,X41)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15424,plain,
spl107_879,
inference(avatar_split_clause,[],[f5163,f15422]) ).
fof(f15422,plain,
( spl107_879
<=> ! [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,[spl107_879])]) ).
fof(f5163,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,[],[f2899]) ).
fof(f2899,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,[],[f1875]) ).
fof(f1875,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,[],[f404]) ).
fof(f404,axiom,
! [X4,X5,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X4),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15420,plain,
spl107_878,
inference(avatar_split_clause,[],[f5073,f15418]) ).
fof(f15418,plain,
( spl107_878
<=> ! [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,[spl107_878])]) ).
fof(f5073,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,[],[f2782]) ).
fof(f2782,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,[],[f2781]) ).
fof(f2781,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,[],[f1806]) ).
fof(f1806,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,[],[f902]) ).
fof(f902,axiom,
! [X41,X5,X3] :
( class_Rings_Oring__1__no__zero__divisors(X3)
=> ( c_Groups_Ozero__class_Ozero(X3) != X5
=> c_Groups_Ozero__class_Ozero(X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X3),X5),X41) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15416,plain,
spl107_877,
inference(avatar_split_clause,[],[f5035,f15414]) ).
fof(f15414,plain,
( spl107_877
<=> ! [X2,X0,X1] :
( c_Groups_Oabs__class_Oabs(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_Groups_Oabs__class_Oabs(X2,c_Groups_Ominus__class_Ominus(X2,X0,X1))
| ~ class_Groups_Oordered__ab__group__add__abs(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_877])]) ).
fof(f5035,plain,
! [X2,X0,X1] :
( c_Groups_Oabs__class_Oabs(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_Groups_Oabs__class_Oabs(X2,c_Groups_Ominus__class_Ominus(X2,X0,X1))
| ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
inference(cnf_transformation,[],[f2733]) ).
fof(f2733,plain,
! [X0,X1,X2] :
( c_Groups_Oabs__class_Oabs(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_Groups_Oabs__class_Oabs(X2,c_Groups_Ominus__class_Ominus(X2,X0,X1))
| ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
inference(ennf_transformation,[],[f1771]) ).
fof(f1771,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add__abs(X2)
=> c_Groups_Oabs__class_Oabs(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_Groups_Oabs__class_Oabs(X2,c_Groups_Ominus__class_Ominus(X2,X0,X1)) ),
inference(rectify,[],[f168]) ).
fof(f168,axiom,
! [X4,X5,X3] :
( class_Groups_Oordered__ab__group__add__abs(X3)
=> c_Groups_Oabs__class_Oabs(X3,c_Groups_Ominus__class_Ominus(X3,X5,X4)) = c_Groups_Oabs__class_Oabs(X3,c_Groups_Ominus__class_Ominus(X3,X4,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15412,plain,
spl107_876,
inference(avatar_split_clause,[],[f4983,f15410]) ).
fof(f15410,plain,
( spl107_876
<=> ! [X2,X0,X1] :
( c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X0,X1))
| ~ class_RealVector_Oreal__normed__vector(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_876])]) ).
fof(f4983,plain,
! [X2,X0,X1] :
( c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X0,X1))
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(cnf_transformation,[],[f2702]) ).
fof(f2702,plain,
! [X0,X1,X2] :
( c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X0,X1))
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(ennf_transformation,[],[f1747]) ).
fof(f1747,plain,
! [X0,X1,X2] :
( class_RealVector_Oreal__normed__vector(X2)
=> c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) = c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ominus__class_Ominus(X2,X0,X1)) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X4,X5,X3] :
( class_RealVector_Oreal__normed__vector(X3)
=> c_RealVector_Onorm__class_Onorm(X3,c_Groups_Ominus__class_Ominus(X3,X5,X4)) = c_RealVector_Onorm__class_Onorm(X3,c_Groups_Ominus__class_Ominus(X3,X4,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15408,plain,
spl107_875,
inference(avatar_split_clause,[],[f4896,f15406]) ).
fof(f15406,plain,
( spl107_875
<=> ! [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,[spl107_875])]) ).
fof(f4896,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,[],[f1696]) ).
fof(f1696,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,[],[f521]) ).
fof(f521,axiom,
! [X13,X41,X42] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X41),X13) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15404,plain,
spl107_874,
inference(avatar_split_clause,[],[f4895,f15402]) ).
fof(f15402,plain,
( spl107_874
<=> ! [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,[spl107_874])]) ).
fof(f4895,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,[],[f1695]) ).
fof(f1695,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,[],[f522]) ).
fof(f522,axiom,
! [X12,X21,X6] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X12)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15400,plain,
spl107_873,
inference(avatar_split_clause,[],[f4893,f15398]) ).
fof(f15398,plain,
( spl107_873
<=> ! [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,[spl107_873])]) ).
fof(f15396,plain,
spl107_872,
inference(avatar_split_clause,[],[f4892,f15394]) ).
fof(f15394,plain,
( spl107_872
<=> ! [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,[spl107_872])]) ).
fof(f4892,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,[],[f1692]) ).
fof(f1692,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,[],[f518]) ).
fof(f518,axiom,
! [X41,X13,X42] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X42,X41) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X13),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15392,plain,
spl107_871,
inference(avatar_split_clause,[],[f4891,f15390]) ).
fof(f15390,plain,
( spl107_871
<=> ! [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,[spl107_871])]) ).
fof(f4891,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,[],[f1691]) ).
fof(f1691,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,[],[f517]) ).
fof(f517,axiom,
! [X41,X42,X13] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X42,X41) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,X42),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,X41)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15374,plain,
spl107_870,
inference(avatar_split_clause,[],[f4877,f15372]) ).
fof(f15372,plain,
( spl107_870
<=> ! [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,[spl107_870])]) ).
fof(f4877,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,[],[f3772]) ).
fof(f3772,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,[],[f3771]) ).
fof(f3771,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,[],[f1686]) ).
fof(f1686,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,[],[f549]) ).
fof(f549,axiom,
! [X65,X66] :
( 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),X66),X65))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X65)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X66) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15370,plain,
spl107_869,
inference(avatar_split_clause,[],[f4876,f15368]) ).
fof(f15368,plain,
( spl107_869
<=> ! [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,[spl107_869])]) ).
fof(f4876,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,[],[f3772]) ).
fof(f15366,plain,
spl107_868,
inference(avatar_split_clause,[],[f4874,f15364]) ).
fof(f15364,plain,
( spl107_868
<=> ! [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,[spl107_868])]) ).
fof(f4874,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,[],[f3770]) ).
fof(f3770,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
& ~ 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_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,[],[f3769]) ).
fof(f3769,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
& ~ 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_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,[],[f1685]) ).
fof(f1685,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
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
inference(rectify,[],[f894]) ).
fof(f894,axiom,
! [X65,X16] :
( 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),X16),X65))
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X65
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15362,plain,
spl107_867,
inference(avatar_split_clause,[],[f4784,f15360]) ).
fof(f15360,plain,
( spl107_867
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_867])]) ).
fof(f4784,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
inference(cnf_transformation,[],[f2636]) ).
fof(f2636,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
inference(ennf_transformation,[],[f1646]) ).
fof(f1646,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X0)) ),
inference(rectify,[],[f687]) ).
fof(f687,axiom,
! [X41,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X12),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X41)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X12,c_RealDef_Oreal(tc_Nat_Onat,X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15358,plain,
spl107_866,
inference(avatar_split_clause,[],[f4736,f15356]) ).
fof(f15356,plain,
( spl107_866
<=> ! [X0,X1] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) = X1
| ~ c_Orderings_Oord__class_Oless(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,[spl107_866])]) ).
fof(f4736,plain,
! [X0,X1] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) = X1
| ~ c_Orderings_Oord__class_Oless(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,[],[f2577]) ).
fof(f2577,plain,
! [X0,X1] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(flattening,[],[f2576]) ).
fof(f2576,plain,
! [X0,X1] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) = X1
| ~ c_Orderings_Oord__class_Oless(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,[],[f1604]) ).
fof(f1604,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(tc_Int_Oint,X1,X0)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) = X1 ) ),
inference(rectify,[],[f990]) ).
fof(f990,axiom,
! [X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X5,X4) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15354,plain,
spl107_865,
inference(avatar_split_clause,[],[f4734,f15352]) ).
fof(f15352,plain,
( spl107_865
<=> ! [X0,X1] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_865])]) ).
fof(f4734,plain,
! [X0,X1] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f2574]) ).
fof(f2574,plain,
! [X0,X1] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(flattening,[],[f2573]) ).
fof(f2573,plain,
! [X0,X1] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(ennf_transformation,[],[f1602]) ).
fof(f1602,plain,
! [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,X0,X1)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) = X1 ) ),
inference(rectify,[],[f994]) ).
fof(f994,axiom,
! [X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X5)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X5,X4) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15350,plain,
spl107_864,
inference(avatar_split_clause,[],[f4731,f15348]) ).
fof(f15348,plain,
( spl107_864
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK66(X0,X1),X0)
| ~ hBOOL(hAPP(X1,X0))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_864])]) ).
fof(f4731,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK66(X0,X1),X0)
| ~ hBOOL(hAPP(X1,X0))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(cnf_transformation,[],[f3708]) ).
fof(f3708,plain,
! [X0,X1] :
( ( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK66(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,sK66(X0,X1)) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK66(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,[sK66])],[f2572,f3707]) ).
fof(f3707,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,sK66(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,sK66(X0,X1)) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK66(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f2572,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,[],[f2571]) ).
fof(f2571,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,[],[f1601]) ).
fof(f1601,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,[],[f655]) ).
fof(f655,axiom,
! [X65,X70] :
( ~ hBOOL(hAPP(X70,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X70,X65))
=> ? [X73] :
( hBOOL(hAPP(X70,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X73,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [X80] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X80,X73)
=> ~ hBOOL(hAPP(X70,X80)) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X73,X65) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15346,plain,
spl107_863,
inference(avatar_split_clause,[],[f4700,f15344]) ).
fof(f15344,plain,
( spl107_863
<=> ! [X0,X1] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_863])]) ).
fof(f4700,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f2534]) ).
fof(f2534,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ),
inference(flattening,[],[f2533]) ).
fof(f2533,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ),
inference(ennf_transformation,[],[f1573]) ).
fof(f1573,plain,
! [X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1)
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1) ) ),
inference(rectify,[],[f954]) ).
fof(f954,axiom,
! [X4,X5] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5,X4)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X4,X5)
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,X5) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15342,plain,
spl107_862,
inference(avatar_split_clause,[],[f4698,f15340]) ).
fof(f15340,plain,
( spl107_862
<=> ! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X1)) = X0
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_862])]) ).
fof(f4698,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X1)) = X0
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f2531]) ).
fof(f2531,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X1)) = X0
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ),
inference(ennf_transformation,[],[f1571]) ).
fof(f1571,plain,
! [X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X1)) = X0 ),
inference(rectify,[],[f946]) ).
fof(f946,axiom,
! [X42,X41] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X41,X42)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X41),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X42,X41)) = X42 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15338,plain,
spl107_861,
inference(avatar_split_clause,[],[f4663,f15336]) ).
fof(f15336,plain,
( spl107_861
<=> ! [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,[spl107_861])]) ).
fof(f4663,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,[],[f2495]) ).
fof(f2495,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,[],[f1540]) ).
fof(f1540,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,[],[f468]) ).
fof(f468,axiom,
! [X57,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),X57) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15300,plain,
spl107_860,
inference(avatar_split_clause,[],[f4662,f15298]) ).
fof(f15298,plain,
( spl107_860
<=> ! [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,[spl107_860])]) ).
fof(f4662,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,[],[f2494]) ).
fof(f2494,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,[],[f1539]) ).
fof(f1539,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,[],[f469]) ).
fof(f469,axiom,
! [X58,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X58),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15296,plain,
spl107_859,
inference(avatar_split_clause,[],[f4624,f15294]) ).
fof(f15294,plain,
( spl107_859
<=> ! [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,[spl107_859])]) ).
fof(f4624,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,[],[f3695]) ).
fof(f3695,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,[],[f2458]) ).
fof(f2458,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,[],[f1504]) ).
fof(f1504,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,[],[f431]) ).
fof(f431,axiom,
! [X10,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X10,X10),c_Groups_Ozero__class_Ozero(X3))
<=> c_Orderings_Oord__class_Oless(X3,X10,c_Groups_Ozero__class_Ozero(X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15292,plain,
spl107_858,
inference(avatar_split_clause,[],[f4623,f15290]) ).
fof(f15290,plain,
( spl107_858
<=> ! [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,[spl107_858])]) ).
fof(f4623,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,[],[f3695]) ).
fof(f15288,plain,
spl107_857,
inference(avatar_split_clause,[],[f4609,f15286]) ).
fof(f15286,plain,
( spl107_857
<=> ! [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,[spl107_857])]) ).
fof(f4609,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,[],[f3691]) ).
fof(f3691,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,[],[f2445]) ).
fof(f2445,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,[],[f1493]) ).
fof(f1493,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,[],[f143]) ).
fof(f143,axiom,
! [X10,X3] :
( class_Groups_Olinordered__ab__group__add(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X10,X10),c_Groups_Ozero__class_Ozero(X3))
<=> c_Orderings_Oord__class_Oless(X3,X10,c_Groups_Ozero__class_Ozero(X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15284,plain,
spl107_856,
inference(avatar_split_clause,[],[f4608,f15282]) ).
fof(f15282,plain,
( spl107_856
<=> ! [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,[spl107_856])]) ).
fof(f4608,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,[],[f3691]) ).
fof(f15280,plain,
spl107_855,
inference(avatar_split_clause,[],[f4607,f15278]) ).
fof(f15278,plain,
( spl107_855
<=> ! [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,[spl107_855])]) ).
fof(f4607,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,[],[f3690]) ).
fof(f3690,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,[],[f2444]) ).
fof(f2444,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,[],[f1492]) ).
fof(f1492,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,[],[f144]) ).
fof(f144,axiom,
! [X10,X3] :
( class_Groups_Olinordered__ab__group__add(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,X10,X10))
<=> c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15276,plain,
spl107_854,
inference(avatar_split_clause,[],[f4606,f15274]) ).
fof(f15274,plain,
( spl107_854
<=> ! [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,[spl107_854])]) ).
fof(f4606,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,[],[f3690]) ).
fof(f15272,plain,
spl107_853,
inference(avatar_split_clause,[],[f4605,f15270]) ).
fof(f15270,plain,
( spl107_853
<=> ! [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,[spl107_853])]) ).
fof(f4605,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,[],[f3689]) ).
fof(f3689,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,[],[f2443]) ).
fof(f2443,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,[],[f1491]) ).
fof(f1491,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,[],[f138]) ).
fof(f138,axiom,
! [X10,X3] :
( class_Groups_Olinordered__ab__group__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X10,X10),c_Groups_Ozero__class_Ozero(X3))
<=> c_Orderings_Oord__class_Oless__eq(X3,X10,c_Groups_Ozero__class_Ozero(X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15268,plain,
spl107_852,
inference(avatar_split_clause,[],[f4604,f15266]) ).
fof(f15266,plain,
( spl107_852
<=> ! [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,[spl107_852])]) ).
fof(f4604,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,[],[f3689]) ).
fof(f15264,plain,
spl107_851,
inference(avatar_split_clause,[],[f4603,f15262]) ).
fof(f15262,plain,
( spl107_851
<=> ! [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,[spl107_851])]) ).
fof(f4603,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,[],[f3688]) ).
fof(f3688,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,[],[f2442]) ).
fof(f2442,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,[],[f1490]) ).
fof(f1490,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,[],[f139]) ).
fof(f139,axiom,
! [X10,X3] :
( class_Groups_Olinordered__ab__group__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,X10,X10))
<=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f15260,plain,
( spl107_850
| ~ spl107_483
| ~ spl107_821 ),
inference(avatar_split_clause,[],[f12920,f12862,f8592,f15258]) ).
fof(f8592,plain,
( spl107_483
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_RComplete_Onatceiling(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_483])]) ).
fof(f12862,plain,
( spl107_821
<=> ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),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,[spl107_821])]) ).
fof(f12920,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatceiling(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),X0) )
| ~ spl107_483
| ~ spl107_821 ),
inference(resolution,[],[f12863,f8593]) ).
fof(f8593,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_RComplete_Onatceiling(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) )
| ~ spl107_483 ),
inference(avatar_component_clause,[],[f8592]) ).
fof(f12863,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) )
| ~ spl107_821 ),
inference(avatar_component_clause,[],[f12862]) ).
fof(f15256,plain,
spl107_849,
inference(avatar_split_clause,[],[f4602,f15254]) ).
fof(f15254,plain,
( spl107_849
<=> ! [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,[spl107_849])]) ).
fof(f4602,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,[],[f3688]) ).
fof(f15252,plain,
spl107_848,
inference(avatar_split_clause,[],[f4536,f15250]) ).
fof(f15250,plain,
( spl107_848
<=> ! [X0,X1] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_848])]) ).
fof(f4536,plain,
! [X0,X1] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X0)),
inference(cnf_transformation,[],[f1437]) ).
fof(f1437,plain,
! [X0,X1] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X0)),
inference(rectify,[],[f668]) ).
fof(f668,axiom,
! [X41,X42] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X41)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X42),c_RealDef_Oreal(tc_Nat_Onat,X41)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14433,plain,
( spl107_847
| ~ spl107_809
| ~ spl107_842 ),
inference(avatar_split_clause,[],[f14108,f12962,f12809,f14431]) ).
fof(f14431,plain,
( spl107_847
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_847])]) ).
fof(f12809,plain,
( spl107_809
<=> ! [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,[spl107_809])]) ).
fof(f12962,plain,
( spl107_842
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_842])]) ).
fof(f14108,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))))
| ~ spl107_809
| ~ spl107_842 ),
inference(resolution,[],[f12810,f12963]) ).
fof(f12963,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),X0))
| ~ spl107_842 ),
inference(avatar_component_clause,[],[f12962]) ).
fof(f12810,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) )
| ~ spl107_809 ),
inference(avatar_component_clause,[],[f12809]) ).
fof(f13740,plain,
( ~ spl107_845
| spl107_846
| ~ spl107_390
| ~ spl107_821 ),
inference(avatar_split_clause,[],[f12915,f12862,f8011,f13737,f13733]) ).
fof(f13733,plain,
( spl107_845
<=> class_Groups_Oordered__ab__group__add__abs(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_845])]) ).
fof(f13737,plain,
( spl107_846
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oabs__class_Oabs(tc_Nat_Onat,c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_846])]) ).
fof(f8011,plain,
( spl107_390
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oabs__class_Oabs(X1,X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_390])]) ).
fof(f12915,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oabs__class_Oabs(tc_Nat_Onat,c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_Nat_Onat)
| ~ spl107_390
| ~ spl107_821 ),
inference(resolution,[],[f12863,f8012]) ).
fof(f8012,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oabs__class_Oabs(X1,X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) )
| ~ spl107_390 ),
inference(avatar_component_clause,[],[f8011]) ).
fof(f13561,plain,
( spl107_844
| ~ spl107_389
| ~ spl107_821 ),
inference(avatar_split_clause,[],[f12906,f12862,f8007,f13559]) ).
fof(f13559,plain,
( spl107_844
<=> ! [X0] :
( 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,X0,c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_844])]) ).
fof(f8007,plain,
( spl107_389
<=> ! [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,[spl107_389])]) ).
fof(f12906,plain,
( ! [X0] :
( 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,X0,c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))) )
| ~ spl107_389
| ~ spl107_821 ),
inference(resolution,[],[f12863,f8008]) ).
fof(f8008,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) )
| ~ spl107_389 ),
inference(avatar_component_clause,[],[f8007]) ).
fof(f13076,plain,
( spl107_843
| ~ spl107_357
| ~ spl107_821 ),
inference(avatar_split_clause,[],[f12917,f12862,f7852,f13074]) ).
fof(f13074,plain,
( spl107_843
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_843])]) ).
fof(f7852,plain,
( spl107_357
<=> ! [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,[spl107_357])]) ).
fof(f12917,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))))
| ~ spl107_357
| ~ spl107_821 ),
inference(resolution,[],[f12863,f7853]) ).
fof(f7853,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ spl107_357 ),
inference(avatar_component_clause,[],[f7852]) ).
fof(f12964,plain,
( spl107_842
| ~ spl107_356
| ~ spl107_821 ),
inference(avatar_split_clause,[],[f12916,f12862,f7848,f12962]) ).
fof(f7848,plain,
( spl107_356
<=> ! [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,[spl107_356])]) ).
fof(f12916,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),X0))
| ~ spl107_356
| ~ spl107_821 ),
inference(resolution,[],[f12863,f7849]) ).
fof(f7849,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ spl107_356 ),
inference(avatar_component_clause,[],[f7848]) ).
fof(f12960,plain,
spl107_841,
inference(avatar_split_clause,[],[f6125,f12958]) ).
fof(f12958,plain,
( spl107_841
<=> ! [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,[spl107_841])]) ).
fof(f6125,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,[],[f5858]) ).
fof(f5858,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,[],[f4089]) ).
fof(f4089,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,[],[f3503]) ).
fof(f3503,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,[],[f3502]) ).
fof(f3502,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,[],[f2264]) ).
fof(f2264,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,[],[f79]) ).
fof(f79,axiom,
! [X7,X8,X9,X10,X3] :
( class_Groups_Oab__group__add(X3)
=> ( c_Groups_Ominus__class_Ominus(X3,X10,X9) = c_Groups_Ominus__class_Ominus(X3,X8,X7)
=> ( X9 = X10
<=> X7 = X8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12956,plain,
spl107_840,
inference(avatar_split_clause,[],[f6081,f12954]) ).
fof(f12954,plain,
( spl107_840
<=> ! [X2,X0,X1] :
( sP42(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,[spl107_840])]) ).
fof(f6081,plain,
! [X2,X0,X1] :
( sP42(X0,X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2))
| c_Groups_Ozero__class_Ozero(X1) = X2 ),
inference(equality_resolution,[],[f5565]) ).
fof(f5565,plain,
! [X2,X3,X0,X1] :
( sP42(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,[],[f4027]) ).
fof(f4027,plain,
! [X0,X1,X2,X3] :
( ( sP42(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 ) )
| ~ sP42(X0,X1,X2,X3) ) ),
inference(rectify,[],[f4026]) ).
fof(f4026,plain,
! [X2,X3,X0,X1] :
( ( sP42(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 ) )
| ~ sP42(X2,X3,X0,X1) ) ),
inference(flattening,[],[f4025]) ).
fof(f4025,plain,
! [X2,X3,X0,X1] :
( ( sP42(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 ) )
| ~ sP42(X2,X3,X0,X1) ) ),
inference(nnf_transformation,[],[f3636]) ).
fof(f3636,plain,
! [X2,X3,X0,X1] :
( sP42(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,[sP42])]) ).
fof(f12952,plain,
spl107_839,
inference(avatar_split_clause,[],[f6073,f12950]) ).
fof(f12950,plain,
( spl107_839
<=> ! [X2,X0,X1] :
( sP40(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,[spl107_839])]) ).
fof(f6073,plain,
! [X2,X0,X1] :
( sP40(X0,X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X2))
| c_Groups_Ozero__class_Ozero(X1) = X2 ),
inference(equality_resolution,[],[f5556]) ).
fof(f5556,plain,
! [X2,X3,X0,X1] :
( sP40(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,[],[f4022]) ).
fof(f4022,plain,
! [X0,X1,X2,X3] :
( ( sP40(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 ) )
| ~ sP40(X0,X1,X2,X3) ) ),
inference(rectify,[],[f4021]) ).
fof(f4021,plain,
! [X0,X3,X1,X2] :
( ( sP40(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 ) )
| ~ sP40(X0,X3,X1,X2) ) ),
inference(flattening,[],[f4020]) ).
fof(f4020,plain,
! [X0,X3,X1,X2] :
( ( sP40(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 ) )
| ~ sP40(X0,X3,X1,X2) ) ),
inference(nnf_transformation,[],[f3633]) ).
fof(f3633,plain,
! [X0,X3,X1,X2] :
( sP40(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,[sP40])]) ).
fof(f12948,plain,
spl107_838,
inference(avatar_split_clause,[],[f5790,f12946]) ).
fof(f12946,plain,
( spl107_838
<=> ! [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,[spl107_838])]) ).
fof(f5790,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,[],[f3423]) ).
fof(f3423,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,[],[f3422]) ).
fof(f3422,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,[],[f2221]) ).
fof(f2221,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,[],[f36]) ).
fof(f36,axiom,
! [X12,X6,X21,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X21,X6)
=> ( c_Orderings_Oord__class_Oless(X3,X12,X21)
=> c_Orderings_Oord__class_Oless(X3,X12,X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12944,plain,
spl107_837,
inference(avatar_split_clause,[],[f5789,f12942]) ).
fof(f12942,plain,
( spl107_837
<=> ! [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,[spl107_837])]) ).
fof(f5789,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,[],[f3421]) ).
fof(f3421,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,[],[f3420]) ).
fof(f3420,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,[],[f2220]) ).
fof(f2220,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,[],[f41]) ).
fof(f41,axiom,
! [X12,X6,X21,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X21,X6)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X12,X21)
=> c_Orderings_Oord__class_Oless(X3,X12,X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12940,plain,
spl107_836,
inference(avatar_split_clause,[],[f5787,f12938]) ).
fof(f12938,plain,
( spl107_836
<=> ! [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,[spl107_836])]) ).
fof(f5787,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,[],[f3417]) ).
fof(f3417,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,[],[f3416]) ).
fof(f3416,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,[],[f2218]) ).
fof(f2218,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,[],[f39]) ).
fof(f39,axiom,
! [X12,X6,X21,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X21,X6)
=> ( c_Orderings_Oord__class_Oless(X3,X12,X21)
=> c_Orderings_Oord__class_Oless(X3,X12,X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12936,plain,
spl107_835,
inference(avatar_split_clause,[],[f5786,f12934]) ).
fof(f12934,plain,
( spl107_835
<=> ! [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,[spl107_835])]) ).
fof(f5786,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,[],[f3415]) ).
fof(f3415,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,[],[f3414]) ).
fof(f3414,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,[],[f2217]) ).
fof(f2217,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,[],[f65]) ).
fof(f65,axiom,
! [X12,X6,X21,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X21,X6)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X12,X21)
=> c_Orderings_Oord__class_Oless__eq(X3,X12,X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12932,plain,
spl107_834,
inference(avatar_split_clause,[],[f5782,f12930]) ).
fof(f12930,plain,
( spl107_834
<=> ! [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,[spl107_834])]) ).
fof(f5782,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,[],[f3407]) ).
fof(f3407,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,[],[f3406]) ).
fof(f3406,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,[],[f2213]) ).
fof(f2213,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,[],[f35]) ).
fof(f35,axiom,
! [X12,X21,X6,X3] :
( class_Orderings_Opreorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X6,X21)
=> ( c_Orderings_Oord__class_Oless(X3,X21,X12)
=> c_Orderings_Oord__class_Oless(X3,X6,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12928,plain,
spl107_833,
inference(avatar_split_clause,[],[f5781,f12926]) ).
fof(f12926,plain,
( spl107_833
<=> ! [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,[spl107_833])]) ).
fof(f5781,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,[],[f3405]) ).
fof(f3405,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,[],[f3404]) ).
fof(f3404,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,[],[f2212]) ).
fof(f2212,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,[],[f42]) ).
fof(f42,axiom,
! [X12,X21,X6,X3] :
( class_Orderings_Opreorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X6,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X21,X12)
=> c_Orderings_Oord__class_Oless(X3,X6,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12924,plain,
spl107_832,
inference(avatar_split_clause,[],[f5780,f12922]) ).
fof(f5780,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,[],[f3403]) ).
fof(f3403,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,[],[f3402]) ).
fof(f3402,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,[],[f2211]) ).
fof(f2211,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,[],[f40]) ).
fof(f40,axiom,
! [X12,X21,X6,X3] :
( class_Orderings_Opreorder(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X6,X21)
=> ( c_Orderings_Oord__class_Oless(X3,X21,X12)
=> c_Orderings_Oord__class_Oless(X3,X6,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12904,plain,
spl107_831,
inference(avatar_split_clause,[],[f5779,f12902]) ).
fof(f12902,plain,
( spl107_831
<=> ! [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,[spl107_831])]) ).
fof(f5779,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,[],[f3401]) ).
fof(f3401,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,[],[f3400]) ).
fof(f3400,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,[],[f2210]) ).
fof(f2210,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,[],[f67]) ).
fof(f67,axiom,
! [X12,X21,X6,X3] :
( class_Orderings_Opreorder(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X6,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X21,X12)
=> c_Orderings_Oord__class_Oless__eq(X3,X6,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12900,plain,
spl107_830,
inference(avatar_split_clause,[],[f5777,f12898]) ).
fof(f12898,plain,
( spl107_830
<=> ! [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,[spl107_830])]) ).
fof(f5777,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,[],[f4071]) ).
fof(f4071,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,[],[f4070]) ).
fof(f4070,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,[],[f3399]) ).
fof(f3399,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,[],[f2209]) ).
fof(f2209,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,[],[f108]) ).
fof(f108,axiom,
! [X0,X1,X3,X19] :
( class_Orderings_Oord(X19)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X3,X19),X1,X0)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X19),X0,X1)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X19),X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12896,plain,
spl107_829,
inference(avatar_split_clause,[],[f5776,f12894]) ).
fof(f12894,plain,
( spl107_829
<=> ! [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,[spl107_829])]) ).
fof(f5776,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,[],[f4071]) ).
fof(f12892,plain,
spl107_828,
inference(avatar_split_clause,[],[f5766,f12890]) ).
fof(f12890,plain,
( spl107_828
<=> ! [X0,X3,X2,X1] :
( c_Rings_Odvd__class_Odvd(X3,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(X3,X1,X0)
| ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_828])]) ).
fof(f5766,plain,
! [X2,X3,X0,X1] :
( c_Rings_Odvd__class_Odvd(X3,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(X3,X1,X0)
| ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3383]) ).
fof(f3383,plain,
! [X0,X1,X2,X3] :
( c_Rings_Odvd__class_Odvd(X3,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(X3,X1,X0)
| ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(flattening,[],[f3382]) ).
fof(f3382,plain,
! [X0,X1,X2,X3] :
( c_Rings_Odvd__class_Odvd(X3,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(X3,X1,X0)
| ~ c_Rings_Odvd__class_Odvd(X3,X2,X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2200]) ).
fof(f2200,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X2,X1)
=> ( c_Rings_Odvd__class_Odvd(X3,X1,X0)
=> c_Rings_Odvd__class_Odvd(X3,X2,X0) ) ) ),
inference(rectify,[],[f813]) ).
fof(f813,axiom,
! [X22,X4,X5,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X5,X4)
=> ( c_Rings_Odvd__class_Odvd(X3,X4,X22)
=> c_Rings_Odvd__class_Odvd(X3,X5,X22) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12888,plain,
spl107_827,
inference(avatar_split_clause,[],[f5734,f12886]) ).
fof(f12886,plain,
( spl107_827
<=> ! [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,[spl107_827])]) ).
fof(f5734,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,[],[f3346]) ).
fof(f3346,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,[],[f3345]) ).
fof(f3345,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,[],[f2170]) ).
fof(f2170,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,[],[f122]) ).
fof(f122,axiom,
! [X22,X5,X4,X3] :
( class_Groups_Ocancel__semigroup__add(X3)
=> ( c_Groups_Oplus__class_Oplus(X3,X4,X5) = c_Groups_Oplus__class_Oplus(X3,X22,X5)
=> X4 = X22 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12884,plain,
spl107_826,
inference(avatar_split_clause,[],[f5733,f12882]) ).
fof(f12882,plain,
( spl107_826
<=> ! [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,[spl107_826])]) ).
fof(f5733,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,[],[f3344]) ).
fof(f3344,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,[],[f3343]) ).
fof(f3343,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,[],[f2169]) ).
fof(f2169,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,[],[f120]) ).
fof(f120,axiom,
! [X22,X4,X5,X3] :
( class_Groups_Ocancel__semigroup__add(X3)
=> ( c_Groups_Oplus__class_Oplus(X3,X5,X4) = c_Groups_Oplus__class_Oplus(X3,X5,X22)
=> X4 = X22 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12880,plain,
spl107_825,
inference(avatar_split_clause,[],[f5730,f12878]) ).
fof(f12878,plain,
( spl107_825
<=> ! [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,[spl107_825])]) ).
fof(f5730,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,[],[f3339]) ).
fof(f3339,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,[],[f3338]) ).
fof(f3338,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,[],[f2166]) ).
fof(f2166,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,[],[f121]) ).
fof(f121,axiom,
! [X22,X4,X5,X3] :
( class_Groups_Ocancel__ab__semigroup__add(X3)
=> ( c_Groups_Oplus__class_Oplus(X3,X5,X4) = c_Groups_Oplus__class_Oplus(X3,X5,X22)
=> X4 = X22 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12876,plain,
spl107_824,
inference(avatar_split_clause,[],[f5629,f12874]) ).
fof(f12874,plain,
( spl107_824
<=> ! [X0,X3,X2,X1] :
( sP46(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,[spl107_824])]) ).
fof(f5629,plain,
! [X2,X3,X0,X1] :
( sP46(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,[],[f4047]) ).
fof(f12872,plain,
spl107_823,
inference(avatar_split_clause,[],[f5628,f12870]) ).
fof(f12870,plain,
( spl107_823
<=> ! [X0,X3,X2,X1] :
( sP46(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,[spl107_823])]) ).
fof(f5628,plain,
! [X2,X3,X0,X1] :
( sP46(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,[],[f4047]) ).
fof(f12868,plain,
spl107_822,
inference(avatar_split_clause,[],[f5626,f12866]) ).
fof(f12866,plain,
( spl107_822
<=> ! [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)
| ~ sP46(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_822])]) ).
fof(f5626,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)
| ~ sP46(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4047]) ).
fof(f12864,plain,
( spl107_821
| ~ spl107_659
| ~ spl107_709 ),
inference(avatar_split_clause,[],[f11453,f11409,f10505,f12862]) ).
fof(f10505,plain,
( spl107_659
<=> ! [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,[spl107_659])]) ).
fof(f11409,plain,
( spl107_709
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_709])]) ).
fof(f11453,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) )
| ~ spl107_659
| ~ spl107_709 ),
inference(resolution,[],[f11411,f10506]) ).
fof(f10506,plain,
( ! [X2,X0,X1] :
( ~ 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) )
| ~ spl107_659 ),
inference(avatar_component_clause,[],[f10505]) ).
fof(f11411,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))))
| ~ spl107_709 ),
inference(avatar_component_clause,[],[f11409]) ).
fof(f12860,plain,
spl107_820,
inference(avatar_split_clause,[],[f5625,f12858]) ).
fof(f12858,plain,
( spl107_820
<=> ! [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)
| ~ sP46(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_820])]) ).
fof(f5625,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)
| ~ sP46(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4047]) ).
fof(f12856,plain,
spl107_819,
inference(avatar_split_clause,[],[f5620,f12854]) ).
fof(f12854,plain,
( spl107_819
<=> ! [X0,X3,X2,X1] :
( sP44(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,[spl107_819])]) ).
fof(f5620,plain,
! [X2,X3,X0,X1] :
( sP44(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,[],[f4042]) ).
fof(f12852,plain,
spl107_818,
inference(avatar_split_clause,[],[f5619,f12850]) ).
fof(f12850,plain,
( spl107_818
<=> ! [X0,X3,X2,X1] :
( sP44(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,[spl107_818])]) ).
fof(f5619,plain,
! [X2,X3,X0,X1] :
( sP44(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,[],[f4042]) ).
fof(f12848,plain,
spl107_817,
inference(avatar_split_clause,[],[f5617,f12846]) ).
fof(f12846,plain,
( spl107_817
<=> ! [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)
| ~ sP44(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_817])]) ).
fof(f5617,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)
| ~ sP44(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4042]) ).
fof(f12844,plain,
spl107_816,
inference(avatar_split_clause,[],[f5616,f12842]) ).
fof(f12842,plain,
( spl107_816
<=> ! [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)
| ~ sP44(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_816])]) ).
fof(f5616,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)
| ~ sP44(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4042]) ).
fof(f12840,plain,
spl107_815,
inference(avatar_split_clause,[],[f5422,f12838]) ).
fof(f12838,plain,
( spl107_815
<=> ! [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,[spl107_815])]) ).
fof(f5422,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,[],[f3958]) ).
fof(f3958,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,[],[f2000]) ).
fof(f2000,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,[],[f570]) ).
fof(f570,axiom,
! [X65,X66,X63] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X63,X66),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X63,X65))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X66,X65) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12836,plain,
spl107_814,
inference(avatar_split_clause,[],[f5421,f12834]) ).
fof(f12834,plain,
( spl107_814
<=> ! [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,[spl107_814])]) ).
fof(f5421,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,[],[f3958]) ).
fof(f12832,plain,
spl107_813,
inference(avatar_split_clause,[],[f5420,f12830]) ).
fof(f12830,plain,
( spl107_813
<=> ! [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,[spl107_813])]) ).
fof(f5420,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,[],[f3957]) ).
fof(f3957,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,[],[f1999]) ).
fof(f1999,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,[],[f590]) ).
fof(f590,axiom,
! [X65,X66,X63] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X63,X66),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X63,X65))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,X65) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12828,plain,
spl107_812,
inference(avatar_split_clause,[],[f5419,f12826]) ).
fof(f12826,plain,
( spl107_812
<=> ! [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,[spl107_812])]) ).
fof(f5419,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,[],[f3957]) ).
fof(f12824,plain,
spl107_811,
inference(avatar_split_clause,[],[f5412,f12822]) ).
fof(f12822,plain,
( spl107_811
<=> ! [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,[spl107_811])]) ).
fof(f5412,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,[],[f3953]) ).
fof(f3953,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,[],[f1995]) ).
fof(f1995,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,[],[f569]) ).
fof(f569,axiom,
! [X63,X68,X69] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X69,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X68,X63))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X69,X63),X68) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12815,plain,
spl107_810,
inference(avatar_split_clause,[],[f5411,f12813]) ).
fof(f12813,plain,
( spl107_810
<=> ! [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,[spl107_810])]) ).
fof(f5411,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,[],[f3953]) ).
fof(f12811,plain,
spl107_809,
inference(avatar_split_clause,[],[f5410,f12809]) ).
fof(f5410,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,[],[f3952]) ).
fof(f3952,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,[],[f1994]) ).
fof(f1994,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,[],[f589]) ).
fof(f589,axiom,
! [X69,X63,X68] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X68,X63),X69)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X68,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X69,X63)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12807,plain,
spl107_808,
inference(avatar_split_clause,[],[f5409,f12805]) ).
fof(f12805,plain,
( spl107_808
<=> ! [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,[spl107_808])]) ).
fof(f5409,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,[],[f3952]) ).
fof(f12803,plain,
spl107_807,
inference(avatar_split_clause,[],[f5317,f12801]) ).
fof(f12801,plain,
( spl107_807
<=> ! [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,[spl107_807])]) ).
fof(f5317,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,[],[f3888]) ).
fof(f3888,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,[],[f3060]) ).
fof(f3060,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,[],[f3059]) ).
fof(f3059,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,[],[f1981]) ).
fof(f1981,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,[],[f472]) ).
fof(f472,axiom,
! [X59,X60,X3] :
( ( class_Rings_Oidom(X3)
& class_Int_Oring__char__0(X3) )
=> ( c_Polynomial_Opoly(X3,X60) = c_Polynomial_Opoly(X3,X59)
<=> X59 = X60 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12799,plain,
spl107_806,
inference(avatar_split_clause,[],[f5260,f12797]) ).
fof(f12797,plain,
( spl107_806
<=> ! [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,[spl107_806])]) ).
fof(f5260,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,[],[f3004]) ).
fof(f3004,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,[],[f1946]) ).
fof(f1946,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,[],[f574]) ).
fof(f574,axiom,
! [X13,X14,X15] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X14)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X13),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12795,plain,
spl107_805,
inference(avatar_split_clause,[],[f5229,f12793]) ).
fof(f12793,plain,
( spl107_805
<=> ! [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,[spl107_805])]) ).
fof(f5229,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,[],[f2975]) ).
fof(f2975,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,[],[f1924]) ).
fof(f1924,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,[],[f594]) ).
fof(f594,axiom,
! [X13,X14,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X14)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X13),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12791,plain,
spl107_804,
inference(avatar_split_clause,[],[f5228,f12789]) ).
fof(f12789,plain,
( spl107_804
<=> ! [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,[spl107_804])]) ).
fof(f5228,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,[],[f2974]) ).
fof(f2974,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,[],[f1923]) ).
fof(f1923,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,[],[f537]) ).
fof(f537,axiom,
! [X72,X41,X42] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X41)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X72,X41),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X72,X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12787,plain,
spl107_803,
inference(avatar_split_clause,[],[f5227,f12785]) ).
fof(f12785,plain,
( spl107_803
<=> ! [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,[spl107_803])]) ).
fof(f5227,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,[],[f2973]) ).
fof(f2973,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,[],[f1922]) ).
fof(f1922,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,[],[f536]) ).
fof(f536,axiom,
! [X72,X41,X42] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X41)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X42,X72),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X41,X72)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12783,plain,
spl107_802,
inference(avatar_split_clause,[],[f5226,f12781]) ).
fof(f12781,plain,
( spl107_802
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X0),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_802])]) ).
fof(f5226,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X0),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2972]) ).
fof(f2972,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X0),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1921]) ).
fof(f1921,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_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X0),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)) ),
inference(rectify,[],[f705]) ).
fof(f705,axiom,
! [X13,X41,X42] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X41)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X42,X13),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X41,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12779,plain,
spl107_801,
inference(avatar_split_clause,[],[f5225,f12777]) ).
fof(f12777,plain,
( spl107_801
<=> ! [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,[spl107_801])]) ).
fof(f5225,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,[],[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,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,[],[f1920]) ).
fof(f1920,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,[],[f593]) ).
fof(f593,axiom,
! [X42,X41,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,X41)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X42),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12775,plain,
( ~ spl107_207
| ~ spl107_800
| ~ spl107_495
| ~ spl107_688 ),
inference(avatar_split_clause,[],[f11365,f11317,f8641,f12772,f7206]) ).
fof(f12772,plain,
( spl107_800
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_800])]) ).
fof(f8641,plain,
( spl107_495
<=> ! [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,[spl107_495])]) ).
fof(f11317,plain,
( spl107_688
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_688])]) ).
fof(f11365,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ spl107_495
| ~ spl107_688 ),
inference(resolution,[],[f11319,f8642]) ).
fof(f8642,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) )
| ~ spl107_495 ),
inference(avatar_component_clause,[],[f8641]) ).
fof(f11319,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))))
| ~ spl107_688 ),
inference(avatar_component_clause,[],[f11317]) ).
fof(f12770,plain,
spl107_799,
inference(avatar_split_clause,[],[f5219,f12768]) ).
fof(f12768,plain,
( spl107_799
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_799])]) ).
fof(f5219,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(cnf_transformation,[],[f2964]) ).
fof(f2964,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(ennf_transformation,[],[f1914]) ).
fof(f1914,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)) ),
inference(rectify,[],[f190]) ).
fof(f190,axiom,
! [X12,X21,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,X21)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X12,X6),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X12,X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12766,plain,
spl107_798,
inference(avatar_split_clause,[],[f5177,f12764]) ).
fof(f12764,plain,
( spl107_798
<=> ! [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,[spl107_798])]) ).
fof(f5177,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,[],[f3847]) ).
fof(f3847,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,[],[f3846]) ).
fof(f3846,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,[],[f2917]) ).
fof(f2917,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,[],[f1886]) ).
fof(f1886,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,[],[f55]) ).
fof(f55,axiom,
! [X20,X16,X3] :
( class_Orderings_Opreorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X16,X20)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(X3,X20,X16)
& c_Orderings_Oord__class_Oless__eq(X3,X16,X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12762,plain,
spl107_797,
inference(avatar_split_clause,[],[f5060,f12760]) ).
fof(f12760,plain,
( spl107_797
<=> ! [X2,X0,X1] :
( c_Divides_Odiv__class_Omod(X2,X1,X0) = c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0)
| ~ class_Divides_Osemiring__div(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_797])]) ).
fof(f5060,plain,
! [X2,X0,X1] :
( c_Divides_Odiv__class_Omod(X2,X1,X0) = c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0)
| ~ class_Divides_Osemiring__div(X2) ),
inference(cnf_transformation,[],[f2762]) ).
fof(f2762,plain,
! [X0,X1,X2] :
( c_Divides_Odiv__class_Omod(X2,X1,X0) = c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0)
| ~ class_Divides_Osemiring__div(X2) ),
inference(ennf_transformation,[],[f1794]) ).
fof(f1794,plain,
! [X0,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,X1,X0) = c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) ),
inference(rectify,[],[f762]) ).
fof(f762,axiom,
! [X4,X5,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,X5,X4) = c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X5,X4),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12758,plain,
spl107_796,
inference(avatar_split_clause,[],[f5059,f12756]) ).
fof(f12756,plain,
( spl107_796
<=> ! [X2,X0,X1] :
( c_Divides_Odiv__class_Omod(X2,X0,X1) = c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X1)
| ~ class_Divides_Osemiring__div(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_796])]) ).
fof(f5059,plain,
! [X2,X0,X1] :
( c_Divides_Odiv__class_Omod(X2,X0,X1) = c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X1)
| ~ class_Divides_Osemiring__div(X2) ),
inference(cnf_transformation,[],[f2761]) ).
fof(f2761,plain,
! [X0,X1,X2] :
( c_Divides_Odiv__class_Omod(X2,X0,X1) = c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X1)
| ~ class_Divides_Osemiring__div(X2) ),
inference(ennf_transformation,[],[f1793]) ).
fof(f1793,plain,
! [X0,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,X0,X1) = c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X1) ),
inference(rectify,[],[f761]) ).
fof(f761,axiom,
! [X5,X4,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,X5,X4) = c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X4,X5),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12754,plain,
spl107_795,
inference(avatar_split_clause,[],[f5058,f12752]) ).
fof(f12752,plain,
( spl107_795
<=> ! [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,[spl107_795])]) ).
fof(f5058,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,[],[f2760]) ).
fof(f2760,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,[],[f1792]) ).
fof(f1792,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,[],[f748]) ).
fof(f748,axiom,
! [X4,X5,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,X5,X4) = c_Divides_Odiv__class_Omod(X3,c_Divides_Odiv__class_Omod(X3,X5,X4),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12750,plain,
spl107_794,
inference(avatar_split_clause,[],[f5057,f12748]) ).
fof(f12748,plain,
( spl107_794
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X0)
| ~ class_Divides_Osemiring__div(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_794])]) ).
fof(f5057,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X0)
| ~ class_Divides_Osemiring__div(X2) ),
inference(cnf_transformation,[],[f2759]) ).
fof(f2759,plain,
! [X0,X1,X2] :
( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X0)
| ~ class_Divides_Osemiring__div(X2) ),
inference(ennf_transformation,[],[f1791]) ).
fof(f1791,plain,
! [X0,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X0) ),
inference(rectify,[],[f732]) ).
fof(f732,axiom,
! [X4,X5,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Groups_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),X4),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12746,plain,
spl107_793,
inference(avatar_split_clause,[],[f5056,f12744]) ).
fof(f12744,plain,
( spl107_793
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1)
| ~ class_Divides_Osemiring__div(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_793])]) ).
fof(f5056,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1)
| ~ class_Divides_Osemiring__div(X2) ),
inference(cnf_transformation,[],[f2758]) ).
fof(f2758,plain,
! [X0,X1,X2] :
( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1)
| ~ class_Divides_Osemiring__div(X2) ),
inference(ennf_transformation,[],[f1790]) ).
fof(f1790,plain,
! [X0,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1) ),
inference(rectify,[],[f731]) ).
fof(f731,axiom,
! [X5,X4,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Groups_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X4),X5),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12742,plain,
spl107_792,
inference(avatar_split_clause,[],[f5043,f12740]) ).
fof(f12740,plain,
( spl107_792
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Oabs__class_Oabs(X2,X1)),X0))
| ~ class_Rings_Olinordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_792])]) ).
fof(f5043,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),c_Groups_Oabs__class_Oabs(X2,X1)),X0))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(cnf_transformation,[],[f2742]) ).
fof(f2742,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),c_Groups_Oabs__class_Oabs(X2,X1)),X0))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(ennf_transformation,[],[f1779]) ).
fof(f1779,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Oabs__class_Oabs(X2,X1)),X0)) ),
inference(rectify,[],[f928]) ).
fof(f928,axiom,
! [X41,X5,X3] :
( class_Rings_Olinordered__idom(X3)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Groups_Oabs__class_Oabs(X3,X5)),X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12738,plain,
spl107_791,
inference(avatar_split_clause,[],[f5024,f12736]) ).
fof(f12736,plain,
( spl107_791
<=> ! [X2,X0,X1] :
( sP11(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,[spl107_791])]) ).
fof(f5024,plain,
! [X2,X0,X1] :
( sP11(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,[],[f3817]) ).
fof(f3817,plain,
! [X0,X1,X2] :
( ( sP11(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) )
| ~ sP11(X0,X1,X2) ) ),
inference(rectify,[],[f3816]) ).
fof(f3816,plain,
! [X0,X2,X1] :
( ( sP11(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) )
| ~ sP11(X0,X2,X1) ) ),
inference(flattening,[],[f3815]) ).
fof(f3815,plain,
! [X0,X2,X1] :
( ( sP11(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) )
| ~ sP11(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f3590]) ).
fof(f3590,plain,
! [X0,X2,X1] :
( sP11(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,[sP11])]) ).
fof(f12734,plain,
spl107_790,
inference(avatar_split_clause,[],[f5023,f12732]) ).
fof(f12732,plain,
( spl107_790
<=> ! [X2,X0,X1] :
( sP11(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,[spl107_790])]) ).
fof(f5023,plain,
! [X2,X0,X1] :
( sP11(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,[],[f3817]) ).
fof(f12730,plain,
spl107_789,
inference(avatar_split_clause,[],[f5022,f12728]) ).
fof(f12728,plain,
( spl107_789
<=> ! [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))
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_789])]) ).
fof(f5022,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))
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f3817]) ).
fof(f12726,plain,
spl107_788,
inference(avatar_split_clause,[],[f5021,f12724]) ).
fof(f12724,plain,
( spl107_788
<=> ! [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)
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_788])]) ).
fof(f5021,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)
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f3817]) ).
fof(f12722,plain,
spl107_787,
inference(avatar_split_clause,[],[f5020,f12720]) ).
fof(f12720,plain,
( spl107_787
<=> ! [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))
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_787])]) ).
fof(f5020,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))
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f3817]) ).
fof(f12718,plain,
spl107_786,
inference(avatar_split_clause,[],[f5019,f12716]) ).
fof(f12716,plain,
( spl107_786
<=> ! [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)
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_786])]) ).
fof(f5019,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)
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f3817]) ).
fof(f12714,plain,
spl107_785,
inference(avatar_split_clause,[],[f5015,f12712]) ).
fof(f12712,plain,
( spl107_785
<=> ! [X2,X0,X1] :
( sP9(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,[spl107_785])]) ).
fof(f5015,plain,
! [X2,X0,X1] :
( sP9(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,[],[f3812]) ).
fof(f3812,plain,
! [X0,X1,X2] :
( ( sP9(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) )
| ~ sP9(X0,X1,X2) ) ),
inference(rectify,[],[f3811]) ).
fof(f3811,plain,
! [X2,X0,X1] :
( ( sP9(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) )
| ~ sP9(X2,X0,X1) ) ),
inference(flattening,[],[f3810]) ).
fof(f3810,plain,
! [X2,X0,X1] :
( ( sP9(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) )
| ~ sP9(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f3587]) ).
fof(f3587,plain,
! [X2,X0,X1] :
( sP9(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,[sP9])]) ).
fof(f12710,plain,
spl107_784,
inference(avatar_split_clause,[],[f5014,f12708]) ).
fof(f12708,plain,
( spl107_784
<=> ! [X2,X0,X1] :
( sP9(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,[spl107_784])]) ).
fof(f5014,plain,
! [X2,X0,X1] :
( sP9(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,[],[f3812]) ).
fof(f12706,plain,
spl107_783,
inference(avatar_split_clause,[],[f5013,f12704]) ).
fof(f12704,plain,
( spl107_783
<=> ! [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)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_783])]) ).
fof(f5013,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)
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f3812]) ).
fof(f12702,plain,
spl107_782,
inference(avatar_split_clause,[],[f5012,f12700]) ).
fof(f12700,plain,
( spl107_782
<=> ! [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)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_782])]) ).
fof(f5012,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)
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f3812]) ).
fof(f12698,plain,
spl107_781,
inference(avatar_split_clause,[],[f5011,f12696]) ).
fof(f12696,plain,
( spl107_781
<=> ! [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)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_781])]) ).
fof(f5011,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)
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f3812]) ).
fof(f12694,plain,
spl107_780,
inference(avatar_split_clause,[],[f5010,f12692]) ).
fof(f12692,plain,
( spl107_780
<=> ! [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)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_780])]) ).
fof(f5010,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)
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f3812]) ).
fof(f12690,plain,
( ~ spl107_779
| spl107_748
| ~ spl107_655
| ~ spl107_738 ),
inference(avatar_split_clause,[],[f12523,f12174,f10489,f12562,f12687]) ).
fof(f12687,plain,
( spl107_779
<=> class_Groups_Oab__group__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_779])]) ).
fof(f12562,plain,
( spl107_748
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_748])]) ).
fof(f10489,plain,
( spl107_655
<=> ! [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,[spl107_655])]) ).
fof(f12174,plain,
( spl107_738
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_738])]) ).
fof(f12523,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))
| ~ class_Groups_Oab__group__add(tc_Nat_Onat)
| ~ spl107_655
| ~ spl107_738 ),
inference(trivial_inequality_removal,[],[f12520]) ).
fof(f12520,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))
| ~ class_Groups_Oab__group__add(tc_Nat_Onat)
| ~ spl107_655
| ~ spl107_738 ),
inference(superposition,[],[f10490,f12176]) ).
fof(f12176,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))))
| ~ spl107_738 ),
inference(avatar_component_clause,[],[f12174]) ).
fof(f10490,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) )
| ~ spl107_655 ),
inference(avatar_component_clause,[],[f10489]) ).
fof(f12685,plain,
spl107_778,
inference(avatar_split_clause,[],[f5003,f12683]) ).
fof(f12683,plain,
( spl107_778
<=> ! [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,[spl107_778])]) ).
fof(f5003,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,[],[f3807]) ).
fof(f3807,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,[],[f2721]) ).
fof(f2721,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,[],[f1762]) ).
fof(f1762,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,[],[f208]) ).
fof(f208,axiom,
! [X9,X10,X3] :
( class_Groups_Oordered__ab__group__add(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X10,X9)
<=> c_Orderings_Oord__class_Oless(X3,c_Groups_Ominus__class_Ominus(X3,X10,X9),c_Groups_Ozero__class_Ozero(X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12681,plain,
spl107_777,
inference(avatar_split_clause,[],[f5002,f12679]) ).
fof(f12679,plain,
( spl107_777
<=> ! [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,[spl107_777])]) ).
fof(f5002,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,[],[f3807]) ).
fof(f12677,plain,
spl107_776,
inference(avatar_split_clause,[],[f5001,f12675]) ).
fof(f12675,plain,
( spl107_776
<=> ! [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,[spl107_776])]) ).
fof(f5001,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,[],[f3806]) ).
fof(f3806,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,[],[f2720]) ).
fof(f2720,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,[],[f1761]) ).
fof(f1761,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,[],[f207]) ).
fof(f207,axiom,
! [X9,X10,X3] :
( class_Groups_Oordered__ab__group__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X10,X9)
<=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ominus__class_Ominus(X3,X10,X9),c_Groups_Ozero__class_Ozero(X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12673,plain,
spl107_775,
inference(avatar_split_clause,[],[f5000,f12671]) ).
fof(f12671,plain,
( spl107_775
<=> ! [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,[spl107_775])]) ).
fof(f5000,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,[],[f3806]) ).
fof(f12669,plain,
spl107_774,
inference(avatar_split_clause,[],[f4963,f12667]) ).
fof(f12667,plain,
( spl107_774
<=> ! [X2,X0,X1] :
( sP7(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_774])]) ).
fof(f4963,plain,
! [X2,X0,X1] :
( sP7(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(cnf_transformation,[],[f3804]) ).
fof(f3804,plain,
! [X0,X1,X2] :
( ( sP7(X0,X1,X2)
| ( ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,X2,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),X2) ) ) )
& ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
& c_Orderings_Oord__class_Oless(X1,X2,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),X2) )
| ~ sP7(X0,X1,X2) ) ),
inference(rectify,[],[f3803]) ).
fof(f3803,plain,
! [X0,X2,X1] :
( ( sP7(X0,X2,X1)
| ( ( ~ 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)) )
& ( ~ 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) ) ) )
& ( ( 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)) )
| ( 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) )
| ~ sP7(X0,X2,X1) ) ),
inference(flattening,[],[f3802]) ).
fof(f3802,plain,
! [X0,X2,X1] :
( ( sP7(X0,X2,X1)
| ( ( ~ 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)) )
& ( ~ 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) ) ) )
& ( ( 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)) )
| ( 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) )
| ~ sP7(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f3584]) ).
fof(f3584,plain,
! [X0,X2,X1] :
( sP7(X0,X2,X1)
<=> ( ( 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)) )
| ( 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) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f12665,plain,
spl107_773,
inference(avatar_split_clause,[],[f4962,f12663]) ).
fof(f12663,plain,
( spl107_773
<=> ! [X2,X0,X1] :
( sP7(X0,X1,X2)
| ~ 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),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_773])]) ).
fof(f4962,plain,
! [X2,X0,X1] :
( sP7(X0,X1,X2)
| ~ 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),X2) ),
inference(cnf_transformation,[],[f3804]) ).
fof(f12661,plain,
spl107_772,
inference(avatar_split_clause,[],[f4961,f12659]) ).
fof(f12659,plain,
( spl107_772
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_772])]) ).
fof(f4961,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f3804]) ).
fof(f12657,plain,
spl107_771,
inference(avatar_split_clause,[],[f4960,f12655]) ).
fof(f12655,plain,
( spl107_771
<=> ! [X2,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),X2)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_771])]) ).
fof(f4960,plain,
! [X2,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),X2)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f3804]) ).
fof(f12653,plain,
spl107_770,
inference(avatar_split_clause,[],[f4959,f12651]) ).
fof(f12651,plain,
( spl107_770
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_770])]) ).
fof(f4959,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f3804]) ).
fof(f12649,plain,
spl107_769,
inference(avatar_split_clause,[],[f4958,f12647]) ).
fof(f12647,plain,
( spl107_769
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_769])]) ).
fof(f4958,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f3804]) ).
fof(f12645,plain,
spl107_768,
inference(avatar_split_clause,[],[f4954,f12643]) ).
fof(f12643,plain,
( spl107_768
<=> ! [X2,X0,X1] :
( sP5(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_768])]) ).
fof(f4954,plain,
! [X2,X0,X1] :
( sP5(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3799]) ).
fof(f3799,plain,
! [X0,X1,X2] :
( ( sP5(X0,X1,X2)
| ( ( ~ c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0)) )
& ( ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X2) ) ) )
& ( ( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
& c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0)) )
| ( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
& c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X2) )
| ~ sP5(X0,X1,X2) ) ),
inference(rectify,[],[f3798]) ).
fof(f3798,plain,
! [X2,X0,X1] :
( ( sP5(X2,X0,X1)
| ( ( ~ 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)) )
& ( ~ 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,X0,c_Groups_Ozero__class_Ozero(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,c_Groups_Ozero__class_Ozero(X2),X1) )
| ~ sP5(X2,X0,X1) ) ),
inference(flattening,[],[f3797]) ).
fof(f3797,plain,
! [X2,X0,X1] :
( ( sP5(X2,X0,X1)
| ( ( ~ 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)) )
& ( ~ 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,X0,c_Groups_Ozero__class_Ozero(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,c_Groups_Ozero__class_Ozero(X2),X1) )
| ~ sP5(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f3581]) ).
fof(f3581,plain,
! [X2,X0,X1] :
( sP5(X2,X0,X1)
<=> ( ( 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)) )
| ( 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) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f12641,plain,
spl107_767,
inference(avatar_split_clause,[],[f4953,f12639]) ).
fof(f12639,plain,
( spl107_767
<=> ! [X2,X0,X1] :
( sP5(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_767])]) ).
fof(f4953,plain,
! [X2,X0,X1] :
( sP5(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X2) ),
inference(cnf_transformation,[],[f3799]) ).
fof(f12637,plain,
spl107_766,
inference(avatar_split_clause,[],[f4952,f12635]) ).
fof(f12635,plain,
( spl107_766
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_766])]) ).
fof(f4952,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f3799]) ).
fof(f12633,plain,
spl107_765,
inference(avatar_split_clause,[],[f4951,f12631]) ).
fof(f12631,plain,
( spl107_765
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_765])]) ).
fof(f4951,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f3799]) ).
fof(f12629,plain,
spl107_764,
inference(avatar_split_clause,[],[f4950,f12627]) ).
fof(f12627,plain,
( spl107_764
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_764])]) ).
fof(f4950,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f3799]) ).
fof(f12625,plain,
spl107_763,
inference(avatar_split_clause,[],[f4949,f12623]) ).
fof(f12623,plain,
( spl107_763
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_763])]) ).
fof(f4949,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f3799]) ).
fof(f12621,plain,
spl107_762,
inference(avatar_split_clause,[],[f4945,f12619]) ).
fof(f12619,plain,
( spl107_762
<=> ! [X2,X0,X1] :
( sP3(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,[spl107_762])]) ).
fof(f4945,plain,
! [X2,X0,X1] :
( sP3(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,[],[f3794]) ).
fof(f3794,plain,
! [X0,X1,X2] :
( ( sP3(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) )
| ~ sP3(X0,X1,X2) ) ),
inference(rectify,[],[f3793]) ).
fof(f3793,plain,
! [X0,X2,X1] :
( ( sP3(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) )
| ~ sP3(X0,X2,X1) ) ),
inference(flattening,[],[f3792]) ).
fof(f3792,plain,
! [X0,X2,X1] :
( ( sP3(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) )
| ~ sP3(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f3578]) ).
fof(f3578,plain,
! [X0,X2,X1] :
( sP3(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,[sP3])]) ).
fof(f12617,plain,
spl107_761,
inference(avatar_split_clause,[],[f4944,f12615]) ).
fof(f12615,plain,
( spl107_761
<=> ! [X2,X0,X1] :
( sP3(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,[spl107_761])]) ).
fof(f4944,plain,
! [X2,X0,X1] :
( sP3(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,[],[f3794]) ).
fof(f12613,plain,
spl107_760,
inference(avatar_split_clause,[],[f4943,f12611]) ).
fof(f12611,plain,
( spl107_760
<=> ! [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))
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_760])]) ).
fof(f4943,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))
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f3794]) ).
fof(f12609,plain,
spl107_759,
inference(avatar_split_clause,[],[f4942,f12607]) ).
fof(f12607,plain,
( spl107_759
<=> ! [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)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_759])]) ).
fof(f4942,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)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f3794]) ).
fof(f12605,plain,
spl107_758,
inference(avatar_split_clause,[],[f4941,f12603]) ).
fof(f12603,plain,
( spl107_758
<=> ! [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))
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_758])]) ).
fof(f4941,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))
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f3794]) ).
fof(f12601,plain,
spl107_757,
inference(avatar_split_clause,[],[f4940,f12599]) ).
fof(f12599,plain,
( spl107_757
<=> ! [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)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_757])]) ).
fof(f4940,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)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f3794]) ).
fof(f12597,plain,
spl107_756,
inference(avatar_split_clause,[],[f4936,f12595]) ).
fof(f12595,plain,
( spl107_756
<=> ! [X2,X0,X1] :
( sP1(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,[spl107_756])]) ).
fof(f4936,plain,
! [X2,X0,X1] :
( sP1(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,[],[f3789]) ).
fof(f3789,plain,
! [X0,X1,X2] :
( ( sP1(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) )
| ~ sP1(X0,X1,X2) ) ),
inference(rectify,[],[f3788]) ).
fof(f3788,plain,
! [X2,X0,X1] :
( ( sP1(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) )
| ~ sP1(X2,X0,X1) ) ),
inference(flattening,[],[f3787]) ).
fof(f3787,plain,
! [X2,X0,X1] :
( ( sP1(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) )
| ~ sP1(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f3575]) ).
fof(f3575,plain,
! [X2,X0,X1] :
( sP1(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,[sP1])]) ).
fof(f12593,plain,
spl107_755,
inference(avatar_split_clause,[],[f4935,f12591]) ).
fof(f12591,plain,
( spl107_755
<=> ! [X2,X0,X1] :
( sP1(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,[spl107_755])]) ).
fof(f4935,plain,
! [X2,X0,X1] :
( sP1(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,[],[f3789]) ).
fof(f12589,plain,
spl107_754,
inference(avatar_split_clause,[],[f4934,f12587]) ).
fof(f12587,plain,
( spl107_754
<=> ! [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)
| ~ sP1(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_754])]) ).
fof(f4934,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)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f3789]) ).
fof(f12585,plain,
spl107_753,
inference(avatar_split_clause,[],[f4933,f12583]) ).
fof(f12583,plain,
( spl107_753
<=> ! [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)
| ~ sP1(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_753])]) ).
fof(f4933,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)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f3789]) ).
fof(f12581,plain,
spl107_752,
inference(avatar_split_clause,[],[f4932,f12579]) ).
fof(f12579,plain,
( spl107_752
<=> ! [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)
| ~ sP1(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_752])]) ).
fof(f4932,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)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f3789]) ).
fof(f12577,plain,
spl107_751,
inference(avatar_split_clause,[],[f4931,f12575]) ).
fof(f12575,plain,
( spl107_751
<=> ! [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)
| ~ sP1(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_751])]) ).
fof(f4931,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)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f3789]) ).
fof(f12573,plain,
spl107_750,
inference(avatar_split_clause,[],[f4927,f12571]) ).
fof(f12571,plain,
( spl107_750
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,sK74(X0,X1,X2),c_Groups_Oone__class_Oone(X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_750])]) ).
fof(f4927,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,sK74(X0,X1,X2),c_Groups_Oone__class_Oone(X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(cnf_transformation,[],[f3784]) ).
fof(f3784,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ( ~ c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),sK74(X0,X1,X2)),X1),X0)
& c_Orderings_Oord__class_Oless(X2,sK74(X0,X1,X2),c_Groups_Oone__class_Oone(X2))
& c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),sK74(X0,X1,X2)) )
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK74])],[f2667,f3783]) ).
fof(f3783,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1),X0)
& c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Oone__class_Oone(X2))
& c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) )
=> ( ~ c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),sK74(X0,X1,X2)),X1),X0)
& c_Orderings_Oord__class_Oless(X2,sK74(X0,X1,X2),c_Groups_Oone__class_Oone(X2))
& c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),sK74(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f2667,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ? [X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1),X0)
& c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Oone__class_Oone(X2))
& c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) )
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(flattening,[],[f2666]) ).
fof(f2666,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ? [X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1),X0)
& c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Oone__class_Oone(X2))
& c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) )
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(ennf_transformation,[],[f1725]) ).
fof(f1725,plain,
! [X0,X1,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( ! [X3] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
=> ( c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Oone__class_Oone(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1),X0) ) )
=> c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ),
inference(rectify,[],[f720]) ).
fof(f720,axiom,
! [X21,X6,X3] :
( class_Fields_Olinordered__field__inverse__zero(X3)
=> ( ! [X55] :
( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X55)
=> ( c_Orderings_Oord__class_Oless(X3,X55,c_Groups_Oone__class_Oone(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X55),X6),X21) ) )
=> c_Orderings_Oord__class_Oless__eq(X3,X6,X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12569,plain,
spl107_749,
inference(avatar_split_clause,[],[f4926,f12567]) ).
fof(f12567,plain,
( spl107_749
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),sK74(X0,X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_749])]) ).
fof(f4926,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),sK74(X0,X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(cnf_transformation,[],[f3784]) ).
fof(f12565,plain,
( ~ spl107_747
| spl107_748
| ~ spl107_654
| ~ spl107_738 ),
inference(avatar_split_clause,[],[f12522,f12174,f10485,f12562,f12558]) ).
fof(f12558,plain,
( spl107_747
<=> class_Groups_Ogroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_747])]) ).
fof(f10485,plain,
( spl107_654
<=> ! [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,[spl107_654])]) ).
fof(f12522,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))
| ~ class_Groups_Ogroup__add(tc_Nat_Onat)
| ~ spl107_654
| ~ spl107_738 ),
inference(trivial_inequality_removal,[],[f12521]) ).
fof(f12521,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))
| ~ class_Groups_Ogroup__add(tc_Nat_Onat)
| ~ spl107_654
| ~ spl107_738 ),
inference(superposition,[],[f10486,f12176]) ).
fof(f10486,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) )
| ~ spl107_654 ),
inference(avatar_component_clause,[],[f10485]) ).
fof(f12556,plain,
spl107_746,
inference(avatar_split_clause,[],[f4799,f12554]) ).
fof(f12554,plain,
( spl107_746
<=> ! [X0,X1] :
( X0 = X1
| hAPP(X1,sK67(X0,X1)) != hAPP(X0,sK67(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_746])]) ).
fof(f4799,plain,
! [X0,X1] :
( X0 = X1
| hAPP(X1,sK67(X0,X1)) != hAPP(X0,sK67(X0,X1)) ),
inference(cnf_transformation,[],[f3715]) ).
fof(f3715,plain,
! [X0,X1] :
( X0 = X1
| hAPP(X1,sK67(X0,X1)) != hAPP(X0,sK67(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67])],[f2658,f3714]) ).
fof(f3714,plain,
! [X0,X1] :
( ? [X2] : hAPP(X1,X2) != hAPP(X0,X2)
=> hAPP(X1,sK67(X0,X1)) != hAPP(X0,sK67(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f2658,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/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12552,plain,
spl107_745,
inference(avatar_split_clause,[],[f4765,f12550]) ).
fof(f12550,plain,
( spl107_745
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ 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,[spl107_745])]) ).
fof(f4765,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ 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,[],[f2611]) ).
fof(f2611,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ 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,[],[f2610]) ).
fof(f2610,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ 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,[],[f1629]) ).
fof(f1629,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
=> ( 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,[],[f869]) ).
fof(f869,axiom,
! [X42,X41] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X41)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X42,X41)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X42) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12548,plain,
spl107_744,
inference(avatar_split_clause,[],[f4595,f12546]) ).
fof(f12546,plain,
( spl107_744
<=> ! [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,[spl107_744])]) ).
fof(f4595,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,[],[f2437]) ).
fof(f2437,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,[],[f1485]) ).
fof(f1485,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,[],[f641]) ).
fof(f641,axiom,
! [X21,X3] :
( class_Fields_Ofield(X3)
=> c_Polynomial_Opdivmod__rel(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X21,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12544,plain,
spl107_743,
inference(avatar_split_clause,[],[f4535,f12542]) ).
fof(f12542,plain,
( spl107_743
<=> ! [X0,X1] : c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(X1)),c_Complex_Oexpi(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_743])]) ).
fof(f4535,plain,
! [X0,X1] : c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(X1)),c_Complex_Oexpi(X0)),
inference(cnf_transformation,[],[f1436]) ).
fof(f1436,plain,
! [X0,X1] : c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(X1)),c_Complex_Oexpi(X0)),
inference(rectify,[],[f788]) ).
fof(f788,axiom,
! [X4,X5] : c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X5,X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(X5)),c_Complex_Oexpi(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12540,plain,
spl107_742,
inference(avatar_split_clause,[],[f4518,f12538]) ).
fof(f12538,plain,
( spl107_742
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_742])]) ).
fof(f4518,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0)) ),
inference(cnf_transformation,[],[f3670]) ).
fof(f3670,plain,
! [X0] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0)) ) ),
inference(nnf_transformation,[],[f1420]) ).
fof(f1420,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0))
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 ),
inference(rectify,[],[f399]) ).
fof(f399,axiom,
! [X16] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X16),X16))
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12536,plain,
spl107_741,
inference(avatar_split_clause,[],[f4409,f12534]) ).
fof(f12534,plain,
( spl107_741
<=> ! [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,[spl107_741])]) ).
fof(f4409,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,[],[f1324]) ).
fof(f1324,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,[],[f542]) ).
fof(f542,axiom,
! [X42] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X42))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12532,plain,
spl107_740,
inference(avatar_split_clause,[],[f4408,f12530]) ).
fof(f12530,plain,
( spl107_740
<=> ! [X0] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,v_z)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_740])]) ).
fof(f4408,plain,
! [X0] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,v_z)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0),
inference(cnf_transformation,[],[f1323]) ).
fof(f1323,plain,
! [X0] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,v_z)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0),
inference(rectify,[],[f449]) ).
fof(f449,axiom,
! [X56] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X56,v_z)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X56),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12528,plain,
spl107_739,
inference(avatar_split_clause,[],[f4368,f12526]) ).
fof(f12526,plain,
( spl107_739
<=> ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK53),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_739])]) ).
fof(f4368,plain,
! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK53),X1),
inference(cnf_transformation,[],[f3654]) ).
fof(f3654,plain,
( ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK53),X1)
& c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Polynomial_Odegree(tc_Complex_Ocomplex,sK53) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53])],[f2319,f3653]) ).
fof(f3653,plain,
( ? [X0] :
( ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,X1))
& c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Polynomial_Odegree(tc_Complex_Ocomplex,X0) )
=> ( ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK53),X1)
& c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Polynomial_Odegree(tc_Complex_Ocomplex,sK53) ) ),
introduced(choice_axiom,[]) ).
fof(f2319,plain,
? [X0] :
( ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,X1))
& c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Polynomial_Odegree(tc_Complex_Ocomplex,X0) ),
inference(ennf_transformation,[],[f1283]) ).
fof(f1283,plain,
~ ! [X0] :
( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Polynomial_Odegree(tc_Complex_Ocomplex,X0)
=> ~ ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,X1)) ),
inference(rectify,[],[f475]) ).
fof(f475,axiom,
~ ! [X61] :
( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Polynomial_Odegree(tc_Complex_Ocomplex,X61)
=> ~ ! [X2] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X61),X2) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f12177,plain,
( spl107_738
| ~ spl107_539
| ~ spl107_709 ),
inference(avatar_split_clause,[],[f11458,f11409,f9249,f12174]) ).
fof(f9249,plain,
( spl107_539
<=> ! [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,[spl107_539])]) ).
fof(f11458,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))))
| ~ spl107_539
| ~ spl107_709 ),
inference(resolution,[],[f11411,f9250]) ).
fof(f9250,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) )
| ~ spl107_539 ),
inference(avatar_component_clause,[],[f9249]) ).
fof(f11740,plain,
( spl107_737
| ~ spl107_388
| ~ spl107_685 ),
inference(avatar_split_clause,[],[f11259,f11188,f8003,f11738]) ).
fof(f11738,plain,
( spl107_737
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_737])]) ).
fof(f11188,plain,
( spl107_685
<=> ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_685])]) ).
fof(f11259,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))) )
| ~ spl107_388
| ~ spl107_685 ),
inference(resolution,[],[f11189,f8004]) ).
fof(f11189,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) )
| ~ spl107_685 ),
inference(avatar_component_clause,[],[f11188]) ).
fof(f11539,plain,
spl107_736,
inference(avatar_split_clause,[],[f6122,f11537]) ).
fof(f11537,plain,
( spl107_736
<=> ! [X4,X0,X1,X3] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X3
| ~ sP49(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_736])]) ).
fof(f6122,plain,
! [X3,X0,X1,X4] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X3
| ~ sP49(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X3,X4) ),
inference(equality_resolution,[],[f5831]) ).
fof(f5831,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
| ~ sP49(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f4082]) ).
fof(f4082,plain,
! [X0,X1,X2,X3,X4] :
( ( sP49(X0,X1,X2,X3,X4)
| ~ sP48(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 )
& ( ( sP48(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 )
| ~ sP49(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f4081]) ).
fof(f4081,plain,
! [X0,X4,X2,X1,X3] :
( ( sP49(X0,X4,X2,X1,X3)
| ~ sP48(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 )
& ( ( sP48(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 )
| ~ sP49(X0,X4,X2,X1,X3) ) ),
inference(flattening,[],[f4080]) ).
fof(f4080,plain,
! [X0,X4,X2,X1,X3] :
( ( sP49(X0,X4,X2,X1,X3)
| ~ sP48(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 )
& ( ( sP48(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 )
| ~ sP49(X0,X4,X2,X1,X3) ) ),
inference(nnf_transformation,[],[f3646]) ).
fof(f3646,plain,
! [X0,X4,X2,X1,X3] :
( sP49(X0,X4,X2,X1,X3)
<=> ( sP48(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,[sP49])]) ).
fof(f11534,plain,
spl107_735,
inference(avatar_split_clause,[],[f6050,f11532]) ).
fof(f11532,plain,
( spl107_735
<=> ! [X2,X1] :
( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_735])]) ).
fof(f6050,plain,
! [X2,X1] :
( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(equality_resolution,[],[f5361]) ).
fof(f5361,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f3919]) ).
fof(f11523,plain,
( spl107_734
| ~ spl107_182
| ~ spl107_621
| ~ spl107_733 ),
inference(avatar_split_clause,[],[f11518,f11515,f10351,f7081,f11520]) ).
fof(f11520,plain,
( spl107_734
<=> 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,[spl107_734])]) ).
fof(f7081,plain,
( spl107_182
<=> class_Power_Opower(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_182])]) ).
fof(f10351,plain,
( spl107_621
<=> ! [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,[spl107_621])]) ).
fof(f11515,plain,
( spl107_733
<=> ! [X1] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_733])]) ).
fof(f11518,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))
| ~ spl107_182
| ~ spl107_621
| ~ spl107_733 ),
inference(forward_demodulation,[],[f11516,f10812]) ).
fof(f10812,plain,
( ! [X0] : c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl107_182
| ~ spl107_621 ),
inference(resolution,[],[f10352,f7083]) ).
fof(f7083,plain,
( class_Power_Opower(tc_Int_Oint)
| ~ spl107_182 ),
inference(avatar_component_clause,[],[f7081]) ).
fof(f10352,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)) )
| ~ spl107_621 ),
inference(avatar_component_clause,[],[f10351]) ).
fof(f11516,plain,
( ! [X1] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ spl107_733 ),
inference(avatar_component_clause,[],[f11515]) ).
fof(f11517,plain,
spl107_733,
inference(avatar_split_clause,[],[f5990,f11515]) ).
fof(f5990,plain,
! [X1] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f4881]) ).
fof(f4881,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f3774]) ).
fof(f3774,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X0))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| 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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X0)) ) ),
inference(flattening,[],[f3773]) ).
fof(f3773,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X0))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| 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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X0)) ) ),
inference(nnf_transformation,[],[f1687]) ).
fof(f1687,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X0))
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1 ) ),
inference(rectify,[],[f896]) ).
fof(f896,axiom,
! [X65,X16] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X16)),X65))
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X65
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11513,plain,
spl107_732,
inference(avatar_split_clause,[],[f5627,f11511]) ).
fof(f11511,plain,
( spl107_732
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ sP46(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_732])]) ).
fof(f5627,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ sP46(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4047]) ).
fof(f11509,plain,
spl107_731,
inference(avatar_split_clause,[],[f5618,f11507]) ).
fof(f11507,plain,
( spl107_731
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ sP44(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_731])]) ).
fof(f5618,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ sP44(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4042]) ).
fof(f11505,plain,
( ~ spl107_208
| ~ spl107_730
| ~ spl107_495
| ~ spl107_709 ),
inference(avatar_split_clause,[],[f11459,f11409,f8641,f11502,f7211]) ).
fof(f7211,plain,
( spl107_208
<=> class_Orderings_Opreorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_208])]) ).
fof(f11502,plain,
( spl107_730
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_730])]) ).
fof(f11459,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ spl107_495
| ~ spl107_709 ),
inference(resolution,[],[f11411,f8642]) ).
fof(f11500,plain,
spl107_729,
inference(avatar_split_clause,[],[f5596,f11498]) ).
fof(f11498,plain,
( spl107_729
<=> ! [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,[spl107_729])]) ).
fof(f5596,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,[],[f4031]) ).
fof(f11496,plain,
spl107_728,
inference(avatar_split_clause,[],[f5401,f11494]) ).
fof(f11494,plain,
( spl107_728
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ sP27(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_728])]) ).
fof(f5401,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)
| ~ sP27(X0,X1,X2) ),
inference(cnf_transformation,[],[f3950]) ).
fof(f11492,plain,
spl107_727,
inference(avatar_split_clause,[],[f5393,f11490]) ).
fof(f11490,plain,
( spl107_727
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ sP26(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_727])]) ).
fof(f5393,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)
| ~ sP26(X0,X1,X2) ),
inference(cnf_transformation,[],[f3944]) ).
fof(f11488,plain,
spl107_726,
inference(avatar_split_clause,[],[f5183,f11486]) ).
fof(f11486,plain,
( spl107_726
<=> ! [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,[spl107_726])]) ).
fof(f5183,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,[],[f2929]) ).
fof(f2929,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,[],[f2928]) ).
fof(f2928,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,[],[f1892]) ).
fof(f1892,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,[],[f68]) ).
fof(f68,axiom,
! [X21,X6,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X6,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X21,X6)
=> X6 = X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11484,plain,
spl107_725,
inference(avatar_split_clause,[],[f5178,f11482]) ).
fof(f11482,plain,
( spl107_725
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| X0 = X1
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_725])]) ).
fof(f5178,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| X0 = X1
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f2919]) ).
fof(f2919,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| X0 = X1
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f2918]) ).
fof(f2918,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| X0 = X1
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f1887]) ).
fof(f1887,plain,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( X0 != X1
=> ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
=> c_Orderings_Oord__class_Oless(X2,X0,X1) ) ) ),
inference(rectify,[],[f49]) ).
fof(f49,axiom,
! [X4,X5,X3] :
( class_Orderings_Oorder(X3)
=> ( X4 != X5
=> ( c_Orderings_Oord__class_Oless__eq(X3,X4,X5)
=> c_Orderings_Oord__class_Oless(X3,X4,X5) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11480,plain,
spl107_724,
inference(avatar_split_clause,[],[f5116,f11478]) ).
fof(f11478,plain,
( spl107_724
<=> ! [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,[spl107_724])]) ).
fof(f5116,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,[],[f3836]) ).
fof(f3836,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,[],[f2842]) ).
fof(f2842,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,[],[f2841]) ).
fof(f2841,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,[],[f1839]) ).
fof(f1839,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,[],[f51]) ).
fof(f51,axiom,
! [X20,X16,X3] :
( class_Orderings_Olinorder(X3)
=> ( ~ c_Orderings_Oord__class_Oless(X3,X16,X20)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X16,X20)
<=> X16 = X20 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11476,plain,
spl107_723,
inference(avatar_split_clause,[],[f5108,f11474]) ).
fof(f11474,plain,
( spl107_723
<=> ! [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,[spl107_723])]) ).
fof(f5108,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,[],[f2828]) ).
fof(f2828,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,[],[f2827]) ).
fof(f2827,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,[],[f1832]) ).
fof(f1832,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,[],[f21]) ).
fof(f21,axiom,
! [X21,X6,X3] :
( class_Orderings_Olinorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X21,X6)
| X6 = X21
| c_Orderings_Oord__class_Oless(X3,X6,X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11472,plain,
spl107_722,
inference(avatar_split_clause,[],[f5072,f11470]) ).
fof(f11470,plain,
( spl107_722
<=> ! [X2,X0,X1] :
( 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,[spl107_722])]) ).
fof(f5072,plain,
! [X2,X0,X1] :
( 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,[],[f3826]) ).
fof(f3826,plain,
! [X0,X1,X2] :
( ( ( 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)
| ~ c_Rings_Odvd__class_Odvd(X2,X1,X0) ) )
| ~ class_Divides_Osemiring__div(X2) ),
inference(nnf_transformation,[],[f2780]) ).
fof(f2780,plain,
! [X0,X1,X2] :
( ( 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,[],[f1805]) ).
fof(f1805,plain,
! [X0,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> ( c_Rings_Odvd__class_Odvd(X2,X1,X0)
<=> c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,X0,X1) ) ),
inference(rectify,[],[f805]) ).
fof(f805,axiom,
! [X9,X10,X3] :
( class_Divides_Osemiring__div(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X10,X9)
<=> c_Groups_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(X3,X9,X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11468,plain,
spl107_721,
inference(avatar_split_clause,[],[f5068,f11466]) ).
fof(f11466,plain,
( spl107_721
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,X0,X1)
| ~ c_Rings_Odvd__class_Odvd(X2,X1,X0)
| ~ class_Divides_Osemiring__div(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_721])]) ).
fof(f5068,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,X0,X1)
| ~ c_Rings_Odvd__class_Odvd(X2,X1,X0)
| ~ class_Divides_Osemiring__div(X2) ),
inference(cnf_transformation,[],[f2775]) ).
fof(f2775,plain,
! [X0,X1,X2] :
( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,X0,X1)
| ~ c_Rings_Odvd__class_Odvd(X2,X1,X0)
| ~ class_Divides_Osemiring__div(X2) ),
inference(flattening,[],[f2774]) ).
fof(f2774,plain,
! [X0,X1,X2] :
( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,X0,X1)
| ~ c_Rings_Odvd__class_Odvd(X2,X1,X0)
| ~ class_Divides_Osemiring__div(X2) ),
inference(ennf_transformation,[],[f1802]) ).
fof(f1802,plain,
! [X0,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> ( c_Rings_Odvd__class_Odvd(X2,X1,X0)
=> c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,X0,X1) ) ),
inference(rectify,[],[f804]) ).
fof(f804,axiom,
! [X4,X5,X3] :
( class_Divides_Osemiring__div(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X5,X4)
=> c_Groups_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(X3,X4,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11464,plain,
spl107_720,
inference(avatar_split_clause,[],[f5050,f11462]) ).
fof(f11462,plain,
( spl107_720
<=> ! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(X2,X1,X0)
| c_Groups_Oabs__class_Oabs(X2,X1) != c_Groups_Oabs__class_Oabs(X2,X0)
| ~ class_Rings_Olinordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_720])]) ).
fof(f5050,plain,
! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(X2,X1,X0)
| c_Groups_Oabs__class_Oabs(X2,X1) != c_Groups_Oabs__class_Oabs(X2,X0)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(cnf_transformation,[],[f2754]) ).
fof(f2754,plain,
! [X0,X1,X2] :
( c_Rings_Odvd__class_Odvd(X2,X1,X0)
| c_Groups_Oabs__class_Oabs(X2,X1) != c_Groups_Oabs__class_Oabs(X2,X0)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(flattening,[],[f2753]) ).
fof(f2753,plain,
! [X0,X1,X2] :
( c_Rings_Odvd__class_Odvd(X2,X1,X0)
| c_Groups_Oabs__class_Oabs(X2,X1) != c_Groups_Oabs__class_Oabs(X2,X0)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(ennf_transformation,[],[f1786]) ).
fof(f1786,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Groups_Oabs__class_Oabs(X2,X1) = c_Groups_Oabs__class_Oabs(X2,X0)
=> c_Rings_Odvd__class_Odvd(X2,X1,X0) ) ),
inference(rectify,[],[f810]) ).
fof(f810,axiom,
! [X13,X72,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Groups_Oabs__class_Oabs(X3,X72) = c_Groups_Oabs__class_Oabs(X3,X13)
=> c_Rings_Odvd__class_Odvd(X3,X72,X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11452,plain,
spl107_719,
inference(avatar_split_clause,[],[f5046,f11450]) ).
fof(f11450,plain,
( spl107_719
<=> ! [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,[spl107_719])]) ).
fof(f5046,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,[],[f2746]) ).
fof(f2746,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,[],[f2745]) ).
fof(f2745,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,[],[f1782]) ).
fof(f1782,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,[],[f85]) ).
fof(f85,axiom,
! [X21,X6,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( X6 != X21
=> ( ~ c_Orderings_Oord__class_Oless(X3,X6,X21)
=> c_Orderings_Oord__class_Oless(X3,X21,X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11448,plain,
spl107_718,
inference(avatar_split_clause,[],[f4923,f11446]) ).
fof(f11446,plain,
( spl107_718
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,sK73(X0,X1,X2),X0)
| ~ class_Orderings_Odense__linorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_718])]) ).
fof(f4923,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,sK73(X0,X1,X2),X0)
| ~ class_Orderings_Odense__linorder(X2) ),
inference(cnf_transformation,[],[f3782]) ).
fof(f3782,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ( ~ c_Orderings_Oord__class_Oless__eq(X2,sK73(X0,X1,X2),X0)
& c_Orderings_Oord__class_Oless(X2,sK73(X0,X1,X2),X1) )
| ~ class_Orderings_Odense__linorder(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK73])],[f2662,f3781]) ).
fof(f3781,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X2,X3,X0)
& c_Orderings_Oord__class_Oless(X2,X3,X1) )
=> ( ~ c_Orderings_Oord__class_Oless__eq(X2,sK73(X0,X1,X2),X0)
& c_Orderings_Oord__class_Oless(X2,sK73(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f2662,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ? [X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X2,X3,X0)
& c_Orderings_Oord__class_Oless(X2,X3,X1) )
| ~ class_Orderings_Odense__linorder(X2) ),
inference(flattening,[],[f2661]) ).
fof(f2661,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ? [X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X2,X3,X0)
& c_Orderings_Oord__class_Oless(X2,X3,X1) )
| ~ class_Orderings_Odense__linorder(X2) ),
inference(ennf_transformation,[],[f1722]) ).
fof(f1722,plain,
! [X0,X1,X2] :
( class_Orderings_Odense__linorder(X2)
=> ( ! [X3] :
( c_Orderings_Oord__class_Oless(X2,X3,X1)
=> c_Orderings_Oord__class_Oless__eq(X2,X3,X0) )
=> c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ),
inference(rectify,[],[f88]) ).
fof(f88,axiom,
! [X12,X21,X3] :
( class_Orderings_Odense__linorder(X3)
=> ( ! [X2] :
( c_Orderings_Oord__class_Oless(X3,X2,X21)
=> c_Orderings_Oord__class_Oless__eq(X3,X2,X12) )
=> c_Orderings_Oord__class_Oless__eq(X3,X21,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11444,plain,
spl107_717,
inference(avatar_split_clause,[],[f4922,f11442]) ).
fof(f11442,plain,
( spl107_717
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,sK73(X0,X1,X2),X1)
| ~ class_Orderings_Odense__linorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_717])]) ).
fof(f4922,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,sK73(X0,X1,X2),X1)
| ~ class_Orderings_Odense__linorder(X2) ),
inference(cnf_transformation,[],[f3782]) ).
fof(f11440,plain,
spl107_716,
inference(avatar_split_clause,[],[f4865,f11438]) ).
fof(f11438,plain,
( spl107_716
<=> ! [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,[spl107_716])]) ).
fof(f4865,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,[],[f3764]) ).
fof(f3764,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,[],[f3763]) ).
fof(f3763,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,[],[f1682]) ).
fof(f1682,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,[],[f492]) ).
fof(f492,axiom,
! [X65,X66] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X66),X65)
<=> ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X65
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = X66 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11436,plain,
spl107_715,
inference(avatar_split_clause,[],[f4864,f11434]) ).
fof(f11434,plain,
( spl107_715
<=> ! [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,[spl107_715])]) ).
fof(f4864,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,[],[f3764]) ).
fof(f11432,plain,
spl107_714,
inference(avatar_split_clause,[],[f4852,f11430]) ).
fof(f11430,plain,
( spl107_714
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_714])]) ).
fof(f4852,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(cnf_transformation,[],[f3756]) ).
fof(f3756,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) )
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
| ~ sP0(X0,X1) ) ),
inference(flattening,[],[f3755]) ).
fof(f3755,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) )
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f3573]) ).
fof(f3573,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f11428,plain,
spl107_713,
inference(avatar_split_clause,[],[f4851,f11426]) ).
fof(f11426,plain,
( spl107_713
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_713])]) ).
fof(f4851,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(cnf_transformation,[],[f3756]) ).
fof(f11424,plain,
spl107_712,
inference(avatar_split_clause,[],[f4850,f11422]) ).
fof(f11422,plain,
( spl107_712
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_712])]) ).
fof(f4850,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(cnf_transformation,[],[f3756]) ).
fof(f11420,plain,
spl107_711,
inference(avatar_split_clause,[],[f4849,f11418]) ).
fof(f11418,plain,
( spl107_711
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_711])]) ).
fof(f4849,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(cnf_transformation,[],[f3756]) ).
fof(f11416,plain,
spl107_710,
inference(avatar_split_clause,[],[f4848,f11414]) ).
fof(f11414,plain,
( spl107_710
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_710])]) ).
fof(f4848,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f3756]) ).
fof(f11412,plain,
( spl107_709
| ~ spl107_309
| ~ spl107_543
| ~ spl107_688 ),
inference(avatar_split_clause,[],[f11367,f11317,f9265,f7645,f11409]) ).
fof(f7645,plain,
( spl107_309
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_309])]) ).
fof(f9265,plain,
( spl107_543
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_543])]) ).
fof(f11367,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))))
| ~ spl107_309
| ~ spl107_543
| ~ spl107_688 ),
inference(forward_demodulation,[],[f11361,f7647]) ).
fof(f7647,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl107_309 ),
inference(avatar_component_clause,[],[f7645]) ).
fof(f11361,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))))
| ~ spl107_543
| ~ spl107_688 ),
inference(resolution,[],[f11319,f9266]) ).
fof(f9266,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X0) )
| ~ spl107_543 ),
inference(avatar_component_clause,[],[f9265]) ).
fof(f11407,plain,
spl107_708,
inference(avatar_split_clause,[],[f4847,f11405]) ).
fof(f11405,plain,
( spl107_708
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_708])]) ).
fof(f4847,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f3756]) ).
fof(f11403,plain,
spl107_707,
inference(avatar_split_clause,[],[f4767,f11401]) ).
fof(f11401,plain,
( spl107_707
<=> ! [X0,X1] :
( ~ 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,[spl107_707])]) ).
fof(f4767,plain,
! [X0,X1] :
( ~ 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,[],[f2615]) ).
fof(f2615,plain,
! [X0,X1] :
( ~ 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,[],[f2614]) ).
fof(f2614,plain,
! [X0,X1] :
( ~ 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,[],[f1631]) ).
fof(f1631,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)
=> ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1) ) ),
inference(rectify,[],[f857]) ).
fof(f857,axiom,
! [X41,X42] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X42)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X41)
=> ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X41,X42) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11399,plain,
spl107_706,
inference(avatar_split_clause,[],[f4757,f11397]) ).
fof(f11397,plain,
( spl107_706
<=> ! [X0,X1] :
( ~ 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,[spl107_706])]) ).
fof(f4757,plain,
! [X0,X1] :
( ~ 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,[],[f2600]) ).
fof(f2600,plain,
! [X0,X1] :
( ~ 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,[],[f2599]) ).
fof(f2599,plain,
! [X0,X1] :
( ~ 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,[],[f1621]) ).
fof(f1621,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)
=> ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X1) ) ),
inference(rectify,[],[f952]) ).
fof(f952,axiom,
! [X41,X42] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X42)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X42,X41)
=> ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X41,X42) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11395,plain,
spl107_705,
inference(avatar_split_clause,[],[f4754,f11393]) ).
fof(f11393,plain,
( spl107_705
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_705])]) ).
fof(f4754,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(cnf_transformation,[],[f2597]) ).
fof(f2597,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(ennf_transformation,[],[f1619]) ).
fof(f1619,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__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1)) ),
inference(rectify,[],[f985]) ).
fof(f985,axiom,
! [X5,X4] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11391,plain,
spl107_704,
inference(avatar_split_clause,[],[f4750,f11389]) ).
fof(f11389,plain,
( spl107_704
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_704])]) ).
fof(f4750,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f2594]) ).
fof(f2594,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(ennf_transformation,[],[f1616]) ).
fof(f1616,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(rectify,[],[f992]) ).
fof(f992,axiom,
! [X5,X4] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11387,plain,
spl107_703,
inference(avatar_split_clause,[],[f4717,f11385]) ).
fof(f11385,plain,
( spl107_703
<=> ! [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,[spl107_703])]) ).
fof(f4717,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,[],[f2555]) ).
fof(f2555,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,[],[f1587]) ).
fof(f1587,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,[],[f595]) ).
fof(f595,axiom,
! [X42,X41] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,X42)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X42,X41)) = X42 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11383,plain,
spl107_702,
inference(avatar_split_clause,[],[f4716,f11381]) ).
fof(f11381,plain,
( spl107_702
<=> ! [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,[spl107_702])]) ).
fof(f4716,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,[],[f2554]) ).
fof(f2554,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,[],[f1586]) ).
fof(f1586,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,[],[f535]) ).
fof(f535,axiom,
! [X41,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X41)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X41,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X41,X15)) = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11379,plain,
spl107_701,
inference(avatar_split_clause,[],[f4708,f11377]) ).
fof(f11377,plain,
( spl107_701
<=> ! [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)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_701])]) ).
fof(f4708,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)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2546]) ).
fof(f2546,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)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) ),
inference(flattening,[],[f2545]) ).
fof(f2545,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)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1579]) ).
fof(f1579,plain,
! [X0,X1] :
( 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,[],[f860]) ).
fof(f860,axiom,
! [X41,X13] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X13,X41)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X41)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,X41) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11375,plain,
spl107_700,
inference(avatar_split_clause,[],[f4701,f11373]) ).
fof(f11373,plain,
( spl107_700
<=> ! [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)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_700])]) ).
fof(f4701,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)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f2536]) ).
fof(f2536,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)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ),
inference(flattening,[],[f2535]) ).
fof(f2535,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)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X0) ),
inference(ennf_transformation,[],[f1574]) ).
fof(f1574,plain,
! [X0,X1] :
( 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,[],[f953]) ).
fof(f953,axiom,
! [X41,X12] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X12,X41)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X41)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X12,X41) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11371,plain,
spl107_699,
inference(avatar_split_clause,[],[f4696,f11369]) ).
fof(f11369,plain,
( spl107_699
<=> ! [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,[spl107_699])]) ).
fof(f4696,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,[],[f2529]) ).
fof(f2529,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,[],[f1569]) ).
fof(f1569,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,[],[f571]) ).
fof(f571,axiom,
! [X41,X42] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X41)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X42,X41)) = X42 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11360,plain,
spl107_698,
inference(avatar_split_clause,[],[f4684,f11358]) ).
fof(f11358,plain,
( spl107_698
<=> ! [X0,X1] :
( c_SEQ_Odecseq(X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK63(X0,X1),sK64(X0,X1))
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_698])]) ).
fof(f4684,plain,
! [X0,X1] :
( c_SEQ_Odecseq(X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK63(X0,X1),sK64(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(cnf_transformation,[],[f3702]) ).
fof(f3702,plain,
! [X0,X1] :
( ( ( c_SEQ_Odecseq(X1,X0)
| ( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,sK64(X0,X1)),hAPP(X0,sK63(X0,X1)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK63(X0,X1),sK64(X0,X1)) ) )
& ( ! [X4,X5] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X5),hAPP(X0,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5) )
| ~ c_SEQ_Odecseq(X1,X0) ) )
| ~ class_Orderings_Oorder(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK63,sK64])],[f3700,f3701]) ).
fof(f3701,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
=> ( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,sK64(X0,X1)),hAPP(X0,sK63(X0,X1)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK63(X0,X1),sK64(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3700,plain,
! [X0,X1] :
( ( ( c_SEQ_Odecseq(X1,X0)
| ? [X2,X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ) )
& ( ! [X4,X5] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X5),hAPP(X0,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5) )
| ~ c_SEQ_Odecseq(X1,X0) ) )
| ~ class_Orderings_Oorder(X1) ),
inference(rectify,[],[f3699]) ).
fof(f3699,plain,
! [X0,X1] :
( ( ( c_SEQ_Odecseq(X1,X0)
| ? [X2,X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ) )
& ( ! [X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
| ~ c_SEQ_Odecseq(X1,X0) ) )
| ~ class_Orderings_Oorder(X1) ),
inference(nnf_transformation,[],[f2516]) ).
fof(f2516,plain,
! [X0,X1] :
( ( c_SEQ_Odecseq(X1,X0)
<=> ! [X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ) )
| ~ class_Orderings_Oorder(X1) ),
inference(ennf_transformation,[],[f1560]) ).
fof(f1560,plain,
! [X0,X1] :
( class_Orderings_Oorder(X1)
=> ( c_SEQ_Odecseq(X1,X0)
<=> ! [X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
=> c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2)) ) ) ),
inference(rectify,[],[f872]) ).
fof(f872,axiom,
! [X82,X3] :
( class_Orderings_Oorder(X3)
=> ( c_SEQ_Odecseq(X3,X82)
<=> ! [X54,X64] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X54,X64)
=> c_Orderings_Oord__class_Oless__eq(X3,hAPP(X82,X64),hAPP(X82,X54)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11356,plain,
spl107_697,
inference(avatar_split_clause,[],[f4648,f11354]) ).
fof(f11354,plain,
( spl107_697
<=> ! [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,[spl107_697])]) ).
fof(f4648,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,[],[f3698]) ).
fof(f3698,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,[],[f2481]) ).
fof(f2481,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,[],[f1526]) ).
fof(f1526,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,[],[f619]) ).
fof(f619,axiom,
! [X60,X3] :
( class_Groups_Ozero(X3)
=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X60)
<=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X60 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11352,plain,
spl107_696,
inference(avatar_split_clause,[],[f4632,f11350]) ).
fof(f11350,plain,
( spl107_696
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = c_Divides_Odiv__class_Odiv(X1,X0,X0)
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Divides_Osemiring__div(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_696])]) ).
fof(f4632,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = c_Divides_Odiv__class_Odiv(X1,X0,X0)
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Divides_Osemiring__div(X1) ),
inference(cnf_transformation,[],[f2467]) ).
fof(f2467,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = c_Divides_Odiv__class_Odiv(X1,X0,X0)
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Divides_Osemiring__div(X1) ),
inference(flattening,[],[f2466]) ).
fof(f2466,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = c_Divides_Odiv__class_Odiv(X1,X0,X0)
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Divides_Osemiring__div(X1) ),
inference(ennf_transformation,[],[f1512]) ).
fof(f1512,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> ( c_Groups_Ozero__class_Ozero(X1) != X0
=> c_Groups_Oone__class_Oone(X1) = c_Divides_Odiv__class_Odiv(X1,X0,X0) ) ),
inference(rectify,[],[f712]) ).
fof(f712,axiom,
! [X5,X3] :
( class_Divides_Osemiring__div(X3)
=> ( c_Groups_Ozero__class_Ozero(X3) != X5
=> c_Groups_Oone__class_Oone(X3) = c_Divides_Odiv__class_Odiv(X3,X5,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11348,plain,
spl107_695,
inference(avatar_split_clause,[],[f4621,f11346]) ).
fof(f11346,plain,
( spl107_695
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_695])]) ).
fof(f4621,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f3694]) ).
fof(f3694,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
| c_Groups_Ozero__class_Ozero(X1) = X0 )
& ( c_Groups_Ozero__class_Ozero(X1) != X0
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0)) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(nnf_transformation,[],[f2456]) ).
fof(f2456,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
<=> c_Groups_Ozero__class_Ozero(X1) != X0 )
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f1502]) ).
fof(f1502,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
<=> c_Groups_Ozero__class_Ozero(X1) != X0 ) ),
inference(rectify,[],[f131]) ).
fof(f131,axiom,
! [X10,X3] :
( class_Groups_Oordered__ab__group__add__abs(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oabs__class_Oabs(X3,X10))
<=> c_Groups_Ozero__class_Ozero(X3) != X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11344,plain,
spl107_694,
inference(avatar_split_clause,[],[f4618,f11342]) ).
fof(f11342,plain,
( spl107_694
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_694])]) ).
fof(f4618,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f3693]) ).
fof(f3693,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| c_Groups_Ozero__class_Ozero(X1) != X0 )
& ( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X0),c_Groups_Ozero__class_Ozero(X1)) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(nnf_transformation,[],[f2455]) ).
fof(f2455,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f1501]) ).
fof(f1501,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f128]) ).
fof(f128,axiom,
! [X10,X3] :
( class_Groups_Oordered__ab__group__add__abs(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oabs__class_Oabs(X3,X10),c_Groups_Ozero__class_Ozero(X3))
<=> c_Groups_Ozero__class_Ozero(X3) = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11340,plain,
spl107_693,
inference(avatar_split_clause,[],[f4598,f11338]) ).
fof(f11338,plain,
( spl107_693
<=> ! [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,[spl107_693])]) ).
fof(f4598,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,[],[f3686]) ).
fof(f3686,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,[],[f2440]) ).
fof(f2440,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,[],[f1488]) ).
fof(f1488,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,[],[f438]) ).
fof(f438,axiom,
! [X10,X3] :
( class_Groups_Olinordered__ab__group__add(X3)
=> ( c_Groups_Ozero__class_Ozero(X3) = c_Groups_Oplus__class_Oplus(X3,X10,X10)
<=> c_Groups_Ozero__class_Ozero(X3) = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11336,plain,
spl107_692,
inference(avatar_split_clause,[],[f4581,f11334]) ).
fof(f11334,plain,
( spl107_692
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_RealVector_Oreal__normed__vector(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_692])]) ).
fof(f4581,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(cnf_transformation,[],[f3677]) ).
fof(f3677,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
| c_Groups_Ozero__class_Ozero(X1) = X0 )
& ( c_Groups_Ozero__class_Ozero(X1) != X0
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0)) ) )
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(nnf_transformation,[],[f2427]) ).
fof(f2427,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
<=> c_Groups_Ozero__class_Ozero(X1) != X0 )
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(ennf_transformation,[],[f1475]) ).
fof(f1475,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__vector(X1)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
<=> c_Groups_Ozero__class_Ozero(X1) != X0 ) ),
inference(rectify,[],[f171]) ).
fof(f171,axiom,
! [X16,X3] :
( class_RealVector_Oreal__normed__vector(X3)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X16))
<=> c_Groups_Ozero__class_Ozero(X3) != X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11332,plain,
spl107_691,
inference(avatar_split_clause,[],[f4578,f11330]) ).
fof(f11330,plain,
( spl107_691
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_691])]) ).
fof(f4578,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(cnf_transformation,[],[f3676]) ).
fof(f3676,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Ozero__class_Ozero(X1) != X0 )
& ( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(nnf_transformation,[],[f2426]) ).
fof(f2426,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(ennf_transformation,[],[f1474]) ).
fof(f1474,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__vector(X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f170]) ).
fof(f170,axiom,
! [X16,X3] :
( class_RealVector_Oreal__normed__vector(X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3,X16),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Groups_Ozero__class_Ozero(X3) = X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11328,plain,
spl107_690,
inference(avatar_split_clause,[],[f4572,f11326]) ).
fof(f11326,plain,
( spl107_690
<=> ! [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,[spl107_690])]) ).
fof(f4572,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,[],[f2421]) ).
fof(f2421,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,[],[f2420]) ).
fof(f2420,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,[],[f1469]) ).
fof(f1469,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,[],[f117]) ).
fof(f117,axiom,
! [X5,X3] :
( class_Rings_Odivision__ring(X3)
=> ( c_Groups_Ozero__class_Ozero(X3) != X5
=> c_Groups_Oone__class_Oone(X3) = c_Rings_Oinverse__class_Odivide(X3,X5,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11324,plain,
spl107_689,
inference(avatar_split_clause,[],[f4562,f11322]) ).
fof(f11322,plain,
( spl107_689
<=> ! [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,[spl107_689])]) ).
fof(f4562,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,[],[f2410]) ).
fof(f2410,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,[],[f1461]) ).
fof(f1461,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,[],[f109]) ).
fof(f109,axiom,
! [X5,X3] :
( class_Rings_Odivision__ring__inverse__zero(X3)
=> ( ( c_Groups_Ozero__class_Ozero(X3) != X5
=> c_Groups_Oone__class_Oone(X3) = c_Rings_Oinverse__class_Odivide(X3,X5,X5) )
& ( c_Groups_Ozero__class_Ozero(X3) = X5
=> c_Groups_Ozero__class_Ozero(X3) = c_Rings_Oinverse__class_Odivide(X3,X5,X5) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11320,plain,
( spl107_688
| ~ spl107_350
| ~ spl107_685 ),
inference(avatar_split_clause,[],[f11267,f11188,f7824,f11317]) ).
fof(f7824,plain,
( spl107_350
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_350])]) ).
fof(f11267,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))))
| ~ spl107_350
| ~ spl107_685 ),
inference(resolution,[],[f11189,f7825]) ).
fof(f7825,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X0)))
| ~ spl107_350 ),
inference(avatar_component_clause,[],[f7824]) ).
fof(f11315,plain,
spl107_687,
inference(avatar_split_clause,[],[f4534,f11313]) ).
fof(f11313,plain,
( spl107_687
<=> ! [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,[spl107_687])]) ).
fof(f4534,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,[],[f1435]) ).
fof(f1435,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,[],[f489]) ).
fof(f489,axiom,
! [X41,X42] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X41) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X41),X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11311,plain,
spl107_686,
inference(avatar_split_clause,[],[f4533,f11309]) ).
fof(f11309,plain,
( spl107_686
<=> ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_686])]) ).
fof(f4533,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X1),
inference(cnf_transformation,[],[f1434]) ).
fof(f1434,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X1),
inference(rectify,[],[f226]) ).
fof(f226,axiom,
! [X11,X12] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X12),X11) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X11),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f11190,plain,
( spl107_685
| ~ spl107_399
| ~ spl107_658 ),
inference(avatar_split_clause,[],[f11160,f10501,f8081,f11188]) ).
fof(f10501,plain,
( spl107_658
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_658])]) ).
fof(f11160,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) )
| ~ spl107_399
| ~ spl107_658 ),
inference(resolution,[],[f10502,f8083]) ).
fof(f10502,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0) )
| ~ spl107_658 ),
inference(avatar_component_clause,[],[f10501]) ).
fof(f11075,plain,
( spl107_684
| ~ spl107_17
| ~ spl107_421 ),
inference(avatar_split_clause,[],[f8395,f8173,f6256,f11073]) ).
fof(f11073,plain,
( spl107_684
<=> ! [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,[spl107_684])]) ).
fof(f6256,plain,
( spl107_17
<=> class_Rings_Odivision__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_17])]) ).
fof(f8173,plain,
( spl107_421
<=> ! [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,[spl107_421])]) ).
fof(f8395,plain,
( ! [X0] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = X0
| ~ spl107_17
| ~ spl107_421 ),
inference(resolution,[],[f8174,f6258]) ).
fof(f6258,plain,
( class_Rings_Odivision__ring(tc_Complex_Ocomplex)
| ~ spl107_17 ),
inference(avatar_component_clause,[],[f6256]) ).
fof(f8174,plain,
( ! [X0,X1] :
( ~ class_Rings_Odivision__ring(X1)
| c_Rings_Oinverse__class_Odivide(X1,X0,c_Groups_Oone__class_Oone(X1)) = X0 )
| ~ spl107_421 ),
inference(avatar_component_clause,[],[f8173]) ).
fof(f10910,plain,
( spl107_683
| ~ spl107_43
| ~ spl107_410 ),
inference(avatar_split_clause,[],[f8337,f8128,f6386,f10907]) ).
fof(f10907,plain,
( spl107_683
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_683])]) ).
fof(f6386,plain,
( spl107_43
<=> class_Rings_Olinordered__idom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_43])]) ).
fof(f8128,plain,
( spl107_410
<=> ! [X0] :
( c_Groups_Oone__class_Oone(X0) = c_Groups_Oabs__class_Oabs(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_410])]) ).
fof(f8337,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl107_43
| ~ spl107_410 ),
inference(resolution,[],[f8129,f6388]) ).
fof(f6388,plain,
( class_Rings_Olinordered__idom(tc_Int_Oint)
| ~ spl107_43 ),
inference(avatar_component_clause,[],[f6386]) ).
fof(f8129,plain,
( ! [X0] :
( ~ class_Rings_Olinordered__idom(X0)
| c_Groups_Oone__class_Oone(X0) = c_Groups_Oabs__class_Oabs(X0,c_Groups_Oone__class_Oone(X0)) )
| ~ spl107_410 ),
inference(avatar_component_clause,[],[f8128]) ).
fof(f10837,plain,
( spl107_682
| ~ spl107_41
| ~ spl107_409 ),
inference(avatar_split_clause,[],[f8334,f8124,f6376,f10834]) ).
fof(f10834,plain,
( spl107_682
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_682])]) ).
fof(f6376,plain,
( spl107_41
<=> class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_41])]) ).
fof(f8124,plain,
( spl107_409
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Oabs__class_Oabs(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_409])]) ).
fof(f8334,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ spl107_41
| ~ spl107_409 ),
inference(resolution,[],[f8125,f6378]) ).
fof(f6378,plain,
( class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint)
| ~ spl107_41 ),
inference(avatar_component_clause,[],[f6376]) ).
fof(f8125,plain,
( ! [X0] :
( ~ class_Groups_Oordered__ab__group__add__abs(X0)
| c_Groups_Ozero__class_Ozero(X0) = c_Groups_Oabs__class_Oabs(X0,c_Groups_Ozero__class_Ozero(X0)) )
| ~ spl107_409 ),
inference(avatar_component_clause,[],[f8124]) ).
fof(f10676,plain,
( spl107_681
| ~ spl107_20
| ~ spl107_408 ),
inference(avatar_split_clause,[],[f8333,f8120,f6271,f10673]) ).
fof(f10673,plain,
( spl107_681
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_681])]) ).
fof(f6271,plain,
( spl107_20
<=> class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_20])]) ).
fof(f8120,plain,
( spl107_408
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_RealVector_Oreal__normed__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_408])]) ).
fof(f8333,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl107_20
| ~ spl107_408 ),
inference(resolution,[],[f8121,f6273]) ).
fof(f6273,plain,
( class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)
| ~ spl107_20 ),
inference(avatar_component_clause,[],[f6271]) ).
fof(f8121,plain,
( ! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ozero__class_Ozero(X0)) )
| ~ spl107_408 ),
inference(avatar_component_clause,[],[f8120]) ).
fof(f10624,plain,
( spl107_680
| ~ spl107_19
| ~ spl107_408 ),
inference(avatar_split_clause,[],[f8332,f8120,f6266,f10621]) ).
fof(f10621,plain,
( spl107_680
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_680])]) ).
fof(f6266,plain,
( spl107_19
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_19])]) ).
fof(f8332,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ spl107_19
| ~ spl107_408 ),
inference(resolution,[],[f8121,f6268]) ).
fof(f6268,plain,
( class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ spl107_19 ),
inference(avatar_component_clause,[],[f6266]) ).
fof(f10591,plain,
spl107_679,
inference(avatar_split_clause,[],[f6078,f10589]) ).
fof(f10589,plain,
( spl107_679
<=> ! [X2,X1] : sP42(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,[spl107_679])]) ).
fof(f6078,plain,
! [X2,X1] : sP42(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,[],[f6077]) ).
fof(f6077,plain,
! [X2,X3,X1] :
( sP42(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,[],[f5567]) ).
fof(f5567,plain,
! [X2,X3,X0,X1] :
( sP42(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,[],[f4027]) ).
fof(f10587,plain,
spl107_678,
inference(avatar_split_clause,[],[f6070,f10585]) ).
fof(f10585,plain,
( spl107_678
<=> ! [X2,X1] : sP40(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,[spl107_678])]) ).
fof(f6070,plain,
! [X2,X1] : sP40(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,[],[f6069]) ).
fof(f6069,plain,
! [X2,X3,X1] :
( sP40(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,[],[f5558]) ).
fof(f5558,plain,
! [X2,X3,X0,X1] :
( sP40(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,[],[f4022]) ).
fof(f10582,plain,
spl107_677,
inference(avatar_split_clause,[],[f6056,f10580]) ).
fof(f10580,plain,
( spl107_677
<=> ! [X2,X1] :
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_677])]) ).
fof(f6056,plain,
! [X2,X1] :
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(equality_resolution,[],[f5389]) ).
fof(f5389,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f3939]) ).
fof(f10578,plain,
spl107_676,
inference(avatar_split_clause,[],[f6009,f10576]) ).
fof(f10576,plain,
( spl107_676
<=> ! [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,[spl107_676])]) ).
fof(f6009,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,[],[f5104]) ).
fof(f5104,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,[],[f3834]) ).
fof(f3834,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,[],[f3833]) ).
fof(f3833,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,[],[f2822]) ).
fof(f2822,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,[],[f1829]) ).
fof(f1829,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,[],[f620]) ).
fof(f620,axiom,
! [X10,X60,X3] :
( class_Rings_Oidom(X3)
=> ( c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Polynomial_Opoly(X3,X60),X10)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X3,X10,X60)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X60 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10574,plain,
spl107_675,
inference(avatar_split_clause,[],[f6004,f10572]) ).
fof(f10572,plain,
( spl107_675
<=> ! [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,[spl107_675])]) ).
fof(f6004,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,[],[f5075]) ).
fof(f5075,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,[],[f3828]) ).
fof(f3828,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,[],[f3827]) ).
fof(f3827,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,[],[f2783]) ).
fof(f2783,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,[],[f1807]) ).
fof(f1807,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,[],[f234]) ).
fof(f234,axiom,
! [X9,X10,X3] :
( class_Rings_Oring__no__zero__divisors(X3)
=> ( c_Groups_Ozero__class_Ozero(X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X10),X9)
<=> ( c_Groups_Ozero__class_Ozero(X3) = X9
| c_Groups_Ozero__class_Ozero(X3) = X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10570,plain,
spl107_674,
inference(avatar_split_clause,[],[f6003,f10568]) ).
fof(f10568,plain,
( spl107_674
<=> ! [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,[spl107_674])]) ).
fof(f6003,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,[],[f5076]) ).
fof(f5076,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,[],[f3828]) ).
fof(f10566,plain,
spl107_673,
inference(avatar_split_clause,[],[f5979,f10564]) ).
fof(f10564,plain,
( spl107_673
<=> ! [X2,X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_673])]) ).
fof(f5979,plain,
! [X2,X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),X0),
inference(equality_resolution,[],[f4837]) ).
fof(f4837,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) != X1 ),
inference(cnf_transformation,[],[f3749]) ).
fof(f3749,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)
| ! [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) != X1 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),sK71(X0,X1)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK71])],[f3747,f3748]) ).
fof(f3748,plain,
! [X0,X1] :
( ? [X3] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3) = X1
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),sK71(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f3747,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)
| ! [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) != X1 )
& ( ? [X3] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) ) ),
inference(rectify,[],[f3746]) ).
fof(f3746,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)
| ! [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) != X1 )
& ( ? [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f1672]) ).
fof(f1672,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)
<=> ? [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) = X1 ),
inference(rectify,[],[f733]) ).
fof(f733,axiom,
! [X7,X66] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X66,X7)
<=> ? [X61] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X61) = X66 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10562,plain,
spl107_672,
inference(avatar_split_clause,[],[f5978,f10560]) ).
fof(f10560,plain,
( spl107_672
<=> ! [X2,X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_672])]) ).
fof(f5978,plain,
! [X2,X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2),X0),
inference(equality_resolution,[],[f4835]) ).
fof(f4835,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2) != X1 ),
inference(cnf_transformation,[],[f3745]) ).
fof(f3745,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)
| ! [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2) != X1 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),sK70(X0,X1)) = X1
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK70])],[f3743,f3744]) ).
fof(f3744,plain,
! [X0,X1] :
( ? [X3] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3) = X1
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),sK70(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f3743,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)
| ! [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2) != X1 )
& ( ? [X3] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3) = X1
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) ) ),
inference(rectify,[],[f3742]) ).
fof(f3742,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)
| ! [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2) != X1 )
& ( ? [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2) = X1
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) ) ),
inference(nnf_transformation,[],[f1671]) ).
fof(f1671,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)
<=> ? [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2) = X1 ),
inference(rectify,[],[f976]) ).
fof(f976,axiom,
! [X7,X66] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X66,X7)
<=> ? [X61] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7),X61) = X66 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10558,plain,
( spl107_671
| ~ spl107_11
| ~ spl107_407 ),
inference(avatar_split_clause,[],[f8331,f8116,f6226,f10555]) ).
fof(f10555,plain,
( spl107_671
<=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_671])]) ).
fof(f6226,plain,
( spl107_11
<=> class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_11])]) ).
fof(f8116,plain,
( spl107_407
<=> ! [X0] :
( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_RealVector_Oreal__normed__algebra__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_407])]) ).
fof(f8331,plain,
( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl107_11
| ~ spl107_407 ),
inference(resolution,[],[f8117,f6228]) ).
fof(f6228,plain,
( class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal)
| ~ spl107_11 ),
inference(avatar_component_clause,[],[f6226]) ).
fof(f8117,plain,
( ! [X0] :
( ~ class_RealVector_Oreal__normed__algebra__1(X0)
| c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Oone__class_Oone(X0)) )
| ~ spl107_407 ),
inference(avatar_component_clause,[],[f8116]) ).
fof(f10553,plain,
~ spl107_670,
inference(avatar_split_clause,[],[f5936,f10550]) ).
fof(f10550,plain,
( spl107_670
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_670])]) ).
fof(f5936,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(equality_resolution,[],[f4519]) ).
fof(f4519,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X0))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0 ),
inference(cnf_transformation,[],[f3670]) ).
fof(f10548,plain,
spl107_669,
inference(avatar_split_clause,[],[f5838,f10546]) ).
fof(f10546,plain,
( spl107_669
<=> ! [X2,X0,X1] :
( sP48(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,[spl107_669])]) ).
fof(f5838,plain,
! [X2,X0,X1] :
( sP48(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X1,X0)) ),
inference(cnf_transformation,[],[f4085]) ).
fof(f4085,plain,
! [X0,X1,X2] :
( ( sP48(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
| ~ sP48(X0,X1,X2) ) ),
inference(rectify,[],[f4084]) ).
fof(f4084,plain,
! [X2,X4,X0] :
( ( sP48(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
| ~ sP48(X2,X4,X0) ) ),
inference(flattening,[],[f4083]) ).
fof(f4083,plain,
! [X2,X4,X0] :
( ( sP48(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
| ~ sP48(X2,X4,X0) ) ),
inference(nnf_transformation,[],[f3645]) ).
fof(f3645,plain,
! [X2,X4,X0] :
( sP48(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,[sP48])]) ).
fof(f10544,plain,
spl107_668,
inference(avatar_split_clause,[],[f5417,f10542]) ).
fof(f10542,plain,
( spl107_668
<=> ! [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,[spl107_668])]) ).
fof(f5417,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,[],[f3956]) ).
fof(f3956,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,[],[f1998]) ).
fof(f1998,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,[],[f520]) ).
fof(f520,axiom,
! [X65,X66,X63] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X63,X66) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X63,X65)
<=> X65 = X66 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10540,plain,
spl107_667,
inference(avatar_split_clause,[],[f5415,f10538]) ).
fof(f10538,plain,
( spl107_667
<=> ! [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,[spl107_667])]) ).
fof(f5415,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,[],[f3955]) ).
fof(f3955,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,[],[f1997]) ).
fof(f1997,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,[],[f519]) ).
fof(f519,axiom,
! [X65,X63,X66] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X66,X63) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X65,X63)
<=> X65 = X66 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10536,plain,
spl107_666,
inference(avatar_split_clause,[],[f5378,f10534]) ).
fof(f10534,plain,
( spl107_666
<=> ! [X2,X0,X1] :
( sP22(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK92(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_666])]) ).
fof(f5378,plain,
! [X2,X0,X1] :
( sP22(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK92(X0,X1,X2)) ),
inference(cnf_transformation,[],[f3931]) ).
fof(f3931,plain,
! [X0,X1,X2] :
( ( sP22(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK92(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK91(X0,X1,X2)),sK92(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,sK92(X0,X1,X2),X2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK92(X0,X1,X2))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X0,X6))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ sP22(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK91,sK92])],[f3929,f3930]) ).
fof(f3930,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(X0,X4))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4) )
=> ( ~ hBOOL(hAPP(X0,sK92(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK91(X0,X1,X2)),sK92(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,sK92(X0,X1,X2),X2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK92(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3929,plain,
! [X0,X1,X2] :
( ( sP22(X0,X1,X2)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X0,X4))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X0,X6))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ sP22(X0,X1,X2) ) ),
inference(rectify,[],[f3928]) ).
fof(f3928,plain,
! [X2,X1,X0] :
( ( sP22(X2,X1,X0)
| ( ? [X5,X6] :
( ~ hBOOL(hAPP(X2,X6))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5),X6) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X0)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X2,X6))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ sP22(X2,X1,X0) ) ),
inference(flattening,[],[f3927]) ).
fof(f3927,plain,
! [X2,X1,X0] :
( ( sP22(X2,X1,X0)
| ( ? [X5,X6] :
( ~ hBOOL(hAPP(X2,X6))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5),X6) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X0)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X2,X6))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ sP22(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f3607]) ).
fof(f3607,plain,
! [X2,X1,X0] :
( sP22(X2,X1,X0)
<=> ( ! [X5,X6] :
( hBOOL(hAPP(X2,X6))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP22])]) ).
fof(f10532,plain,
spl107_665,
inference(avatar_split_clause,[],[f5373,f10530]) ).
fof(f10530,plain,
( spl107_665
<=> ! [X2,X0,X1] :
( sP23(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK90(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_665])]) ).
fof(f5373,plain,
! [X2,X0,X1] :
( sP23(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK90(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3926]) ).
fof(f3926,plain,
! [X0,X1,X2] :
( ( sP23(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK90(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK89(X0,X1,X2)),sK90(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK90(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,sK90(X0,X1,X2))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X0,X6))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X6,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X6) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP23(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK89,sK90])],[f3924,f3925]) ).
fof(f3925,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(X0,X4))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) )
=> ( ~ hBOOL(hAPP(X0,sK90(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK89(X0,X1,X2)),sK90(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK90(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,sK90(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3924,plain,
! [X0,X1,X2] :
( ( sP23(X0,X1,X2)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X0,X4))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X0,X6))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X6,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X6) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP23(X0,X1,X2) ) ),
inference(rectify,[],[f3923]) ).
fof(f3923,plain,
! [X2,X1,X0] :
( ( sP23(X2,X1,X0)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X2,X4))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
& ( ! [X3,X4] :
( hBOOL(hAPP(X2,X4))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4) != X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP23(X2,X1,X0) ) ),
inference(flattening,[],[f3922]) ).
fof(f3922,plain,
! [X2,X1,X0] :
( ( sP23(X2,X1,X0)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X2,X4))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
& ( ! [X3,X4] :
( hBOOL(hAPP(X2,X4))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4) != X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP23(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f3608]) ).
fof(f3608,plain,
! [X2,X1,X0] :
( sP23(X2,X1,X0)
<=> ( ! [X3,X4] :
( hBOOL(hAPP(X2,X4))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4) != X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP23])]) ).
fof(f10528,plain,
spl107_664,
inference(avatar_split_clause,[],[f5350,f10526]) ).
fof(f10526,plain,
( spl107_664
<=> ! [X2,X0,X1] :
( sP18(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK86(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_664])]) ).
fof(f5350,plain,
! [X2,X0,X1] :
( sP18(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK86(X0,X1,X2)) ),
inference(cnf_transformation,[],[f3911]) ).
fof(f3911,plain,
! [X0,X1,X2] :
( ( sP18(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK85(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK85(X0,X1,X2)),sK86(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,sK86(X0,X1,X2),X2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK86(X0,X1,X2))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ) )
& ( ! [X5] :
( hBOOL(hAPP(X0,X5))
| ! [X6] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ sP18(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK85,sK86])],[f3908,f3910,f3909]) ).
fof(f3909,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(X0,X3))
& ? [X4] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4) ) )
=> ( ~ hBOOL(hAPP(X0,sK85(X0,X1,X2)))
& ? [X4] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK85(X0,X1,X2)),X4) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4) ) ) ),
introduced(choice_axiom,[]) ).
fof(f3910,plain,
! [X0,X1,X2] :
( ? [X4] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK85(X0,X1,X2)),X4) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4) )
=> ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK85(X0,X1,X2)),sK86(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,sK86(X0,X1,X2),X2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK86(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3908,plain,
! [X0,X1,X2] :
( ( sP18(X0,X1,X2)
| ( ? [X3] :
( ~ hBOOL(hAPP(X0,X3))
& ? [X4] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4) ) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ) )
& ( ! [X5] :
( hBOOL(hAPP(X0,X5))
| ! [X6] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ sP18(X0,X1,X2) ) ),
inference(rectify,[],[f3907]) ).
fof(f3907,plain,
! [X2,X1,X0] :
( ( sP18(X2,X1,X0)
| ( ? [X5] :
( ~ hBOOL(hAPP(X2,X5))
& ? [X6] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5),X6) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X0)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6) ) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ) )
& ( ! [X5] :
( hBOOL(hAPP(X2,X5))
| ! [X6] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ sP18(X2,X1,X0) ) ),
inference(flattening,[],[f3906]) ).
fof(f3906,plain,
! [X2,X1,X0] :
( ( sP18(X2,X1,X0)
| ( ? [X5] :
( ~ hBOOL(hAPP(X2,X5))
& ? [X6] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5),X6) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X0)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6) ) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ) )
& ( ! [X5] :
( hBOOL(hAPP(X2,X5))
| ! [X6] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ sP18(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f3601]) ).
fof(f3601,plain,
! [X2,X1,X0] :
( sP18(X2,X1,X0)
<=> ( ! [X5] :
( hBOOL(hAPP(X2,X5))
| ! [X6] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).
fof(f10524,plain,
spl107_663,
inference(avatar_split_clause,[],[f5345,f10522]) ).
fof(f10522,plain,
( spl107_663
<=> ! [X2,X0,X1] :
( sP19(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK84(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_663])]) ).
fof(f5345,plain,
! [X2,X0,X1] :
( sP19(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK84(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3905]) ).
fof(f3905,plain,
! [X0,X1,X2] :
( ( sP19(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK83(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK83(X0,X1,X2)),sK84(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK84(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,sK84(X0,X1,X2))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
& ( ! [X5] :
( hBOOL(hAPP(X0,X5))
| ! [X6] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X6,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X6) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP19(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK83,sK84])],[f3902,f3904,f3903]) ).
fof(f3903,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(X0,X3))
& ? [X4] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ) )
=> ( ~ hBOOL(hAPP(X0,sK83(X0,X1,X2)))
& ? [X4] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK83(X0,X1,X2)),X4) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ) ) ),
introduced(choice_axiom,[]) ).
fof(f3904,plain,
! [X0,X1,X2] :
( ? [X4] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK83(X0,X1,X2)),X4) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) )
=> ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK83(X0,X1,X2)),sK84(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK84(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,sK84(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3902,plain,
! [X0,X1,X2] :
( ( sP19(X0,X1,X2)
| ( ? [X3] :
( ~ hBOOL(hAPP(X0,X3))
& ? [X4] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
& ( ! [X5] :
( hBOOL(hAPP(X0,X5))
| ! [X6] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X6,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X6) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP19(X0,X1,X2) ) ),
inference(rectify,[],[f3901]) ).
fof(f3901,plain,
! [X2,X1,X0] :
( ( sP19(X2,X1,X0)
| ( ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& ? [X4] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4) ) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
& ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| ! [X4] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4) != X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP19(X2,X1,X0) ) ),
inference(flattening,[],[f3900]) ).
fof(f3900,plain,
! [X2,X1,X0] :
( ( sP19(X2,X1,X0)
| ( ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& ? [X4] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4) ) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
& ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| ! [X4] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4) != X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP19(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f3602]) ).
fof(f3602,plain,
! [X2,X1,X0] :
( sP19(X2,X1,X0)
<=> ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| ! [X4] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4) != X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP19])]) ).
fof(f10520,plain,
spl107_662,
inference(avatar_split_clause,[],[f5279,f10518]) ).
fof(f10518,plain,
( spl107_662
<=> ! [X2,X0,X1] :
( sP15(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK80(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_662])]) ).
fof(f5279,plain,
! [X2,X0,X1] :
( sP15(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK80(X0,X1,X2)) ),
inference(cnf_transformation,[],[f3880]) ).
fof(f3880,plain,
! [X0,X1,X2] :
( ( sP15(X0,X1,X2)
| ( ~ hBOOL(hAPP(hAPP(X0,sK79(X0,X1,X2)),sK80(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK79(X0,X1,X2)),sK80(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,sK80(X0,X1,X2),X2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK80(X0,X1,X2)) ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(hAPP(X0,X5),X6))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6) )
| ~ sP15(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK79,sK80])],[f3878,f3879]) ).
fof(f3879,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(hAPP(X0,X3),X4))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4) )
=> ( ~ hBOOL(hAPP(hAPP(X0,sK79(X0,X1,X2)),sK80(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK79(X0,X1,X2)),sK80(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,sK80(X0,X1,X2),X2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK80(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3878,plain,
! [X0,X1,X2] :
( ( sP15(X0,X1,X2)
| ? [X3,X4] :
( ~ hBOOL(hAPP(hAPP(X0,X3),X4))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4) ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(hAPP(X0,X5),X6))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6) )
| ~ sP15(X0,X1,X2) ) ),
inference(rectify,[],[f3877]) ).
fof(f3877,plain,
! [X1,X0,X2] :
( ( sP15(X1,X0,X2)
| ? [X3,X4] :
( ~ hBOOL(hAPP(hAPP(X1,X3),X4))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) = X0
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4) ) )
& ( ! [X3,X4] :
( hBOOL(hAPP(hAPP(X1,X3),X4))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) != X0
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4) )
| ~ sP15(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f3596]) ).
fof(f3596,plain,
! [X1,X0,X2] :
( sP15(X1,X0,X2)
<=> ! [X3,X4] :
( hBOOL(hAPP(hAPP(X1,X3),X4))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) != X0
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f10516,plain,
spl107_661,
inference(avatar_split_clause,[],[f5270,f10514]) ).
fof(f10514,plain,
( spl107_661
<=> ! [X2,X0,X1] :
( sP13(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK78(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_661])]) ).
fof(f5270,plain,
! [X2,X0,X1] :
( sP13(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK78(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3874]) ).
fof(f3874,plain,
! [X0,X1,X2] :
( ( sP13(X0,X1,X2)
| ( ~ hBOOL(hAPP(hAPP(X0,sK77(X0,X1,X2)),sK78(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK77(X0,X1,X2)),sK78(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK78(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,sK78(X0,X1,X2)) ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(hAPP(X0,X5),X6))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X6,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X6) )
| ~ sP13(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK77,sK78])],[f3872,f3873]) ).
fof(f3873,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(hAPP(X0,X3),X4))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) )
=> ( ~ hBOOL(hAPP(hAPP(X0,sK77(X0,X1,X2)),sK78(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK77(X0,X1,X2)),sK78(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK78(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,sK78(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3872,plain,
! [X0,X1,X2] :
( ( sP13(X0,X1,X2)
| ? [X3,X4] :
( ~ hBOOL(hAPP(hAPP(X0,X3),X4))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(hAPP(X0,X5),X6))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X6,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X6) )
| ~ sP13(X0,X1,X2) ) ),
inference(rectify,[],[f3871]) ).
fof(f3871,plain,
! [X1,X0,X2] :
( ( sP13(X1,X0,X2)
| ? [X3,X4] :
( ~ hBOOL(hAPP(hAPP(X1,X3),X4))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) = X0
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ) )
& ( ! [X3,X4] :
( hBOOL(hAPP(hAPP(X1,X3),X4))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) != X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) )
| ~ sP13(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f3593]) ).
fof(f3593,plain,
! [X1,X0,X2] :
( sP13(X1,X0,X2)
<=> ! [X3,X4] :
( hBOOL(hAPP(hAPP(X1,X3),X4))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) != X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f10512,plain,
( spl107_660
| ~ spl107_8
| ~ spl107_407 ),
inference(avatar_split_clause,[],[f8330,f8116,f6211,f10509]) ).
fof(f10509,plain,
( spl107_660
<=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_660])]) ).
fof(f6211,plain,
( spl107_8
<=> class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_8])]) ).
fof(f8330,plain,
( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ~ spl107_8
| ~ spl107_407 ),
inference(resolution,[],[f8117,f6213]) ).
fof(f6213,plain,
( class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex)
| ~ spl107_8 ),
inference(avatar_component_clause,[],[f6211]) ).
fof(f10507,plain,
spl107_659,
inference(avatar_split_clause,[],[f5237,f10505]) ).
fof(f5237,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,[],[f2984]) ).
fof(f2984,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,[],[f2983]) ).
fof(f2983,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,[],[f1932]) ).
fof(f1932,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,[],[f530]) ).
fof(f530,axiom,
! [X13,X14,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X14)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X13)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10503,plain,
spl107_658,
inference(avatar_split_clause,[],[f5220,f10501]) ).
fof(f5220,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(cnf_transformation,[],[f2966]) ).
fof(f2966,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(flattening,[],[f2965]) ).
fof(f2965,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(ennf_transformation,[],[f1915]) ).
fof(f1915,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0) ) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X13,X14,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14,X13)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10499,plain,
spl107_657,
inference(avatar_split_clause,[],[f5215,f10497]) ).
fof(f10497,plain,
( spl107_657
<=> ! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_657])]) ).
fof(f5215,plain,
! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2959]) ).
fof(f2959,plain,
! [X0,X1,X2] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(flattening,[],[f2958]) ).
fof(f2958,plain,
! [X0,X1,X2] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1911]) ).
fof(f1911,plain,
! [X0,X1,X2] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X0) ) ),
inference(rectify,[],[f840]) ).
fof(f840,axiom,
! [X12,X21,X6] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X6,X21)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X12)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X6,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10495,plain,
spl107_656,
inference(avatar_split_clause,[],[f5147,f10493]) ).
fof(f10493,plain,
( spl107_656
<=> ! [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,[spl107_656])]) ).
fof(f5147,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,[],[f3844]) ).
fof(f3844,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,[],[f2883]) ).
fof(f2883,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,[],[f1862]) ).
fof(f1862,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,[],[f422]) ).
fof(f422,axiom,
! [X10,X9,X3] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3)
=> ( c_Groups_Oplus__class_Oplus(X3,X9,X10) = X9
<=> c_Groups_Ozero__class_Ozero(X3) = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10491,plain,
spl107_655,
inference(avatar_split_clause,[],[f5088,f10489]) ).
fof(f5088,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,[],[f3830]) ).
fof(f3830,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,[],[f2797]) ).
fof(f2797,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,[],[f1816]) ).
fof(f1816,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,[],[f193]) ).
fof(f193,axiom,
! [X9,X10,X3] :
( class_Groups_Oab__group__add(X3)
=> ( X9 = X10
<=> c_Groups_Ominus__class_Ominus(X3,X10,X9) = c_Groups_Ozero__class_Ozero(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10487,plain,
spl107_654,
inference(avatar_split_clause,[],[f5085,f10485]) ).
fof(f5085,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,[],[f3829]) ).
fof(f3829,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,[],[f2796]) ).
fof(f2796,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,[],[f1815]) ).
fof(f1815,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,[],[f194]) ).
fof(f194,axiom,
! [X9,X10,X3] :
( class_Groups_Ogroup__add(X3)
=> ( c_Groups_Ominus__class_Ominus(X3,X10,X9) = c_Groups_Ozero__class_Ozero(X3)
<=> X9 = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10483,plain,
spl107_653,
inference(avatar_split_clause,[],[f5055,f10481]) ).
fof(f10481,plain,
( spl107_653
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Odiv(X2,c_Divides_Odiv__class_Omod(X2,X1,X0),X0)
| ~ class_Divides_Osemiring__div(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_653])]) ).
fof(f5055,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Odiv(X2,c_Divides_Odiv__class_Omod(X2,X1,X0),X0)
| ~ class_Divides_Osemiring__div(X2) ),
inference(cnf_transformation,[],[f2757]) ).
fof(f2757,plain,
! [X0,X1,X2] :
( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Odiv(X2,c_Divides_Odiv__class_Omod(X2,X1,X0),X0)
| ~ class_Divides_Osemiring__div(X2) ),
inference(ennf_transformation,[],[f1789]) ).
fof(f1789,plain,
! [X0,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Odiv(X2,c_Divides_Odiv__class_Omod(X2,X1,X0),X0) ),
inference(rectify,[],[f724]) ).
fof(f724,axiom,
! [X4,X5,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Groups_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Odiv(X3,c_Divides_Odiv__class_Omod(X3,X5,X4),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10479,plain,
spl107_652,
inference(avatar_split_clause,[],[f5054,f10477]) ).
fof(f10477,plain,
( spl107_652
<=> ! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(X2,c_Groups_Oabs__class_Oabs(X2,X1),X0)
| ~ c_Rings_Odvd__class_Odvd(X2,X1,X0)
| ~ class_Rings_Olinordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_652])]) ).
fof(f5054,plain,
! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(X2,c_Groups_Oabs__class_Oabs(X2,X1),X0)
| ~ c_Rings_Odvd__class_Odvd(X2,X1,X0)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(cnf_transformation,[],[f3825]) ).
fof(f3825,plain,
! [X0,X1,X2] :
( ( ( c_Rings_Odvd__class_Odvd(X2,c_Groups_Oabs__class_Oabs(X2,X1),X0)
| ~ c_Rings_Odvd__class_Odvd(X2,X1,X0) )
& ( c_Rings_Odvd__class_Odvd(X2,X1,X0)
| ~ c_Rings_Odvd__class_Odvd(X2,c_Groups_Oabs__class_Oabs(X2,X1),X0) ) )
| ~ class_Rings_Olinordered__idom(X2) ),
inference(nnf_transformation,[],[f2756]) ).
fof(f2756,plain,
! [X0,X1,X2] :
( ( c_Rings_Odvd__class_Odvd(X2,c_Groups_Oabs__class_Oabs(X2,X1),X0)
<=> c_Rings_Odvd__class_Odvd(X2,X1,X0) )
| ~ class_Rings_Olinordered__idom(X2) ),
inference(ennf_transformation,[],[f1788]) ).
fof(f1788,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Rings_Odvd__class_Odvd(X2,c_Groups_Oabs__class_Oabs(X2,X1),X0)
<=> c_Rings_Odvd__class_Odvd(X2,X1,X0) ) ),
inference(rectify,[],[f811]) ).
fof(f811,axiom,
! [X63,X66,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,c_Groups_Oabs__class_Oabs(X3,X66),X63)
<=> c_Rings_Odvd__class_Odvd(X3,X66,X63) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10475,plain,
spl107_651,
inference(avatar_split_clause,[],[f5053,f10473]) ).
fof(f10473,plain,
( spl107_651
<=> ! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(X2,X1,X0)
| ~ c_Rings_Odvd__class_Odvd(X2,c_Groups_Oabs__class_Oabs(X2,X1),X0)
| ~ class_Rings_Olinordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_651])]) ).
fof(f5053,plain,
! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(X2,X1,X0)
| ~ c_Rings_Odvd__class_Odvd(X2,c_Groups_Oabs__class_Oabs(X2,X1),X0)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(cnf_transformation,[],[f3825]) ).
fof(f10471,plain,
spl107_650,
inference(avatar_split_clause,[],[f5052,f10469]) ).
fof(f10469,plain,
( spl107_650
<=> ! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Oabs__class_Oabs(X2,X0))
| ~ c_Rings_Odvd__class_Odvd(X2,X1,X0)
| ~ class_Rings_Olinordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_650])]) ).
fof(f5052,plain,
! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Oabs__class_Oabs(X2,X0))
| ~ c_Rings_Odvd__class_Odvd(X2,X1,X0)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(cnf_transformation,[],[f3824]) ).
fof(f3824,plain,
! [X0,X1,X2] :
( ( ( c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Oabs__class_Oabs(X2,X0))
| ~ c_Rings_Odvd__class_Odvd(X2,X1,X0) )
& ( c_Rings_Odvd__class_Odvd(X2,X1,X0)
| ~ c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Oabs__class_Oabs(X2,X0)) ) )
| ~ class_Rings_Olinordered__idom(X2) ),
inference(nnf_transformation,[],[f2755]) ).
fof(f2755,plain,
! [X0,X1,X2] :
( ( c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Oabs__class_Oabs(X2,X0))
<=> c_Rings_Odvd__class_Odvd(X2,X1,X0) )
| ~ class_Rings_Olinordered__idom(X2) ),
inference(ennf_transformation,[],[f1787]) ).
fof(f1787,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Oabs__class_Oabs(X2,X0))
<=> c_Rings_Odvd__class_Odvd(X2,X1,X0) ) ),
inference(rectify,[],[f812]) ).
fof(f812,axiom,
! [X63,X66,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X66,c_Groups_Oabs__class_Oabs(X3,X63))
<=> c_Rings_Odvd__class_Odvd(X3,X66,X63) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10467,plain,
( spl107_649
| ~ spl107_337
| ~ spl107_402 ),
inference(avatar_split_clause,[],[f8319,f8096,f7765,f10464]) ).
fof(f10464,plain,
( spl107_649
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_649])]) ).
fof(f7765,plain,
( spl107_337
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_337])]) ).
fof(f8096,plain,
( spl107_402
<=> ! [X0] : c_RealDef_Oreal(tc_Nat_Onat,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_402])]) ).
fof(f8319,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl107_337
| ~ spl107_402 ),
inference(superposition,[],[f8097,f7767]) ).
fof(f7767,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl107_337 ),
inference(avatar_component_clause,[],[f7765]) ).
fof(f8097,plain,
( ! [X0] : c_RealDef_Oreal(tc_Nat_Onat,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0))
| ~ spl107_402 ),
inference(avatar_component_clause,[],[f8096]) ).
fof(f10462,plain,
spl107_648,
inference(avatar_split_clause,[],[f5051,f10460]) ).
fof(f10460,plain,
( spl107_648
<=> ! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(X2,X1,X0)
| ~ c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Oabs__class_Oabs(X2,X0))
| ~ class_Rings_Olinordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_648])]) ).
fof(f5051,plain,
! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(X2,X1,X0)
| ~ c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Oabs__class_Oabs(X2,X0))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(cnf_transformation,[],[f3824]) ).
fof(f10458,plain,
spl107_647,
inference(avatar_split_clause,[],[f5042,f10456]) ).
fof(f10456,plain,
( spl107_647
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oabs__class_Oabs(X2,X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_647])]) ).
fof(f5042,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oabs__class_Oabs(X2,X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
inference(cnf_transformation,[],[f2741]) ).
fof(f2741,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oabs__class_Oabs(X2,X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
inference(flattening,[],[f2740]) ).
fof(f2740,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oabs__class_Oabs(X2,X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
inference(ennf_transformation,[],[f1778]) ).
fof(f1778,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add__abs(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oabs__class_Oabs(X2,X1),X0)
=> c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ),
inference(rectify,[],[f167]) ).
fof(f167,axiom,
! [X4,X5,X3] :
( class_Groups_Oordered__ab__group__add__abs(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oabs__class_Oabs(X3,X5),X4)
=> c_Orderings_Oord__class_Oless__eq(X3,X5,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10454,plain,
spl107_646,
inference(avatar_split_clause,[],[f4860,f10452]) ).
fof(f10452,plain,
( spl107_646
<=> ! [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,[spl107_646])]) ).
fof(f4860,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,[],[f3760]) ).
fof(f3760,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,[],[f1680]) ).
fof(f1680,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,[],[f557]) ).
fof(f557,axiom,
! [X66,X65] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X65,X66))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X66,X65) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10450,plain,
spl107_645,
inference(avatar_split_clause,[],[f4859,f10448]) ).
fof(f10448,plain,
( spl107_645
<=> ! [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,[spl107_645])]) ).
fof(f4859,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,[],[f3760]) ).
fof(f10446,plain,
spl107_644,
inference(avatar_split_clause,[],[f4858,f10444]) ).
fof(f10444,plain,
( spl107_644
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_644])]) ).
fof(f4858,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3759]) ).
fof(f3759,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,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_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X0)) ) ),
inference(nnf_transformation,[],[f1679]) ).
fof(f1679,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f665]) ).
fof(f665,axiom,
! [X66,X65] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X65),c_RealDef_Oreal(tc_Nat_Onat,X66))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X65,X66) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10442,plain,
spl107_643,
inference(avatar_split_clause,[],[f4857,f10440]) ).
fof(f10440,plain,
( spl107_643
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_643])]) ).
fof(f4857,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X0)) ),
inference(cnf_transformation,[],[f3759]) ).
fof(f10438,plain,
spl107_642,
inference(avatar_split_clause,[],[f4856,f10436]) ).
fof(f10436,plain,
( spl107_642
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_642])]) ).
fof(f4856,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3758]) ).
fof(f3758,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,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_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X0)) ) ),
inference(nnf_transformation,[],[f1678]) ).
fof(f1678,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f666]) ).
fof(f666,axiom,
! [X66,X65] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X65),c_RealDef_Oreal(tc_Nat_Onat,X66))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X65,X66) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10434,plain,
spl107_641,
inference(avatar_split_clause,[],[f4855,f10432]) ).
fof(f10432,plain,
( spl107_641
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_641])]) ).
fof(f4855,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X0)) ),
inference(cnf_transformation,[],[f3758]) ).
fof(f10430,plain,
spl107_640,
inference(avatar_split_clause,[],[f4822,f10428]) ).
fof(f10428,plain,
( spl107_640
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK69(X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_640])]) ).
fof(f4822,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK69(X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3735]) ).
fof(f3735,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,sK69(X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK69])],[f3733,f3734]) ).
fof(f3734,plain,
! [X0,X1] :
( ? [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) = X0
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK69(X0,X1)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f3733,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,[],[f3732]) ).
fof(f3732,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,[],[f1666]) ).
fof(f1666,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,[],[f479]) ).
fof(f479,axiom,
! [X62,X63] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X63,X62)
<=> ? [X64] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X63,X64) = X62 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10426,plain,
spl107_639,
inference(avatar_split_clause,[],[f4820,f10424]) ).
fof(f10424,plain,
( spl107_639
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK68(X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_639])]) ).
fof(f4820,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK68(X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3731]) ).
fof(f3731,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,sK68(X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK68])],[f3729,f3730]) ).
fof(f3730,plain,
! [X0,X1] :
( ? [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) = X0
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK68(X0,X1)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f3729,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,[],[f3728]) ).
fof(f3728,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,[],[f1665]) ).
fof(f1665,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,[],[f587]) ).
fof(f587,axiom,
! [X65,X66] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,X65)
<=> ? [X73] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X66,X73) = X65 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10422,plain,
( spl107_638
| ~ spl107_336
| ~ spl107_402 ),
inference(avatar_split_clause,[],[f8318,f8096,f7760,f10419]) ).
fof(f10419,plain,
( spl107_638
<=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_638])]) ).
fof(f7760,plain,
( spl107_336
<=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_336])]) ).
fof(f8318,plain,
( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl107_336
| ~ spl107_402 ),
inference(superposition,[],[f8097,f7762]) ).
fof(f7762,plain,
( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl107_336 ),
inference(avatar_component_clause,[],[f7760]) ).
fof(f10417,plain,
spl107_637,
inference(avatar_split_clause,[],[f4811,f10415]) ).
fof(f10415,plain,
( spl107_637
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_637])]) ).
fof(f4811,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(cnf_transformation,[],[f3722]) ).
fof(f3722,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
inference(nnf_transformation,[],[f1661]) ).
fof(f1661,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(rectify,[],[f211]) ).
fof(f211,axiom,
! [X20,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16,X20)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X16,X20),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10413,plain,
spl107_636,
inference(avatar_split_clause,[],[f4810,f10411]) ).
fof(f10411,plain,
( spl107_636
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_636])]) ).
fof(f4810,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f3722]) ).
fof(f10409,plain,
spl107_635,
inference(avatar_split_clause,[],[f4761,f10407]) ).
fof(f10407,plain,
( spl107_635
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(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,[spl107_635])]) ).
fof(f4761,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(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,[],[f2606]) ).
fof(f2606,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(ennf_transformation,[],[f1625]) ).
fof(f1625,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_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1),X1) ),
inference(rectify,[],[f751]) ).
fof(f751,axiom,
! [X42,X41] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X41)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X42,X41),X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10405,plain,
spl107_634,
inference(avatar_split_clause,[],[f4760,f10403]) ).
fof(f10403,plain,
( spl107_634
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(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,[spl107_634])]) ).
fof(f4760,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(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,[],[f2605]) ).
fof(f2605,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(ennf_transformation,[],[f1624]) ).
fof(f1624,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__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1),X1) ),
inference(rectify,[],[f771]) ).
fof(f771,axiom,
! [X42,X41] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X41)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X42,X41),X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10401,plain,
spl107_633,
inference(avatar_split_clause,[],[f4753,f10399]) ).
fof(f10399,plain,
( spl107_633
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_633])]) ).
fof(f4753,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(cnf_transformation,[],[f2596]) ).
fof(f2596,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(ennf_transformation,[],[f1618]) ).
fof(f1618,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,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1),X1) ),
inference(rectify,[],[f987]) ).
fof(f987,axiom,
! [X5,X4] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5,X4),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10397,plain,
spl107_632,
inference(avatar_split_clause,[],[f4749,f10395]) ).
fof(f10395,plain,
( spl107_632
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_632])]) ).
fof(f4749,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f2593]) ).
fof(f2593,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(ennf_transformation,[],[f1615]) ).
fof(f1615,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1)) ),
inference(rectify,[],[f991]) ).
fof(f991,axiom,
! [X5,X4] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10393,plain,
spl107_631,
inference(avatar_split_clause,[],[f4735,f10391]) ).
fof(f10391,plain,
( spl107_631
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_631])]) ).
fof(f4735,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(cnf_transformation,[],[f2575]) ).
fof(f2575,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(ennf_transformation,[],[f1603]) ).
fof(f1603,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_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0),X1) ),
inference(rectify,[],[f988]) ).
fof(f988,axiom,
! [X13,X42] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X42)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X42,X13),X42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10389,plain,
spl107_630,
inference(avatar_split_clause,[],[f4675,f10387]) ).
fof(f10387,plain,
( spl107_630
<=> ! [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,[spl107_630])]) ).
fof(f4675,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,[],[f2507]) ).
fof(f2507,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,[],[f1552]) ).
fof(f1552,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,[],[f418]) ).
fof(f418,axiom,
! [X5,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Ozero__class_Ozero(X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Ozero__class_Ozero(X3)),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10385,plain,
spl107_629,
inference(avatar_split_clause,[],[f4674,f10383]) ).
fof(f10383,plain,
( spl107_629
<=> ! [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,[spl107_629])]) ).
fof(f4674,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,[],[f2506]) ).
fof(f2506,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,[],[f1551]) ).
fof(f1551,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,[],[f419]) ).
fof(f419,axiom,
! [X5,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Ozero__class_Ozero(X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),c_Groups_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10381,plain,
spl107_628,
inference(avatar_split_clause,[],[f4673,f10379]) ).
fof(f10379,plain,
( spl107_628
<=> ! [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,[spl107_628])]) ).
fof(f4673,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,[],[f2505]) ).
fof(f2505,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,[],[f1550]) ).
fof(f1550,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,[],[f452]) ).
fof(f452,axiom,
! [X6,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oone__class_Oone(X3) = hAPP(c_Polynomial_Opoly(X3,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X3))),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10377,plain,
( spl107_627
| ~ spl107_363
| ~ spl107_392 ),
inference(avatar_split_clause,[],[f8075,f8019,f7876,f10375]) ).
fof(f10375,plain,
( spl107_627
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK72(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_627])]) ).
fof(f7876,plain,
( spl107_363
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK72(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_363])]) ).
fof(f8075,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK72(X0,X1))
| ~ spl107_363
| ~ spl107_392 ),
inference(resolution,[],[f8020,f7877]) ).
fof(f7877,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK72(X0,X1))
| ~ spl107_363 ),
inference(avatar_component_clause,[],[f7876]) ).
fof(f10373,plain,
spl107_626,
inference(avatar_split_clause,[],[f4672,f10371]) ).
fof(f10371,plain,
( spl107_626
<=> ! [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,[spl107_626])]) ).
fof(f4672,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,[],[f2504]) ).
fof(f2504,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,[],[f1549]) ).
fof(f1549,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,[],[f878]) ).
fof(f878,axiom,
! [X6,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oone__class_Oone(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X6),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10369,plain,
spl107_625,
inference(avatar_split_clause,[],[f4661,f10367]) ).
fof(f10367,plain,
( spl107_625
<=> ! [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,[spl107_625])]) ).
fof(f4661,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,[],[f2493]) ).
fof(f2493,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,[],[f1538]) ).
fof(f1538,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,[],[f765]) ).
fof(f765,axiom,
! [X22,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = c_Polynomial_Osynthetic__div(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10365,plain,
spl107_624,
inference(avatar_split_clause,[],[f4660,f10363]) ).
fof(f10363,plain,
( spl107_624
<=> ! [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,[spl107_624])]) ).
fof(f4660,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,[],[f2492]) ).
fof(f2492,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,[],[f1537]) ).
fof(f1537,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,[],[f647]) ).
fof(f647,axiom,
! [X57,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = c_Polynomial_Opcompose(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X57) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10361,plain,
spl107_623,
inference(avatar_split_clause,[],[f4659,f10359]) ).
fof(f10359,plain,
( spl107_623
<=> ! [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,[spl107_623])]) ).
fof(f4659,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,[],[f2491]) ).
fof(f2491,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,[],[f1536]) ).
fof(f1536,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,[],[f474]) ).
fof(f474,axiom,
! [X6,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Polynomial_Opoly(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10357,plain,
spl107_622,
inference(avatar_split_clause,[],[f4654,f10355]) ).
fof(f10355,plain,
( spl107_622
<=> ! [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,[spl107_622])]) ).
fof(f4654,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,[],[f2486]) ).
fof(f2486,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,[],[f1531]) ).
fof(f1531,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,[],[f905]) ).
fof(f905,axiom,
! [X41,X3] :
( class_Groups_Omonoid__mult(X3)
=> c_Groups_Oone__class_Oone(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),c_Groups_Oone__class_Oone(X3)),X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10353,plain,
spl107_621,
inference(avatar_split_clause,[],[f4650,f10351]) ).
fof(f4650,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,[],[f2482]) ).
fof(f2482,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,[],[f1527]) ).
fof(f1527,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,[],[f918]) ).
fof(f918,axiom,
! [X5,X3] :
( class_Power_Opower(X3)
=> c_Groups_Oone__class_Oone(X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X3),X5),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10349,plain,
spl107_620,
inference(avatar_split_clause,[],[f4645,f10347]) ).
fof(f10347,plain,
( spl107_620
<=> ! [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,[spl107_620])]) ).
fof(f4645,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,[],[f2479]) ).
fof(f2479,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,[],[f1524]) ).
fof(f1524,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,[],[f232]) ).
fof(f232,axiom,
! [X5,X3] :
( class_Rings_Omult__zero(X3)
=> c_Groups_Ozero__class_Ozero(X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Ozero__class_Ozero(X3)),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10345,plain,
spl107_619,
inference(avatar_split_clause,[],[f4644,f10343]) ).
fof(f10343,plain,
( spl107_619
<=> ! [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,[spl107_619])]) ).
fof(f4644,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,[],[f2478]) ).
fof(f2478,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,[],[f1523]) ).
fof(f1523,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,[],[f233]) ).
fof(f233,axiom,
! [X5,X3] :
( class_Rings_Omult__zero(X3)
=> c_Groups_Ozero__class_Ozero(X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),c_Groups_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10341,plain,
spl107_618,
inference(avatar_split_clause,[],[f4616,f10339]) ).
fof(f10339,plain,
( spl107_618
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oabs__class_Oabs(X1,X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_618])]) ).
fof(f4616,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oabs__class_Oabs(X1,X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f3692]) ).
fof(f3692,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oabs__class_Oabs(X1,X0)
| c_Groups_Ozero__class_Ozero(X1) != X0 )
& ( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oabs__class_Oabs(X1,X0) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(nnf_transformation,[],[f2454]) ).
fof(f2454,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oabs__class_Oabs(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f1500]) ).
fof(f1500,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oabs__class_Oabs(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f110]) ).
fof(f110,axiom,
! [X10,X3] :
( class_Groups_Oordered__ab__group__add__abs(X3)
=> ( c_Groups_Ozero__class_Ozero(X3) = c_Groups_Oabs__class_Oabs(X3,X10)
<=> c_Groups_Ozero__class_Ozero(X3) = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10337,plain,
spl107_617,
inference(avatar_split_clause,[],[f4615,f10335]) ).
fof(f10335,plain,
( spl107_617
<=> ! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_617])]) ).
fof(f4615,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f2453]) ).
fof(f2453,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(flattening,[],[f2452]) ).
fof(f2452,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f1499]) ).
fof(f1499,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
=> c_Groups_Oabs__class_Oabs(X1,X0) = X0 ) ),
inference(rectify,[],[f130]) ).
fof(f130,axiom,
! [X5,X3] :
( class_Groups_Oordered__ab__group__add__abs(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X5)
=> c_Groups_Oabs__class_Oabs(X3,X5) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10333,plain,
( spl107_616
| ~ spl107_372
| ~ spl107_392 ),
inference(avatar_split_clause,[],[f8071,f8019,f7912,f10330]) ).
fof(f10330,plain,
( spl107_616
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sK104,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_616])]) ).
fof(f7912,plain,
( spl107_372
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK104,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_372])]) ).
fof(f8071,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sK104,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
| ~ spl107_372
| ~ spl107_392 ),
inference(resolution,[],[f8020,f7914]) ).
fof(f7914,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK104,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
| ~ spl107_372 ),
inference(avatar_component_clause,[],[f7912]) ).
fof(f10328,plain,
spl107_615,
inference(avatar_split_clause,[],[f4614,f10326]) ).
fof(f10326,plain,
( spl107_615
<=> ! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_615])]) ).
fof(f4614,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f2451]) ).
fof(f2451,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(flattening,[],[f2450]) ).
fof(f2450,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f1498]) ).
fof(f1498,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
=> c_Groups_Oabs__class_Oabs(X1,X0) = X0 ) ),
inference(rectify,[],[f127]) ).
fof(f127,axiom,
! [X5,X3] :
( class_Groups_Oordered__ab__group__add__abs(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X5)
=> c_Groups_Oabs__class_Oabs(X3,X5) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10324,plain,
spl107_614,
inference(avatar_split_clause,[],[f4597,f10322]) ).
fof(f10322,plain,
( spl107_614
<=> ! [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,[spl107_614])]) ).
fof(f4597,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,[],[f2439]) ).
fof(f2439,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,[],[f1487]) ).
fof(f1487,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,[],[f284]) ).
fof(f284,axiom,
! [X5,X3] :
( class_Rings_Olinordered__ring(X3)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10320,plain,
spl107_613,
inference(avatar_split_clause,[],[f4596,f10318]) ).
fof(f10318,plain,
( spl107_613
<=> ! [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,[spl107_613])]) ).
fof(f4596,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,[],[f2438]) ).
fof(f2438,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,[],[f1486]) ).
fof(f1486,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,[],[f311]) ).
fof(f311,axiom,
! [X5,X3] :
( class_Rings_Olinordered__ring(X3)
=> ~ c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),X5),c_Groups_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10316,plain,
spl107_612,
inference(avatar_split_clause,[],[f4594,f10314]) ).
fof(f10314,plain,
( spl107_612
<=> ! [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,[spl107_612])]) ).
fof(f4594,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,[],[f2436]) ).
fof(f2436,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,[],[f1484]) ).
fof(f1484,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,[],[f640]) ).
fof(f640,axiom,
! [X6,X3] :
( class_Fields_Ofield(X3)
=> c_Polynomial_Opdivmod__rel(X3,X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10312,plain,
spl107_611,
inference(avatar_split_clause,[],[f4584,f10310]) ).
fof(f10310,plain,
( spl107_611
<=> ! [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,[spl107_611])]) ).
fof(f4584,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,[],[f2430]) ).
fof(f2430,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,[],[f1478]) ).
fof(f1478,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,[],[f239]) ).
fof(f239,axiom,
! [X21,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> c_Groups_Ozero__class_Ozero(X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Ozero__class_Ozero(X3)),X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10308,plain,
spl107_610,
inference(avatar_split_clause,[],[f4582,f10306]) ).
fof(f10306,plain,
( spl107_610
<=> ! [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,[spl107_610])]) ).
fof(f4582,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,[],[f2428]) ).
fof(f2428,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,[],[f1476]) ).
fof(f1476,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,[],[f238]) ).
fof(f238,axiom,
! [X5,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> c_Groups_Ozero__class_Ozero(X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),c_Groups_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10304,plain,
spl107_609,
inference(avatar_split_clause,[],[f4576,f10302]) ).
fof(f10302,plain,
( spl107_609
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(X1,X0)
| ~ class_RealVector_Oreal__normed__vector(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_609])]) ).
fof(f4576,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(X1,X0)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(cnf_transformation,[],[f3675]) ).
fof(f3675,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X1,X0)
| c_Groups_Ozero__class_Ozero(X1) != X0 )
& ( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(X1,X0) ) )
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(nnf_transformation,[],[f2425]) ).
fof(f2425,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(ennf_transformation,[],[f1473]) ).
fof(f1473,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__vector(X1)
=> ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f149]) ).
fof(f149,axiom,
! [X16,X3] :
( class_RealVector_Oreal__normed__vector(X3)
=> ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X3,X16)
<=> c_Groups_Ozero__class_Ozero(X3) = X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10300,plain,
spl107_608,
inference(avatar_split_clause,[],[f4532,f10298]) ).
fof(f10298,plain,
( spl107_608
<=> ! [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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_608])]) ).
fof(f4532,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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X0)),
inference(cnf_transformation,[],[f1433]) ).
fof(f1433,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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X0)),
inference(rectify,[],[f944]) ).
fof(f944,axiom,
! [X41,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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X6)),X41)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10296,plain,
spl107_607,
inference(avatar_split_clause,[],[f4517,f10294]) ).
fof(f10294,plain,
( spl107_607
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(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,[spl107_607])]) ).
fof(f4517,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(cnf_transformation,[],[f3669]) ).
fof(f3669,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,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),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X0)) ) ),
inference(nnf_transformation,[],[f1419]) ).
fof(f1419,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(rectify,[],[f676]) ).
fof(f676,axiom,
! [X65] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X65))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X65) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10292,plain,
spl107_606,
inference(avatar_split_clause,[],[f4516,f10290]) ).
fof(f10290,plain,
( spl107_606
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_606])]) ).
fof(f4516,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X0)) ),
inference(cnf_transformation,[],[f3669]) ).
fof(f10288,plain,
( spl107_605
| ~ spl107_341
| ~ spl107_392 ),
inference(avatar_split_clause,[],[f8070,f8019,f7786,f10285]) ).
fof(f10285,plain,
( spl107_605
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sK51,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_605])]) ).
fof(f7786,plain,
( spl107_341
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK51,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_341])]) ).
fof(f8070,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sK51,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
| ~ spl107_341
| ~ spl107_392 ),
inference(resolution,[],[f8020,f7788]) ).
fof(f7788,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK51,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
| ~ spl107_341 ),
inference(avatar_component_clause,[],[f7786]) ).
fof(f10283,plain,
spl107_604,
inference(avatar_split_clause,[],[f4497,f10281]) ).
fof(f10281,plain,
( spl107_604
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_RealDef_Oreal(tc_Nat_Onat,sK56(X0)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_604])]) ).
fof(f4497,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_RealDef_Oreal(tc_Nat_Onat,sK56(X0)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(cnf_transformation,[],[f3660]) ).
fof(f3660,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_RealDef_Oreal(tc_Nat_Onat,sK56(X0)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,sK56(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK56])],[f2402,f3659]) ).
fof(f3659,plain,
! [X0] :
( ? [X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_RealDef_Oreal(tc_Nat_Onat,X1))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0) )
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_RealDef_Oreal(tc_Nat_Onat,sK56(X0)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,sK56(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f2402,plain,
! [X0] :
( ? [X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_RealDef_Oreal(tc_Nat_Onat,X1))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(ennf_transformation,[],[f1408]) ).
fof(f1408,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
=> ? [X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_RealDef_Oreal(tc_Nat_Onat,X1))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0) ) ),
inference(rectify,[],[f690]) ).
fof(f690,axiom,
! [X25] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X25)
=> ? [X64] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X25,c_RealDef_Oreal(tc_Nat_Onat,X64))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X64,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10279,plain,
spl107_603,
inference(avatar_split_clause,[],[f4493,f10277]) ).
fof(f10277,plain,
( spl107_603
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X0)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_603])]) ).
fof(f4493,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X0)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(cnf_transformation,[],[f2399]) ).
fof(f2399,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X0)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(ennf_transformation,[],[f1405]) ).
fof(f1405,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X0)),X0) ),
inference(rectify,[],[f673]) ).
fof(f673,axiom,
! [X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X6)),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10275,plain,
spl107_602,
inference(avatar_split_clause,[],[f4464,f10273]) ).
fof(f10273,plain,
( spl107_602
<=> ! [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,[spl107_602])]) ).
fof(f4464,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,[],[f2370]) ).
fof(f2370,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,[],[f1376]) ).
fof(f1376,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,[],[f154]) ).
fof(f154,axiom,
! [X3] :
( class_Rings_Olinordered__semidom(X3)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Oone__class_Oone(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f10228,plain,
( spl107_601
| ~ spl107_340
| ~ spl107_392 ),
inference(avatar_split_clause,[],[f8068,f8019,f7781,f10225]) ).
fof(f10225,plain,
( spl107_601
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_d____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_601])]) ).
fof(f7781,plain,
( spl107_340
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_340])]) ).
fof(f8068,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_d____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
| ~ spl107_340
| ~ spl107_392 ),
inference(resolution,[],[f8020,f7783]) ).
fof(f7783,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
| ~ spl107_340 ),
inference(avatar_component_clause,[],[f7781]) ).
fof(f10149,plain,
( spl107_600
| ~ spl107_339
| ~ spl107_392 ),
inference(avatar_split_clause,[],[f8067,f8019,f7776,f10146]) ).
fof(f10146,plain,
( spl107_600
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_600])]) ).
fof(f7776,plain,
( spl107_339
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_339])]) ).
fof(f8067,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
| ~ spl107_339
| ~ spl107_392 ),
inference(resolution,[],[f8020,f7778]) ).
fof(f7778,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
| ~ spl107_339 ),
inference(avatar_component_clause,[],[f7776]) ).
fof(f9896,plain,
( spl107_598
| spl107_599
| ~ spl107_399
| ~ spl107_545 ),
inference(avatar_split_clause,[],[f9842,f9275,f8081,f9893,f9889]) ).
fof(f9889,plain,
( spl107_598
<=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_598])]) ).
fof(f9893,plain,
( spl107_599
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_599])]) ).
fof(f9275,plain,
( spl107_545
<=> ! [X0,X1] :
( X0 = X1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_545])]) ).
fof(f9842,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))
| c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))
| ~ spl107_399
| ~ spl107_545 ),
inference(resolution,[],[f9276,f8083]) ).
fof(f9276,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| X0 = X1 )
| ~ spl107_545 ),
inference(avatar_component_clause,[],[f9275]) ).
fof(f9593,plain,
( spl107_597
| ~ spl107_489 ),
inference(avatar_split_clause,[],[f8805,f8617,f9591]) ).
fof(f9591,plain,
( spl107_597
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X1)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_597])]) ).
fof(f8617,plain,
( spl107_489
<=> ! [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,[spl107_489])]) ).
fof(f8805,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X1)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl107_489 ),
inference(factoring,[],[f8618]) ).
fof(f8618,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) )
| ~ spl107_489 ),
inference(avatar_component_clause,[],[f8617]) ).
fof(f9491,plain,
spl107_596,
inference(avatar_split_clause,[],[f6144,f9489]) ).
fof(f9489,plain,
( spl107_596
<=> ! [X0,X1] :
( c_RealVector_Onorm__class_Onorm(X1,X0) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0))
| ~ class_RealVector_Oreal__normed__vector(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_596])]) ).
fof(f6144,plain,
! [X0,X1] :
( c_RealVector_Onorm__class_Onorm(X1,X0) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(forward_demodulation,[],[f4575,f4388]) ).
fof(f4388,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(cnf_transformation,[],[f1303]) ).
fof(f1303,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(rectify,[],[f98]) ).
fof(f98,axiom,
! [X25] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X25) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4575,plain,
! [X0,X1] :
( c_RealVector_Onorm__class_Onorm(X1,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(cnf_transformation,[],[f2424]) ).
fof(f2424,plain,
! [X0,X1] :
( c_RealVector_Onorm__class_Onorm(X1,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(ennf_transformation,[],[f1472]) ).
fof(f1472,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__vector(X1)
=> c_RealVector_Onorm__class_Onorm(X1,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0)) ),
inference(rectify,[],[f187]) ).
fof(f187,axiom,
! [X5,X3] :
( class_RealVector_Oreal__normed__vector(X3)
=> c_RealVector_Onorm__class_Onorm(X3,X5) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9487,plain,
spl107_595,
inference(avatar_split_clause,[],[f6141,f9485]) ).
fof(f9485,plain,
( spl107_595
<=> ! [X0] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X0) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK53),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_595])]) ).
fof(f6141,plain,
! [X0] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X0) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK53),X0),
inference(forward_demodulation,[],[f4407,f4368]) ).
fof(f4407,plain,
! [X0] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X0) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,X0)),
inference(cnf_transformation,[],[f1322]) ).
fof(f1322,plain,
! [X0] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X0) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,X0)),
inference(rectify,[],[f448]) ).
fof(f448,axiom,
! [X6] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X6) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9481,plain,
spl107_594,
inference(avatar_split_clause,[],[f6140,f9479]) ).
fof(f9479,plain,
( spl107_594
<=> ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_594])]) ).
fof(f6140,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0))),
inference(forward_demodulation,[],[f4405,f4388]) ).
fof(f4405,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0))),
inference(cnf_transformation,[],[f1320]) ).
fof(f1320,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0))),
inference(rectify,[],[f153]) ).
fof(f153,axiom,
! [X6] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X6))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9477,plain,
spl107_593,
inference(avatar_split_clause,[],[f6100,f9475]) ).
fof(f9475,plain,
( spl107_593
<=> ! [X0,X1,X3] :
( 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,[spl107_593])]) ).
fof(f6100,plain,
! [X3,X0,X1] :
( c_Rings_Odvd__class_Odvd(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ class_Rings_Odvd(X3) ),
inference(equality_resolution,[],[f5732]) ).
fof(f5732,plain,
! [X2,X3,X0,X1] :
( 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,[],[f3342]) ).
fof(f3342,plain,
! [X0,X1,X2,X3] :
( 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,[],[f3341]) ).
fof(f3341,plain,
! [X0,X1,X2,X3] :
( 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,[],[f2168]) ).
fof(f2168,plain,
! [X0,X1,X2,X3] :
( class_Rings_Odvd(X3)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0) = X2
=> c_Rings_Odvd__class_Odvd(X3,X1,X2) ) ),
inference(rectify,[],[f822]) ).
fof(f822,axiom,
! [X13,X4,X5,X3] :
( class_Rings_Odvd(X3)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X4),X13) = X5
=> c_Rings_Odvd__class_Odvd(X3,X4,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9473,plain,
spl107_592,
inference(avatar_split_clause,[],[f6058,f9471]) ).
fof(f9471,plain,
( spl107_592
<=> ! [X4,X0,X2] :
( hBOOL(hAPP(X0,X4))
| ~ sP27(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_592])]) ).
fof(f6058,plain,
! [X2,X0,X4] :
( hBOOL(hAPP(X0,X4))
| ~ sP27(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4),X2) ),
inference(equality_resolution,[],[f5402]) ).
fof(f5402,plain,
! [X2,X0,X1,X4] :
( hBOOL(hAPP(X0,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X1
| ~ sP27(X0,X1,X2) ),
inference(cnf_transformation,[],[f3950]) ).
fof(f9469,plain,
spl107_591,
inference(avatar_split_clause,[],[f6057,f9467]) ).
fof(f9467,plain,
( spl107_591
<=> ! [X4,X0,X2] :
( hBOOL(hAPP(X0,X4))
| ~ sP26(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_591])]) ).
fof(f6057,plain,
! [X2,X0,X4] :
( hBOOL(hAPP(X0,X4))
| ~ sP26(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4),X2) ),
inference(equality_resolution,[],[f5394]) ).
fof(f5394,plain,
! [X2,X0,X1,X4] :
( hBOOL(hAPP(X0,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X1
| ~ sP26(X0,X1,X2) ),
inference(cnf_transformation,[],[f3944]) ).
fof(f9465,plain,
spl107_590,
inference(avatar_split_clause,[],[f5943,f9463]) ).
fof(f9463,plain,
( spl107_590
<=> ! [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,[spl107_590])]) ).
fof(f5943,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,[],[f4599]) ).
fof(f4599,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,[],[f3686]) ).
fof(f9461,plain,
spl107_589,
inference(avatar_split_clause,[],[f5408,f9459]) ).
fof(f9459,plain,
( spl107_589
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP27(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_589])]) ).
fof(f5408,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP27(X2,X1,X0) ),
inference(cnf_transformation,[],[f3951]) ).
fof(f3951,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP27(X2,X1,X0) )
& ( sP27(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
inference(nnf_transformation,[],[f3616]) ).
fof(f3616,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
<=> sP27(X2,X1,X0) ),
inference(definition_folding,[],[f3081,f3615]) ).
fof(f3081,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,[],[f1993]) ).
fof(f1993,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,[],[f615]) ).
fof(f615,axiom,
! [X9,X10,X70] :
( hBOOL(hAPP(X70,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,X9)))
<=> ~ ( ? [X29] :
( ~ hBOOL(hAPP(X70,X29))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,X29) = X10 )
| ( ~ hBOOL(hAPP(X70,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9457,plain,
spl107_588,
inference(avatar_split_clause,[],[f5407,f9455]) ).
fof(f9455,plain,
( spl107_588
<=> ! [X2,X0,X1] :
( sP27(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_588])]) ).
fof(f5407,plain,
! [X2,X0,X1] :
( sP27(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f3951]) ).
fof(f9453,plain,
spl107_587,
inference(avatar_split_clause,[],[f5400,f9451]) ).
fof(f9451,plain,
( spl107_587
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP26(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_587])]) ).
fof(f5400,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP26(X2,X1,X0) ),
inference(cnf_transformation,[],[f3945]) ).
fof(f3945,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP26(X2,X1,X0) )
& ( sP26(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
inference(nnf_transformation,[],[f3614]) ).
fof(f3614,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
<=> sP26(X2,X1,X0) ),
inference(definition_folding,[],[f3080,f3613]) ).
fof(f3080,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,[],[f1992]) ).
fof(f1992,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,[],[f614]) ).
fof(f614,axiom,
! [X9,X10,X70] :
( hBOOL(hAPP(X70,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,X9)))
<=> ( ! [X29] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,X29) = X10
=> hBOOL(hAPP(X70,X29)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X9)
=> hBOOL(hAPP(X70,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9449,plain,
spl107_586,
inference(avatar_split_clause,[],[f5399,f9447]) ).
fof(f9447,plain,
( spl107_586
<=> ! [X2,X0,X1] :
( sP26(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_586])]) ).
fof(f5399,plain,
! [X2,X0,X1] :
( sP26(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f3945]) ).
fof(f9445,plain,
spl107_585,
inference(avatar_split_clause,[],[f5390,f9443]) ).
fof(f9443,plain,
( spl107_585
<=> ! [X2,X0,X1] :
( sP25(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_585])]) ).
fof(f5390,plain,
! [X2,X0,X1] :
( sP25(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f3939]) ).
fof(f9439,plain,
spl107_584,
inference(avatar_split_clause,[],[f5388,f9437]) ).
fof(f9437,plain,
( spl107_584
<=> ! [X2,X0,X1] :
( sP25(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK94(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_584])]) ).
fof(f5388,plain,
! [X2,X0,X1] :
( sP25(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK94(X0,X1,X2))) ),
inference(cnf_transformation,[],[f3937]) ).
fof(f3937,plain,
! [X0,X1,X2] :
( ( sP25(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK94(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK93(X0,X1,X2)),sK94(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK94(X0,X1,X2),X2)
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X0,X6))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X2) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ sP25(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK93,sK94])],[f3935,f3936]) ).
fof(f3936,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(X0,X4))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4) = X1
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X2) )
=> ( ~ hBOOL(hAPP(X0,sK94(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK93(X0,X1,X2)),sK94(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK94(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f3935,plain,
! [X0,X1,X2] :
( ( sP25(X0,X1,X2)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X0,X4))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4) = X1
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X2) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X0,X6))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X2) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ sP25(X0,X1,X2) ) ),
inference(rectify,[],[f3934]) ).
fof(f3934,plain,
! [X2,X1,X0] :
( ( sP25(X2,X1,X0)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X2,X4))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X4) = X1
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X0) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( ! [X3,X4] :
( hBOOL(hAPP(X2,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X4) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X0) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP25(X2,X1,X0) ) ),
inference(flattening,[],[f3933]) ).
fof(f3933,plain,
! [X2,X1,X0] :
( ( sP25(X2,X1,X0)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X2,X4))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X4) = X1
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X0) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( ! [X3,X4] :
( hBOOL(hAPP(X2,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X4) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X0) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP25(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f3611]) ).
fof(f9435,plain,
spl107_583,
inference(avatar_split_clause,[],[f5386,f9433]) ).
fof(f9433,plain,
( spl107_583
<=> ! [X2,X0,X1] :
( sP25(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK94(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_583])]) ).
fof(f5386,plain,
! [X2,X0,X1] :
( sP25(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK94(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f3937]) ).
fof(f9431,plain,
spl107_582,
inference(avatar_split_clause,[],[f5383,f9429]) ).
fof(f9429,plain,
( spl107_582
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)))
| ~ sP24(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_582])]) ).
fof(f5383,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)))
| ~ sP24(X0,X1,X2) ),
inference(cnf_transformation,[],[f3932]) ).
fof(f3932,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)))
| ~ sP24(X0,X1,X2) )
& ( sP24(X0,X1,X2)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))) ) ),
inference(nnf_transformation,[],[f3610]) ).
fof(f3610,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)))
<=> sP24(X0,X1,X2) ),
inference(definition_folding,[],[f3077,f3609,f3608,f3607]) ).
fof(f3609,plain,
! [X0,X1,X2] :
( sP24(X0,X1,X2)
<=> ( sP23(X2,X1,X0)
& sP22(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP24])]) ).
fof(f3077,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)))
<=> ( ( ! [X3,X4] :
( hBOOL(hAPP(X2,X4))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4) != X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X2,X6))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) )
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) ) ),
inference(flattening,[],[f3076]) ).
fof(f3076,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)))
<=> ( ( ! [X3,X4] :
( hBOOL(hAPP(X2,X4))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4) != X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X2,X6))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) )
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) ) ),
inference(ennf_transformation,[],[f1990]) ).
fof(f1990,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)))
<=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ! [X3,X4] :
( ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4) )
=> hBOOL(hAPP(X2,X4)) ) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
=> ! [X5,X6] :
( ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5),X6) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X0)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6) )
=> hBOOL(hAPP(X2,X6)) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
=> hBOOL(hAPP(X2,X1)) ) ) ),
inference(rectify,[],[f982]) ).
fof(f982,axiom,
! [X63,X65,X70] :
( hBOOL(hAPP(X70,c_Divides_Odiv__class_Omod(tc_Int_Oint,X65,X63)))
<=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X63,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ! [X80,X81] :
( ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X63),X80),X81) = X65
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X81,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X63,X81) )
=> hBOOL(hAPP(X70,X81)) ) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X63)
=> ! [X80,X81] :
( ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X63),X80),X81) = X65
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X81,X63)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X81) )
=> hBOOL(hAPP(X70,X81)) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X63
=> hBOOL(hAPP(X70,X65)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9427,plain,
spl107_581,
inference(avatar_split_clause,[],[f5382,f9425]) ).
fof(f9425,plain,
( spl107_581
<=> ! [X2,X0,X1] :
( sP24(X0,X1,X2)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_581])]) ).
fof(f5382,plain,
! [X2,X0,X1] :
( sP24(X0,X1,X2)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))) ),
inference(cnf_transformation,[],[f3932]) ).
fof(f9423,plain,
spl107_580,
inference(avatar_split_clause,[],[f5381,f9421]) ).
fof(f9421,plain,
( spl107_580
<=> ! [X2,X0,X1] :
( sP22(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK92(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_580])]) ).
fof(f5381,plain,
! [X2,X0,X1] :
( sP22(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK92(X0,X1,X2))) ),
inference(cnf_transformation,[],[f3931]) ).
fof(f9419,plain,
spl107_579,
inference(avatar_split_clause,[],[f5379,f9417]) ).
fof(f9417,plain,
( spl107_579
<=> ! [X2,X0,X1] :
( sP22(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,sK92(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_579])]) ).
fof(f5379,plain,
! [X2,X0,X1] :
( sP22(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,sK92(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f3931]) ).
fof(f9415,plain,
spl107_578,
inference(avatar_split_clause,[],[f5375,f9413]) ).
fof(f9413,plain,
( spl107_578
<=> ! [X2,X0,X1] :
( sP23(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK90(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_578])]) ).
fof(f5375,plain,
! [X2,X0,X1] :
( sP23(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK90(X0,X1,X2))) ),
inference(cnf_transformation,[],[f3926]) ).
fof(f9411,plain,
spl107_577,
inference(avatar_split_clause,[],[f5372,f9409]) ).
fof(f9409,plain,
( spl107_577
<=> ! [X2,X0,X1] :
( sP23(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,sK90(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_577])]) ).
fof(f5372,plain,
! [X2,X0,X1] :
( sP23(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,sK90(X0,X1,X2)) ),
inference(cnf_transformation,[],[f3926]) ).
fof(f9407,plain,
spl107_576,
inference(avatar_split_clause,[],[f5362,f9405]) ).
fof(f9405,plain,
( spl107_576
<=> ! [X2,X0,X1] :
( sP21(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_576])]) ).
fof(f5362,plain,
! [X2,X0,X1] :
( sP21(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f3919]) ).
fof(f9403,plain,
spl107_575,
inference(avatar_split_clause,[],[f5360,f9401]) ).
fof(f9401,plain,
( spl107_575
<=> ! [X2,X0,X1] :
( sP21(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK87(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_575])]) ).
fof(f5360,plain,
! [X2,X0,X1] :
( sP21(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK87(X0,X1,X2))) ),
inference(cnf_transformation,[],[f3917]) ).
fof(f3917,plain,
! [X0,X1,X2] :
( ( sP21(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK87(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK87(X0,X1,X2)),sK88(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK88(X0,X1,X2),X2)
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X0,X5))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X2) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ sP21(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK87,sK88])],[f3915,f3916]) ).
fof(f3916,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(X0,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4) = X1
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X2) )
=> ( ~ hBOOL(hAPP(X0,sK87(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK87(X0,X1,X2)),sK88(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK88(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f3915,plain,
! [X0,X1,X2] :
( ( sP21(X0,X1,X2)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X0,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4) = X1
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X2) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X0,X5))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X2) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ sP21(X0,X1,X2) ) ),
inference(rectify,[],[f3914]) ).
fof(f3914,plain,
! [X2,X1,X0] :
( ( sP21(X2,X1,X0)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X2,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X4) = X1
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X0) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( ! [X3,X4] :
( hBOOL(hAPP(X2,X3))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X4) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X0) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP21(X2,X1,X0) ) ),
inference(flattening,[],[f3913]) ).
fof(f3913,plain,
! [X2,X1,X0] :
( ( sP21(X2,X1,X0)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X2,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X4) = X1
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X0) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( ! [X3,X4] :
( hBOOL(hAPP(X2,X3))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X4) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X0) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP21(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f3605]) ).
fof(f9397,plain,
spl107_574,
inference(avatar_split_clause,[],[f5358,f9395]) ).
fof(f9395,plain,
( spl107_574
<=> ! [X2,X0,X1] :
( sP21(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK88(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_574])]) ).
fof(f5358,plain,
! [X2,X0,X1] :
( sP21(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK88(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f3917]) ).
fof(f9393,plain,
spl107_573,
inference(avatar_split_clause,[],[f5355,f9391]) ).
fof(f9391,plain,
( spl107_573
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)))
| ~ sP20(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_573])]) ).
fof(f5355,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)))
| ~ sP20(X0,X1,X2) ),
inference(cnf_transformation,[],[f3912]) ).
fof(f3912,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)))
| ~ sP20(X0,X1,X2) )
& ( sP20(X0,X1,X2)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0))) ) ),
inference(nnf_transformation,[],[f3604]) ).
fof(f3604,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)))
<=> sP20(X0,X1,X2) ),
inference(definition_folding,[],[f3073,f3603,f3602,f3601]) ).
fof(f3603,plain,
! [X0,X1,X2] :
( sP20(X0,X1,X2)
<=> ( sP19(X2,X1,X0)
& sP18(X2,X1,X0)
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP20])]) ).
fof(f3073,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)))
<=> ( ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| ! [X4] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4) != X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ! [X5] :
( hBOOL(hAPP(X2,X5))
| ! [X6] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5),X6) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) ) ),
inference(ennf_transformation,[],[f1988]) ).
fof(f1988,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)))
<=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ! [X3] :
( ? [X4] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4) )
=> hBOOL(hAPP(X2,X3)) ) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
=> ! [X5] :
( ? [X6] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5),X6) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X0)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6) )
=> hBOOL(hAPP(X2,X5)) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
=> hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
inference(rectify,[],[f966]) ).
fof(f966,axiom,
! [X63,X65,X70] :
( hBOOL(hAPP(X70,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X65,X63)))
<=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X63,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ! [X80] :
( ? [X81] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X63),X80),X81) = X65
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X81,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X63,X81) )
=> hBOOL(hAPP(X70,X80)) ) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X63)
=> ! [X80] :
( ? [X81] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X63),X80),X81) = X65
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X81,X63)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X81) )
=> hBOOL(hAPP(X70,X80)) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X63
=> hBOOL(hAPP(X70,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9389,plain,
spl107_572,
inference(avatar_split_clause,[],[f5354,f9387]) ).
fof(f9387,plain,
( spl107_572
<=> ! [X2,X0,X1] :
( sP20(X0,X1,X2)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_572])]) ).
fof(f5354,plain,
! [X2,X0,X1] :
( sP20(X0,X1,X2)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0))) ),
inference(cnf_transformation,[],[f3912]) ).
fof(f9385,plain,
spl107_571,
inference(avatar_split_clause,[],[f5353,f9383]) ).
fof(f9383,plain,
( spl107_571
<=> ! [X2,X0,X1] :
( sP18(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK85(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_571])]) ).
fof(f5353,plain,
! [X2,X0,X1] :
( sP18(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK85(X0,X1,X2))) ),
inference(cnf_transformation,[],[f3911]) ).
fof(f9381,plain,
spl107_570,
inference(avatar_split_clause,[],[f5351,f9379]) ).
fof(f9379,plain,
( spl107_570
<=> ! [X2,X0,X1] :
( sP18(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,sK86(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_570])]) ).
fof(f5351,plain,
! [X2,X0,X1] :
( sP18(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,sK86(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f3911]) ).
fof(f9377,plain,
spl107_569,
inference(avatar_split_clause,[],[f5347,f9375]) ).
fof(f9375,plain,
( spl107_569
<=> ! [X2,X0,X1] :
( sP19(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK83(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_569])]) ).
fof(f5347,plain,
! [X2,X0,X1] :
( sP19(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK83(X0,X1,X2))) ),
inference(cnf_transformation,[],[f3905]) ).
fof(f9373,plain,
spl107_568,
inference(avatar_split_clause,[],[f5344,f9371]) ).
fof(f9371,plain,
( spl107_568
<=> ! [X2,X0,X1] :
( sP19(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,sK84(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_568])]) ).
fof(f5344,plain,
! [X2,X0,X1] :
( sP19(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,sK84(X0,X1,X2)) ),
inference(cnf_transformation,[],[f3905]) ).
fof(f9369,plain,
spl107_567,
inference(avatar_split_clause,[],[f5310,f9367]) ).
fof(f9367,plain,
( spl107_567
<=> ! [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,[spl107_567])]) ).
fof(f5310,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,[],[f3046]) ).
fof(f3046,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,[],[f1974]) ).
fof(f1974,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,[],[f577]) ).
fof(f577,axiom,
! [X13,X14,X15] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X14),X13)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9365,plain,
spl107_566,
inference(avatar_split_clause,[],[f5307,f9363]) ).
fof(f9363,plain,
( spl107_566
<=> ! [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,[spl107_566])]) ).
fof(f5307,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,[],[f3044]) ).
fof(f3044,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,[],[f1972]) ).
fof(f1972,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,[],[f604]) ).
fof(f604,axiom,
! [X41,X13,X42] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X13),X41)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9361,plain,
spl107_565,
inference(avatar_split_clause,[],[f5306,f9359]) ).
fof(f9359,plain,
( spl107_565
<=> ! [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,[spl107_565])]) ).
fof(f5306,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,[],[f3043]) ).
fof(f3043,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,[],[f1971]) ).
fof(f1971,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,[],[f605]) ).
fof(f605,axiom,
! [X41,X13,X42] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X13),X41)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9355,plain,
spl107_564,
inference(avatar_split_clause,[],[f5280,f9353]) ).
fof(f9353,plain,
( spl107_564
<=> ! [X2,X0,X1] :
( sP15(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,sK80(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_564])]) ).
fof(f5280,plain,
! [X2,X0,X1] :
( sP15(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,sK80(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f3880]) ).
fof(f9351,plain,
spl107_563,
inference(avatar_split_clause,[],[f5269,f9349]) ).
fof(f9349,plain,
( spl107_563
<=> ! [X2,X0,X1] :
( sP13(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,sK78(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_563])]) ).
fof(f5269,plain,
! [X2,X0,X1] :
( sP13(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,sK78(X0,X1,X2)) ),
inference(cnf_transformation,[],[f3874]) ).
fof(f9347,plain,
spl107_562,
inference(avatar_split_clause,[],[f5259,f9345]) ).
fof(f9345,plain,
( spl107_562
<=> ! [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,[spl107_562])]) ).
fof(f5259,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,[],[f3003]) ).
fof(f3003,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,[],[f1945]) ).
fof(f1945,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,[],[f512]) ).
fof(f512,axiom,
! [X41,X13,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X13)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X14,X41),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9343,plain,
spl107_561,
inference(avatar_split_clause,[],[f5257,f9341]) ).
fof(f9341,plain,
( spl107_561
<=> ! [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,[spl107_561])]) ).
fof(f5257,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,[],[f3001]) ).
fof(f3001,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,[],[f1943]) ).
fof(f1943,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,[],[f651]) ).
fof(f651,axiom,
! [X21,X12,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X12)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9339,plain,
spl107_560,
inference(avatar_split_clause,[],[f5255,f9337]) ).
fof(f9337,plain,
( spl107_560
<=> ! [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,[spl107_560])]) ).
fof(f5255,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,[],[f2999]) ).
fof(f2999,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,[],[f1941]) ).
fof(f1941,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,[],[f572]) ).
fof(f572,axiom,
! [X42,X14,X15] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X14)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9335,plain,
spl107_559,
inference(avatar_split_clause,[],[f5222,f9333]) ).
fof(f9333,plain,
( spl107_559
<=> ! [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,[spl107_559])]) ).
fof(f5222,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,[],[f2968]) ).
fof(f2968,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,[],[f1917]) ).
fof(f1917,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,[],[f591]) ).
fof(f591,axiom,
! [X42,X14,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X14)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9331,plain,
spl107_558,
inference(avatar_split_clause,[],[f5221,f9329]) ).
fof(f9329,plain,
( spl107_558
<=> ! [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,[spl107_558])]) ).
fof(f5221,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,[],[f2967]) ).
fof(f2967,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,[],[f1916]) ).
fof(f1916,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,[],[f592]) ).
fof(f592,axiom,
! [X42,X14,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X14)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9327,plain,
spl107_557,
inference(avatar_split_clause,[],[f5162,f9325]) ).
fof(f9325,plain,
( spl107_557
<=> ! [X2,X0,X1] :
( 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,[spl107_557])]) ).
fof(f5162,plain,
! [X2,X0,X1] :
( 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,[],[f2898]) ).
fof(f2898,plain,
! [X0,X1,X2] :
( 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,[],[f1874]) ).
fof(f1874,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Rings_Odvd__class_Odvd(X2,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)) ),
inference(rectify,[],[f818]) ).
fof(f818,axiom,
! [X4,X5,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Rings_Odvd__class_Odvd(X3,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X4),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9323,plain,
spl107_556,
inference(avatar_split_clause,[],[f5161,f9321]) ).
fof(f9321,plain,
( spl107_556
<=> ! [X2,X0,X1] :
( 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,[spl107_556])]) ).
fof(f5161,plain,
! [X2,X0,X1] :
( 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,[],[f2897]) ).
fof(f2897,plain,
! [X0,X1,X2] :
( 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,[],[f1873]) ).
fof(f1873,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Rings_Odvd__class_Odvd(X2,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)) ),
inference(rectify,[],[f817]) ).
fof(f817,axiom,
! [X4,X5,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Rings_Odvd__class_Odvd(X3,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9319,plain,
spl107_555,
inference(avatar_split_clause,[],[f5160,f9317]) ).
fof(f9317,plain,
( spl107_555
<=> ! [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,[spl107_555])]) ).
fof(f5160,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,[],[f2896]) ).
fof(f2896,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,[],[f1872]) ).
fof(f1872,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,[],[f412]) ).
fof(f412,axiom,
! [X22,X5,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,X5,X22) = c_Groups_Oplus__class_Oplus(X3,X22,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9313,plain,
spl107_554,
inference(avatar_split_clause,[],[f5078,f9311]) ).
fof(f9311,plain,
( spl107_554
<=> ! [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,[spl107_554])]) ).
fof(f5078,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,[],[f2785]) ).
fof(f2785,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,[],[f1809]) ).
fof(f1809,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,[],[f188]) ).
fof(f188,axiom,
! [X4,X5,X3] :
( class_Groups_Ogroup__add(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X5,X4),X4) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9309,plain,
spl107_553,
inference(avatar_split_clause,[],[f5077,f9307]) ).
fof(f9307,plain,
( spl107_553
<=> ! [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,[spl107_553])]) ).
fof(f5077,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,[],[f2784]) ).
fof(f2784,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,[],[f1808]) ).
fof(f1808,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,[],[f189]) ).
fof(f189,axiom,
! [X4,X5,X3] :
( class_Groups_Ogroup__add(X3)
=> c_Groups_Ominus__class_Ominus(X3,c_Groups_Oplus__class_Oplus(X3,X5,X4),X4) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9305,plain,
spl107_552,
inference(avatar_split_clause,[],[f4854,f9303]) ).
fof(f9303,plain,
( spl107_552
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X0))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_552])]) ).
fof(f4854,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X0))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f3757]) ).
fof(f3757,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X0))
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X0)) ) ),
inference(nnf_transformation,[],[f3574]) ).
fof(f3574,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X0))
<=> sP0(X0,X1) ),
inference(definition_folding,[],[f1677,f3573]) ).
fof(f1677,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X0))
<=> ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ),
inference(rectify,[],[f145]) ).
fof(f145,axiom,
! [X20,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X16,X20))
<=> ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X16) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X20)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9301,plain,
spl107_551,
inference(avatar_split_clause,[],[f4853,f9299]) ).
fof(f9299,plain,
( spl107_551
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_551])]) ).
fof(f4853,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X0)) ),
inference(cnf_transformation,[],[f3757]) ).
fof(f9297,plain,
spl107_550,
inference(avatar_split_clause,[],[f4846,f9295]) ).
fof(f9295,plain,
( spl107_550
<=> ! [X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_550])]) ).
fof(f4846,plain,
! [X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3754]) ).
fof(f3754,plain,
! [X0,X1] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) )
& ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ) ),
inference(nnf_transformation,[],[f1676]) ).
fof(f1676,plain,
! [X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
<=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f853]) ).
fof(f853,axiom,
! [X65,X63] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X63,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X65,X63))
<=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X63,X65) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9293,plain,
spl107_549,
inference(avatar_split_clause,[],[f4845,f9291]) ).
fof(f9291,plain,
( spl107_549
<=> ! [X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
| ~ 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,[spl107_549])]) ).
fof(f4845,plain,
! [X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(cnf_transformation,[],[f3754]) ).
fof(f9289,plain,
spl107_548,
inference(avatar_split_clause,[],[f4841,f9287]) ).
fof(f9287,plain,
( spl107_548
<=> ! [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,[spl107_548])]) ).
fof(f4841,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,[],[f3752]) ).
fof(f3752,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,[],[f3751]) ).
fof(f3751,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,[],[f1674]) ).
fof(f1674,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,[],[f560]) ).
fof(f560,axiom,
! [X65,X66] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X66,X65)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X65
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X66 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9285,plain,
spl107_547,
inference(avatar_split_clause,[],[f4840,f9283]) ).
fof(f9283,plain,
( spl107_547
<=> ! [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,[spl107_547])]) ).
fof(f4840,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,[],[f3752]) ).
fof(f9281,plain,
spl107_546,
inference(avatar_split_clause,[],[f4838,f9279]) ).
fof(f9279,plain,
( spl107_546
<=> ! [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,[spl107_546])]) ).
fof(f4838,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,[],[f3750]) ).
fof(f3750,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,[],[f1673]) ).
fof(f1673,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,[],[f566]) ).
fof(f566,axiom,
! [X65,X66] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X66,X65)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,X65) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9277,plain,
spl107_545,
inference(avatar_split_clause,[],[f4812,f9275]) ).
fof(f4812,plain,
! [X0,X1] :
( X0 = X1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f3724]) ).
fof(f3724,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ( X0 != X1
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) )
& ( X0 = X1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
inference(flattening,[],[f3723]) ).
fof(f3723,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ( X0 != X1
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) )
& ( X0 = X1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
inference(nnf_transformation,[],[f1662]) ).
fof(f1662,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
<=> ( X0 = X1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) ),
inference(rectify,[],[f61]) ).
fof(f61,axiom,
! [X20,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16,X20)
<=> ( X16 = X20
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X16,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9271,plain,
spl107_544,
inference(avatar_split_clause,[],[f4776,f9269]) ).
fof(f4776,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X0) ),
inference(cnf_transformation,[],[f2623]) ).
fof(f2623,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X0) ),
inference(ennf_transformation,[],[f1638]) ).
fof(f1638,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X0)) ),
inference(rectify,[],[f674]) ).
fof(f674,axiom,
! [X5,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X6),X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,c_RComplete_Onatfloor(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9267,plain,
spl107_543,
inference(avatar_split_clause,[],[f4775,f9265]) ).
fof(f4775,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X0)) ),
inference(cnf_transformation,[],[f2622]) ).
fof(f2622,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X0)) ),
inference(ennf_transformation,[],[f1637]) ).
fof(f1637,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X0))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X0) ),
inference(rectify,[],[f675]) ).
fof(f675,axiom,
! [X5,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,c_RealDef_Oreal(tc_Nat_Onat,X5))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X6),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9263,plain,
spl107_542,
inference(avatar_split_clause,[],[f4730,f9261]) ).
fof(f9261,plain,
( spl107_542
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_542])]) ).
fof(f4730,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2570]) ).
fof(f2570,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1600]) ).
fof(f1600,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f713]) ).
fof(f713,axiom,
! [X41,X42] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X41)
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X42,X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9259,plain,
spl107_541,
inference(avatar_split_clause,[],[f4722,f9257]) ).
fof(f9257,plain,
( spl107_541
<=> ! [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,[spl107_541])]) ).
fof(f4722,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,[],[f2562]) ).
fof(f2562,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,[],[f2561]) ).
fof(f2561,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,[],[f1592]) ).
fof(f1592,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,[],[f531]) ).
fof(f531,axiom,
! [X41,X42] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X41)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,X42)
=> X41 = X42 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9255,plain,
spl107_540,
inference(avatar_split_clause,[],[f4721,f9253]) ).
fof(f9253,plain,
( spl107_540
<=> ! [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,[spl107_540])]) ).
fof(f4721,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,[],[f2560]) ).
fof(f2560,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,[],[f2559]) ).
fof(f2559,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,[],[f1591]) ).
fof(f1591,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,[],[f579]) ).
fof(f579,axiom,
! [X41,X42] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X41)
=> ( X41 != X42
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X41) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9251,plain,
spl107_539,
inference(avatar_split_clause,[],[f4715,f9249]) ).
fof(f4715,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,[],[f2553]) ).
fof(f2553,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,[],[f1585]) ).
fof(f1585,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,[],[f565]) ).
fof(f565,axiom,
! [X41,X42] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X41)
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X42,X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9247,plain,
spl107_538,
inference(avatar_split_clause,[],[f4714,f9245]) ).
fof(f9245,plain,
( spl107_538
<=> ! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_538])]) ).
fof(f4714,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f2552]) ).
fof(f2552,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(flattening,[],[f2551]) ).
fof(f2551,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(ennf_transformation,[],[f1584]) ).
fof(f1584,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
=> X0 = X1 ) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X11,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,X11)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11,X12)
=> X11 = X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9243,plain,
spl107_537,
inference(avatar_split_clause,[],[f4689,f9241]) ).
fof(f9241,plain,
( spl107_537
<=> ! [X0,X1] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_537])]) ).
fof(f4689,plain,
! [X0,X1] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f2521]) ).
fof(f2521,plain,
! [X0,X1] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) )
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
| X0 = X1 ),
inference(flattening,[],[f2520]) ).
fof(f2520,plain,
! [X0,X1] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) )
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
| X0 = X1 ),
inference(ennf_transformation,[],[f1563]) ).
fof(f1563,plain,
! [X0,X1] :
( X0 != X1
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0)
=> ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X1)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X0) ) ) ),
inference(rectify,[],[f849]) ).
fof(f849,axiom,
! [X4,X5] :
( X4 != X5
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5,X4)
=> ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X4,X5)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9239,plain,
spl107_536,
inference(avatar_split_clause,[],[f4687,f9237]) ).
fof(f9237,plain,
( spl107_536
<=> ! [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,[spl107_536])]) ).
fof(f4687,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,[],[f2519]) ).
fof(f2519,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,[],[f2518]) ).
fof(f2518,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,[],[f1562]) ).
fof(f1562,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,[],[f509]) ).
fof(f509,axiom,
! [X21,X6] :
( X6 != X21
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X21)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9235,plain,
spl107_535,
inference(avatar_split_clause,[],[f4677,f9233]) ).
fof(f9233,plain,
( spl107_535
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ 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,[spl107_535])]) ).
fof(f4677,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2510]) ).
fof(f2510,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(flattening,[],[f2509]) ).
fof(f2509,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1554]) ).
fof(f1554,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Ozero__class_Ozero(X1),X0)
=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f809]) ).
fof(f809,axiom,
! [X5,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,c_Groups_Ozero__class_Ozero(X3),X5)
=> c_Groups_Ozero__class_Ozero(X3) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9229,plain,
spl107_534,
inference(avatar_split_clause,[],[f4671,f9227]) ).
fof(f9227,plain,
( spl107_534
<=> ! [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,[spl107_534])]) ).
fof(f4671,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,[],[f2503]) ).
fof(f2503,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,[],[f1548]) ).
fof(f1548,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,[],[f429]) ).
fof(f429,axiom,
! [X5,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Oone__class_Oone(X3)),X5) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9225,plain,
spl107_533,
inference(avatar_split_clause,[],[f4670,f9223]) ).
fof(f9223,plain,
( spl107_533
<=> ! [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,[spl107_533])]) ).
fof(f4670,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,[],[f2502]) ).
fof(f2502,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,[],[f1547]) ).
fof(f1547,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,[],[f428]) ).
fof(f428,axiom,
! [X5,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),c_Groups_Oone__class_Oone(X3)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9221,plain,
spl107_532,
inference(avatar_split_clause,[],[f4669,f9219]) ).
fof(f9219,plain,
( spl107_532
<=> ! [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,[spl107_532])]) ).
fof(f4669,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,[],[f2501]) ).
fof(f2501,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,[],[f1546]) ).
fof(f1546,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,[],[f879]) ).
fof(f879,axiom,
! [X6,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X3),X6),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9217,plain,
spl107_531,
inference(avatar_split_clause,[],[f4658,f9215]) ).
fof(f9215,plain,
( spl107_531
<=> ! [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,[spl107_531])]) ).
fof(f4658,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,[],[f2490]) ).
fof(f2490,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,[],[f1535]) ).
fof(f1535,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,[],[f466]) ).
fof(f466,axiom,
! [X57,X3] :
( class_Groups_Ocomm__monoid__add(X3)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X57) = X57 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9213,plain,
spl107_530,
inference(avatar_split_clause,[],[f4657,f9211]) ).
fof(f9211,plain,
( spl107_530
<=> ! [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,[spl107_530])]) ).
fof(f4657,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,[],[f2489]) ).
fof(f2489,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,[],[f1534]) ).
fof(f1534,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,[],[f465]) ).
fof(f465,axiom,
! [X58,X3] :
( class_Groups_Ocomm__monoid__add(X3)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),X58,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))) = X58 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9209,plain,
spl107_529,
inference(avatar_split_clause,[],[f4653,f9207]) ).
fof(f9207,plain,
( spl107_529
<=> ! [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,[spl107_529])]) ).
fof(f4653,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,[],[f2485]) ).
fof(f2485,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,[],[f1530]) ).
fof(f1530,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,[],[f254]) ).
fof(f254,axiom,
! [X5,X3] :
( class_Groups_Omonoid__mult(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Oone__class_Oone(X3)),X5) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9205,plain,
spl107_528,
inference(avatar_split_clause,[],[f4652,f9203]) ).
fof(f9203,plain,
( spl107_528
<=> ! [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,[spl107_528])]) ).
fof(f4652,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,[],[f2484]) ).
fof(f2484,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,[],[f1529]) ).
fof(f1529,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,[],[f252]) ).
fof(f252,axiom,
! [X5,X3] :
( class_Groups_Omonoid__mult(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),c_Groups_Oone__class_Oone(X3)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9201,plain,
spl107_527,
inference(avatar_split_clause,[],[f4651,f9199]) ).
fof(f9199,plain,
( spl107_527
<=> ! [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,[spl107_527])]) ).
fof(f4651,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,[],[f2483]) ).
fof(f2483,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,[],[f1528]) ).
fof(f1528,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,[],[f910]) ).
fof(f910,axiom,
! [X5,X3] :
( class_Groups_Omonoid__mult(X3)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X3),X5),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9197,plain,
spl107_526,
inference(avatar_split_clause,[],[f4643,f9195]) ).
fof(f9195,plain,
( spl107_526
<=> ! [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,[spl107_526])]) ).
fof(f4643,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,[],[f2477]) ).
fof(f2477,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,[],[f1522]) ).
fof(f1522,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,[],[f253]) ).
fof(f253,axiom,
! [X5,X3] :
( class_Groups_Ocomm__monoid__mult(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Oone__class_Oone(X3)),X5) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9193,plain,
spl107_525,
inference(avatar_split_clause,[],[f4642,f9191]) ).
fof(f9191,plain,
( spl107_525
<=> ! [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,[spl107_525])]) ).
fof(f4642,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,[],[f2476]) ).
fof(f2476,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,[],[f1521]) ).
fof(f1521,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,[],[f251]) ).
fof(f251,axiom,
! [X5,X3] :
( class_Groups_Ocomm__monoid__mult(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X5),c_Groups_Oone__class_Oone(X3)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9187,plain,
spl107_524,
inference(avatar_split_clause,[],[f4636,f9185]) ).
fof(f9185,plain,
( spl107_524
<=> ! [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,[spl107_524])]) ).
fof(f4636,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,[],[f2471]) ).
fof(f2471,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,[],[f1516]) ).
fof(f1516,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,[],[f464]) ).
fof(f464,axiom,
! [X58,X3] :
( class_Groups_Oab__group__add(X3)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3),X58,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))) = X58 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9183,plain,
spl107_523,
inference(avatar_split_clause,[],[f4613,f9181]) ).
fof(f9181,plain,
( spl107_523
<=> ! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X1,X0) = c_Groups_Oabs__class_Oabs(X1,c_Groups_Oabs__class_Oabs(X1,X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_523])]) ).
fof(f4613,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X1,X0) = c_Groups_Oabs__class_Oabs(X1,c_Groups_Oabs__class_Oabs(X1,X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f2449]) ).
fof(f2449,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X1,X0) = c_Groups_Oabs__class_Oabs(X1,c_Groups_Oabs__class_Oabs(X1,X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f1497]) ).
fof(f1497,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> c_Groups_Oabs__class_Oabs(X1,X0) = c_Groups_Oabs__class_Oabs(X1,c_Groups_Oabs__class_Oabs(X1,X0)) ),
inference(rectify,[],[f99]) ).
fof(f99,axiom,
! [X5,X3] :
( class_Groups_Oordered__ab__group__add__abs(X3)
=> c_Groups_Oabs__class_Oabs(X3,X5) = c_Groups_Oabs__class_Oabs(X3,c_Groups_Oabs__class_Oabs(X3,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9179,plain,
spl107_522,
inference(avatar_split_clause,[],[f4564,f9177]) ).
fof(f9177,plain,
( spl107_522
<=> ! [X0,X1] :
( c_RealDef_Opositive(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0))
| ~ c_RealDef_Opositive(X0)
| ~ c_RealDef_Opositive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_522])]) ).
fof(f4564,plain,
! [X0,X1] :
( c_RealDef_Opositive(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0))
| ~ c_RealDef_Opositive(X0)
| ~ c_RealDef_Opositive(X1) ),
inference(cnf_transformation,[],[f2414]) ).
fof(f2414,plain,
! [X0,X1] :
( c_RealDef_Opositive(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0))
| ~ c_RealDef_Opositive(X0)
| ~ c_RealDef_Opositive(X1) ),
inference(flattening,[],[f2413]) ).
fof(f2413,plain,
! [X0,X1] :
( c_RealDef_Opositive(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0))
| ~ c_RealDef_Opositive(X0)
| ~ c_RealDef_Opositive(X1) ),
inference(ennf_transformation,[],[f1463]) ).
fof(f1463,plain,
! [X0,X1] :
( c_RealDef_Opositive(X1)
=> ( c_RealDef_Opositive(X0)
=> c_RealDef_Opositive(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0)) ) ),
inference(rectify,[],[f267]) ).
fof(f267,axiom,
! [X21,X6] :
( c_RealDef_Opositive(X6)
=> ( c_RealDef_Opositive(X21)
=> c_RealDef_Opositive(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X6),X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9175,plain,
spl107_521,
inference(avatar_split_clause,[],[f4514,f9173]) ).
fof(f9173,plain,
( spl107_521
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_521])]) ).
fof(f4514,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(cnf_transformation,[],[f3668]) ).
fof(f3668,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| 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_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(nnf_transformation,[],[f1418]) ).
fof(f1418,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(rectify,[],[f671]) ).
fof(f671,axiom,
! [X65] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X65),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X65 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9171,plain,
spl107_520,
inference(avatar_split_clause,[],[f4513,f9169]) ).
fof(f9169,plain,
( spl107_520
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_520])]) ).
fof(f4513,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(cnf_transformation,[],[f3667]) ).
fof(f3667,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(nnf_transformation,[],[f1417]) ).
fof(f1417,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(rectify,[],[f634]) ).
fof(f634,axiom,
! [X16] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X16),c_Groups_Oone__class_Oone(tc_Nat_Onat))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9167,plain,
spl107_519,
inference(avatar_split_clause,[],[f4512,f9165]) ).
fof(f9165,plain,
( spl107_519
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_519])]) ).
fof(f4512,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(cnf_transformation,[],[f3667]) ).
fof(f9163,plain,
spl107_518,
inference(avatar_split_clause,[],[f4511,f9161]) ).
fof(f9161,plain,
( spl107_518
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_518])]) ).
fof(f4511,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) ),
inference(cnf_transformation,[],[f3666]) ).
fof(f3666,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X0)) ) ),
inference(nnf_transformation,[],[f1416]) ).
fof(f1416,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) ),
inference(rectify,[],[f633]) ).
fof(f633,axiom,
! [X16] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X16))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9159,plain,
spl107_517,
inference(avatar_split_clause,[],[f4510,f9157]) ).
fof(f9157,plain,
( spl107_517
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_517])]) ).
fof(f4510,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X0)) ),
inference(cnf_transformation,[],[f3666]) ).
fof(f9155,plain,
spl107_516,
inference(avatar_split_clause,[],[f4503,f9153]) ).
fof(f9153,plain,
( spl107_516
<=> ! [X0] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_516])]) ).
fof(f4503,plain,
! [X0] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0) ),
inference(cnf_transformation,[],[f3662]) ).
fof(f3662,plain,
! [X0] :
( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0) )
& ( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(nnf_transformation,[],[f1412]) ).
fof(f1412,plain,
! [X0] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0) ),
inference(rectify,[],[f955]) ).
fof(f955,axiom,
! [X16] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X16,c_Groups_Oone__class_Oone(tc_Int_Oint))
<=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,X16) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9151,plain,
spl107_515,
inference(avatar_split_clause,[],[f4502,f9149]) ).
fof(f9149,plain,
( spl107_515
<=> ! [X0] :
( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_515])]) ).
fof(f4502,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3662]) ).
fof(f9145,plain,
spl107_514,
inference(avatar_split_clause,[],[f4472,f9143]) ).
fof(f9143,plain,
( spl107_514
<=> ! [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,[spl107_514])]) ).
fof(f4472,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,[],[f2378]) ).
fof(f2378,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,[],[f1384]) ).
fof(f1384,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,[],[f942]) ).
fof(f942,axiom,
! [X3] :
( class_Power_Opower(X3)
=> c_Power_Opower__class_Opower(X3) = c_Power_Opower_Opower(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Otimes__class_Otimes(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9141,plain,
spl107_513,
inference(avatar_split_clause,[],[f4406,f9139]) ).
fof(f9139,plain,
( spl107_513
<=> ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_513])]) ).
fof(f4406,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X0))),
inference(cnf_transformation,[],[f1321]) ).
fof(f1321,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X0))),
inference(rectify,[],[f683]) ).
fof(f683,axiom,
! [X6] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X6,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X6))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9137,plain,
spl107_512,
inference(avatar_split_clause,[],[f4404,f9135]) ).
fof(f9135,plain,
( spl107_512
<=> ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_512])]) ).
fof(f4404,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(cnf_transformation,[],[f1319]) ).
fof(f1319,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(rectify,[],[f681]) ).
fof(f681,axiom,
! [X6] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X6,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X6)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8904,plain,
( ~ spl107_107
| ~ spl107_511
| ~ spl107_399
| ~ spl107_491 ),
inference(avatar_split_clause,[],[f8845,f8625,f8081,f8901,f6706]) ).
fof(f8901,plain,
( spl107_511
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_511])]) ).
fof(f8625,plain,
( spl107_491
<=> ! [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,[spl107_491])]) ).
fof(f8845,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ spl107_399
| ~ spl107_491 ),
inference(resolution,[],[f8626,f8083]) ).
fof(f8626,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl107_491 ),
inference(avatar_component_clause,[],[f8625]) ).
fof(f8704,plain,
spl107_510,
inference(avatar_split_clause,[],[f6139,f8702]) ).
fof(f8702,plain,
( spl107_510
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_510])]) ).
fof(f6139,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0),
inference(forward_demodulation,[],[f4401,f4388]) ).
fof(f4401,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0),
inference(cnf_transformation,[],[f1316]) ).
fof(f1316,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0),
inference(rectify,[],[f163]) ).
fof(f163,axiom,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X6),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8700,plain,
spl107_509,
inference(avatar_split_clause,[],[f6083,f8698]) ).
fof(f8698,plain,
( spl107_509
<=> ! [X0,X1,X3] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ sP42(X0,X1,c_Groups_Ozero__class_Ozero(X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_509])]) ).
fof(f6083,plain,
! [X3,X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ sP42(X0,X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(equality_resolution,[],[f5563]) ).
fof(f5563,plain,
! [X2,X3,X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != X2
| ~ sP42(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4027]) ).
fof(f8696,plain,
spl107_508,
inference(avatar_split_clause,[],[f6075,f8694]) ).
fof(f8694,plain,
( spl107_508
<=> ! [X0,X1,X3] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ sP40(X0,X1,c_Groups_Ozero__class_Ozero(X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_508])]) ).
fof(f6075,plain,
! [X3,X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ sP40(X0,X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(equality_resolution,[],[f5554]) ).
fof(f5554,plain,
! [X2,X3,X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != X2
| ~ sP40(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f4022]) ).
fof(f8692,plain,
spl107_507,
inference(avatar_split_clause,[],[f6045,f8690]) ).
fof(f8690,plain,
( spl107_507
<=> ! [X2,X1] :
( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP20(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_507])]) ).
fof(f6045,plain,
! [X2,X1] :
( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP20(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1,X2) ),
inference(equality_resolution,[],[f5337]) ).
fof(f5337,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| ~ sP20(X0,X1,X2) ),
inference(cnf_transformation,[],[f3899]) ).
fof(f3899,plain,
! [X0,X1,X2] :
( ( sP20(X0,X1,X2)
| ~ sP19(X2,X1,X0)
| ~ sP18(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP19(X2,X1,X0)
& sP18(X2,X1,X0)
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP20(X0,X1,X2) ) ),
inference(flattening,[],[f3898]) ).
fof(f3898,plain,
! [X0,X1,X2] :
( ( sP20(X0,X1,X2)
| ~ sP19(X2,X1,X0)
| ~ sP18(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP19(X2,X1,X0)
& sP18(X2,X1,X0)
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP20(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f3603]) ).
fof(f8688,plain,
spl107_506,
inference(avatar_split_clause,[],[f5952,f8686]) ).
fof(f8686,plain,
( spl107_506
<=> ! [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,[spl107_506])]) ).
fof(f5952,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,[],[f4649]) ).
fof(f4649,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,[],[f3698]) ).
fof(f8684,plain,
spl107_505,
inference(avatar_split_clause,[],[f5947,f8682]) ).
fof(f8682,plain,
( spl107_505
<=> ! [X1] :
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_505])]) ).
fof(f5947,plain,
! [X1] :
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(equality_resolution,[],[f4620]) ).
fof(f4620,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) != X0
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f3694]) ).
fof(f8680,plain,
spl107_504,
inference(avatar_split_clause,[],[f5946,f8678]) ).
fof(f8678,plain,
( spl107_504
<=> ! [X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_504])]) ).
fof(f5946,plain,
! [X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(equality_resolution,[],[f4619]) ).
fof(f4619,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| c_Groups_Ozero__class_Ozero(X1) != X0
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f3693]) ).
fof(f8676,plain,
spl107_503,
inference(avatar_split_clause,[],[f5942,f8674]) ).
fof(f8674,plain,
( spl107_503
<=> ! [X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1)))
| ~ class_RealVector_Oreal__normed__vector(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_503])]) ).
fof(f5942,plain,
! [X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(equality_resolution,[],[f4580]) ).
fof(f4580,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) != X0
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(cnf_transformation,[],[f3677]) ).
fof(f8672,plain,
spl107_502,
inference(avatar_split_clause,[],[f5941,f8670]) ).
fof(f8670,plain,
( spl107_502
<=> ! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_502])]) ).
fof(f5941,plain,
! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(equality_resolution,[],[f4579]) ).
fof(f4579,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Ozero__class_Ozero(X1) != X0
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(cnf_transformation,[],[f3676]) ).
fof(f8668,plain,
spl107_501,
inference(avatar_split_clause,[],[f5937,f8666]) ).
fof(f8666,plain,
( spl107_501
<=> ! [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,[spl107_501])]) ).
fof(f5937,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,[],[f4552]) ).
fof(f4552,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,[],[f2406]) ).
fof(f2406,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,[],[f1453]) ).
fof(f1453,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,[],[f901]) ).
fof(f901,axiom,
! [X58,X42] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X42
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X58),X42) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X58),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X58),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X42,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X42
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X58),X42) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8664,plain,
spl107_500,
inference(avatar_split_clause,[],[f5832,f8662]) ).
fof(f8662,plain,
( spl107_500
<=> ! [X4,X0,X3,X2,X1] :
( sP48(X2,X1,X0)
| ~ sP49(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_500])]) ).
fof(f5832,plain,
! [X2,X3,X0,X1,X4] :
( sP48(X2,X1,X0)
| ~ sP49(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f4082]) ).
fof(f8660,plain,
( spl107_499
| ~ spl107_305
| ~ spl107_392 ),
inference(avatar_split_clause,[],[f8078,f8019,f7627,f8657]) ).
fof(f8657,plain,
( spl107_499
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK106) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_499])]) ).
fof(f7627,plain,
( spl107_305
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK106) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_305])]) ).
fof(f8078,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK106)
| ~ spl107_305
| ~ spl107_392 ),
inference(resolution,[],[f8020,f7629]) ).
fof(f7629,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK106)
| ~ spl107_305 ),
inference(avatar_component_clause,[],[f7627]) ).
fof(f8655,plain,
spl107_498,
inference(avatar_split_clause,[],[f5332,f8653]) ).
fof(f8653,plain,
( spl107_498
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP17(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_498])]) ).
fof(f5332,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP17(X0,X1,X2) ),
inference(cnf_transformation,[],[f3897]) ).
fof(f3897,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
| ~ sP17(X0,X1,X2) ),
inference(rectify,[],[f3896]) ).
fof(f3896,plain,
! [X2,X1,X0] :
( ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
| ~ sP17(X2,X1,X0) ),
inference(nnf_transformation,[],[f3599]) ).
fof(f3599,plain,
! [X2,X1,X0] :
( ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
| ~ sP17(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
fof(f8651,plain,
spl107_497,
inference(avatar_split_clause,[],[f5195,f8649]) ).
fof(f8649,plain,
( spl107_497
<=> ! [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,[spl107_497])]) ).
fof(f5195,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,[],[f3852]) ).
fof(f3852,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,[],[f3851]) ).
fof(f3851,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,[],[f2943]) ).
fof(f2943,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,[],[f1900]) ).
fof(f1900,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,[],[f54]) ).
fof(f54,axiom,
! [X20,X16,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X16,X20)
<=> ( X16 = X20
| c_Orderings_Oord__class_Oless(X3,X16,X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8647,plain,
spl107_496,
inference(avatar_split_clause,[],[f5190,f8645]) ).
fof(f8645,plain,
( spl107_496
<=> ! [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,[spl107_496])]) ).
fof(f5190,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,[],[f2941]) ).
fof(f2941,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,[],[f2940]) ).
fof(f2940,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,[],[f1898]) ).
fof(f1898,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,[],[f30]) ).
fof(f30,axiom,
! [X5,X4,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X4,X5)
=> ~ c_Orderings_Oord__class_Oless(X3,X5,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8643,plain,
spl107_495,
inference(avatar_split_clause,[],[f5176,f8641]) ).
fof(f5176,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,[],[f3847]) ).
fof(f8639,plain,
spl107_494,
inference(avatar_split_clause,[],[f5174,f8637]) ).
fof(f8637,plain,
( spl107_494
<=> ! [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,[spl107_494])]) ).
fof(f5174,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,[],[f2916]) ).
fof(f2916,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,[],[f2915]) ).
fof(f2915,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,[],[f1885]) ).
fof(f1885,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,[],[f47]) ).
fof(f47,axiom,
! [X21,X6,X3] :
( class_Orderings_Opreorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X6,X21)
=> c_Orderings_Oord__class_Oless__eq(X3,X6,X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8635,plain,
spl107_493,
inference(avatar_split_clause,[],[f5170,f8633]) ).
fof(f8633,plain,
( spl107_493
<=> ! [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,[spl107_493])]) ).
fof(f5170,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,[],[f2908]) ).
fof(f2908,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,[],[f2907]) ).
fof(f2907,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,[],[f1881]) ).
fof(f1881,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,[],[f37]) ).
fof(f37,axiom,
! [X21,X6,X3] :
( class_Orderings_Opreorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X6,X21)
=> ~ c_Orderings_Oord__class_Oless(X3,X21,X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8631,plain,
spl107_492,
inference(avatar_split_clause,[],[f5135,f8629]) ).
fof(f5135,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,[],[f3843]) ).
fof(f3843,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,[],[f3842]) ).
fof(f3842,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,[],[f2862]) ).
fof(f2862,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,[],[f1851]) ).
fof(f1851,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,[],[f20]) ).
fof(f20,axiom,
! [X20,X16,X3] :
( class_Orderings_Olinorder(X3)
=> ( ~ c_Orderings_Oord__class_Oless(X3,X16,X20)
<=> ( X16 = X20
| c_Orderings_Oord__class_Oless(X3,X20,X16) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8627,plain,
spl107_491,
inference(avatar_split_clause,[],[f5118,f8625]) ).
fof(f5118,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,[],[f2844]) ).
fof(f2844,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,[],[f2843]) ).
fof(f2843,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,[],[f1840]) ).
fof(f1840,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,[],[f48]) ).
fof(f48,axiom,
! [X6,X21,X3] :
( class_Orderings_Olinorder(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X21,X6)
=> ~ c_Orderings_Oord__class_Oless(X3,X6,X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8623,plain,
spl107_490,
inference(avatar_split_clause,[],[f5107,f8621]) ).
fof(f8621,plain,
( spl107_490
<=> ! [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,[spl107_490])]) ).
fof(f5107,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,[],[f2826]) ).
fof(f2826,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,[],[f2825]) ).
fof(f2825,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,[],[f1831]) ).
fof(f1831,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,[],[f57]) ).
fof(f57,axiom,
! [X21,X6,X3] :
( class_Orderings_Olinorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X21,X6)
| c_Orderings_Oord__class_Oless__eq(X3,X6,X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8619,plain,
spl107_489,
inference(avatar_split_clause,[],[f5106,f8617]) ).
fof(f5106,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,[],[f2824]) ).
fof(f2824,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,[],[f2823]) ).
fof(f2823,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,[],[f1830]) ).
fof(f1830,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,[],[f77]) ).
fof(f77,axiom,
! [X21,X6,X3] :
( class_Orderings_Olinorder(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X21,X6)
| c_Orderings_Oord__class_Oless__eq(X3,X6,X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8615,plain,
( spl107_488
| ~ spl107_304
| ~ spl107_392 ),
inference(avatar_split_clause,[],[f8077,f8019,f7622,f8612]) ).
fof(f8612,plain,
( spl107_488
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK105) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_488])]) ).
fof(f7622,plain,
( spl107_304
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK105) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_304])]) ).
fof(f8077,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK105)
| ~ spl107_304
| ~ spl107_392 ),
inference(resolution,[],[f8020,f7624]) ).
fof(f7624,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK105)
| ~ spl107_304 ),
inference(avatar_component_clause,[],[f7622]) ).
fof(f8610,plain,
spl107_487,
inference(avatar_split_clause,[],[f4843,f8608]) ).
fof(f8608,plain,
( spl107_487
<=> ! [X0,X1] :
( X0 = X1
| c_RealDef_Oreal(tc_Nat_Onat,X0) != c_RealDef_Oreal(tc_Nat_Onat,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_487])]) ).
fof(f4843,plain,
! [X0,X1] :
( X0 = X1
| c_RealDef_Oreal(tc_Nat_Onat,X0) != c_RealDef_Oreal(tc_Nat_Onat,X1) ),
inference(cnf_transformation,[],[f3753]) ).
fof(f3753,plain,
! [X0,X1] :
( ( c_RealDef_Oreal(tc_Nat_Onat,X0) = c_RealDef_Oreal(tc_Nat_Onat,X1)
| X0 != X1 )
& ( X0 = X1
| c_RealDef_Oreal(tc_Nat_Onat,X0) != c_RealDef_Oreal(tc_Nat_Onat,X1) ) ),
inference(nnf_transformation,[],[f1675]) ).
fof(f1675,plain,
! [X0,X1] :
( c_RealDef_Oreal(tc_Nat_Onat,X0) = c_RealDef_Oreal(tc_Nat_Onat,X1)
<=> X0 = X1 ),
inference(rectify,[],[f658]) ).
fof(f658,axiom,
! [X66,X65] :
( c_RealDef_Oreal(tc_Nat_Onat,X65) = c_RealDef_Oreal(tc_Nat_Onat,X66)
<=> X65 = X66 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8606,plain,
spl107_486,
inference(avatar_split_clause,[],[f4774,f8604]) ).
fof(f8604,plain,
( spl107_486
<=> ! [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,[spl107_486])]) ).
fof(f4774,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,[],[f2621]) ).
fof(f2621,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,[],[f1636]) ).
fof(f1636,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,[],[f561]) ).
fof(f561,axiom,
! [X41,X42] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X41) = X42
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X41 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8602,plain,
spl107_485,
inference(avatar_split_clause,[],[f4723,f8600]) ).
fof(f8600,plain,
( spl107_485
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oarctan(X1),c_Transcendental_Oarctan(X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_485])]) ).
fof(f4723,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oarctan(X1),c_Transcendental_Oarctan(X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f2563]) ).
fof(f2563,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oarctan(X1),c_Transcendental_Oarctan(X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(ennf_transformation,[],[f1593]) ).
fof(f1593,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oarctan(X1),c_Transcendental_Oarctan(X0)) ),
inference(rectify,[],[f444]) ).
fof(f444,axiom,
! [X21,X6] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X6,X21)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oarctan(X6),c_Transcendental_Oarctan(X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8598,plain,
spl107_484,
inference(avatar_split_clause,[],[f4713,f8596]) ).
fof(f8596,plain,
( spl107_484
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_RComplete_Onatfloor(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_484])]) ).
fof(f4713,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_RComplete_Onatfloor(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f2550]) ).
fof(f2550,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_RComplete_Onatfloor(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(ennf_transformation,[],[f1583]) ).
fof(f1583,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_RComplete_Onatfloor(X0)) ),
inference(rectify,[],[f625]) ).
fof(f625,axiom,
! [X21,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,X21)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X6),c_RComplete_Onatfloor(X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8594,plain,
spl107_483,
inference(avatar_split_clause,[],[f4712,f8592]) ).
fof(f4712,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_RComplete_Onatceiling(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f2549]) ).
fof(f2549,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_RComplete_Onatceiling(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(ennf_transformation,[],[f1582]) ).
fof(f1582,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_RComplete_Onatceiling(X0)) ),
inference(rectify,[],[f629]) ).
fof(f629,axiom,
! [X21,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,X21)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X6),c_RComplete_Onatceiling(X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8590,plain,
spl107_482,
inference(avatar_split_clause,[],[f4711,f8588]) ).
fof(f8588,plain,
( spl107_482
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oarctan(X1),c_Transcendental_Oarctan(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_482])]) ).
fof(f4711,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oarctan(X1),c_Transcendental_Oarctan(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f2548]) ).
fof(f2548,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oarctan(X1),c_Transcendental_Oarctan(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(ennf_transformation,[],[f1581]) ).
fof(f1581,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oarctan(X1),c_Transcendental_Oarctan(X0)) ),
inference(rectify,[],[f446]) ).
fof(f446,axiom,
! [X21,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,X21)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oarctan(X6),c_Transcendental_Oarctan(X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8586,plain,
spl107_481,
inference(avatar_split_clause,[],[f4637,f8584]) ).
fof(f8584,plain,
( spl107_481
<=> ! [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,[spl107_481])]) ).
fof(f4637,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,[],[f2472]) ).
fof(f2472,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,[],[f1517]) ).
fof(f1517,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,[],[f195]) ).
fof(f195,axiom,
! [X5,X3] :
( class_Rings_Olinordered__semidom(X3)
=> c_Orderings_Oord__class_Oless(X3,X5,c_Groups_Oplus__class_Oplus(X3,X5,c_Groups_Oone__class_Oone(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8582,plain,
spl107_480,
inference(avatar_split_clause,[],[f4631,f8580]) ).
fof(f8580,plain,
( spl107_480
<=> ! [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,[spl107_480])]) ).
fof(f4631,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,[],[f2465]) ).
fof(f2465,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,[],[f1511]) ).
fof(f1511,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,[],[f754]) ).
fof(f754,axiom,
! [X5,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Groups_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(X3,c_Groups_Ozero__class_Ozero(X3),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8578,plain,
spl107_479,
inference(avatar_split_clause,[],[f4630,f8576]) ).
fof(f8576,plain,
( spl107_479
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Oone__class_Oone(X1))
| ~ class_Divides_Osemiring__div(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_479])]) ).
fof(f4630,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Oone__class_Oone(X1))
| ~ class_Divides_Osemiring__div(X1) ),
inference(cnf_transformation,[],[f2464]) ).
fof(f2464,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Oone__class_Oone(X1))
| ~ class_Divides_Osemiring__div(X1) ),
inference(ennf_transformation,[],[f1510]) ).
fof(f1510,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Oone__class_Oone(X1)) ),
inference(rectify,[],[f734]) ).
fof(f734,axiom,
! [X5,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Groups_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(X3,X5,c_Groups_Oone__class_Oone(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8574,plain,
spl107_478,
inference(avatar_split_clause,[],[f4629,f8572]) ).
fof(f8572,plain,
( spl107_478
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Odiv(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Divides_Osemiring__div(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_478])]) ).
fof(f4629,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Odiv(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Divides_Osemiring__div(X1) ),
inference(cnf_transformation,[],[f2463]) ).
fof(f2463,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Odiv(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Divides_Osemiring__div(X1) ),
inference(ennf_transformation,[],[f1509]) ).
fof(f1509,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Odiv(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(rectify,[],[f701]) ).
fof(f701,axiom,
! [X5,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Groups_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Odiv(X3,c_Groups_Ozero__class_Ozero(X3),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8570,plain,
( spl107_477
| ~ spl107_302
| ~ spl107_392 ),
inference(avatar_split_clause,[],[f8076,f8019,f7612,f8567]) ).
fof(f8567,plain,
( spl107_477
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK104) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_477])]) ).
fof(f7612,plain,
( spl107_302
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK104) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_302])]) ).
fof(f8076,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK104)
| ~ spl107_302
| ~ spl107_392 ),
inference(resolution,[],[f8020,f7614]) ).
fof(f7614,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK104)
| ~ spl107_302 ),
inference(avatar_component_clause,[],[f7612]) ).
fof(f8565,plain,
spl107_476,
inference(avatar_split_clause,[],[f4628,f8563]) ).
fof(f8563,plain,
( spl107_476
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Odiv(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Divides_Osemiring__div(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_476])]) ).
fof(f4628,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Odiv(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Divides_Osemiring__div(X1) ),
inference(cnf_transformation,[],[f2462]) ).
fof(f2462,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Odiv(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Divides_Osemiring__div(X1) ),
inference(ennf_transformation,[],[f1508]) ).
fof(f1508,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Odiv(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ),
inference(rectify,[],[f702]) ).
fof(f702,axiom,
! [X5,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Groups_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Odiv(X3,X5,c_Groups_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8561,plain,
spl107_475,
inference(avatar_split_clause,[],[f4571,f8559]) ).
fof(f8559,plain,
( spl107_475
<=> ! [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,[spl107_475])]) ).
fof(f4571,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,[],[f2419]) ).
fof(f2419,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,[],[f1468]) ).
fof(f1468,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,[],[f125]) ).
fof(f125,axiom,
! [X5,X3] :
( class_Rings_Odivision__ring(X3)
=> c_Groups_Ozero__class_Ozero(X3) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ozero__class_Ozero(X3),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8557,plain,
spl107_474,
inference(avatar_split_clause,[],[f4565,f8555]) ).
fof(f8555,plain,
( spl107_474
<=> ! [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,[spl107_474])]) ).
fof(f4565,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,[],[f2415]) ).
fof(f2415,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,[],[f1464]) ).
fof(f1464,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,[],[f101]) ).
fof(f101,axiom,
! [X21,X3] :
( class_RealVector_Oreal__normed__field(X3)
=> c_Groups_Ozero__class_Ozero(X3) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Ozero__class_Ozero(X3),X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8553,plain,
spl107_473,
inference(avatar_split_clause,[],[f4560,f8551]) ).
fof(f8551,plain,
( spl107_473
<=> ! [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,[spl107_473])]) ).
fof(f4560,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,[],[f2409]) ).
fof(f2409,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,[],[f1460]) ).
fof(f1460,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,[],[f124]) ).
fof(f124,axiom,
! [X5,X3] :
( class_Rings_Odivision__ring__inverse__zero(X3)
=> c_Groups_Ozero__class_Ozero(X3) = c_Rings_Oinverse__class_Odivide(X3,X5,c_Groups_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8549,plain,
spl107_472,
inference(avatar_split_clause,[],[f4556,f8547]) ).
fof(f8547,plain,
( spl107_472
<=> ! [X0,X1] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_472])]) ).
fof(f4556,plain,
! [X0,X1] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2408]) ).
fof(f2408,plain,
! [X0,X1] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(ennf_transformation,[],[f1455]) ).
fof(f1455,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),X0) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) = X1 ) ),
inference(rectify,[],[f730]) ).
fof(f730,axiom,
! [X41,X42] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X41)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X42,X41) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X42,X41),X41) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X41)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X42,X41) = X42 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8545,plain,
spl107_471,
inference(avatar_split_clause,[],[f4531,f8543]) ).
fof(f8543,plain,
( spl107_471
<=> ! [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,[spl107_471])]) ).
fof(f4531,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,[],[f1432]) ).
fof(f1432,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,[],[f562]) ).
fof(f562,axiom,
! [X42,X41] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X41,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8541,plain,
spl107_470,
inference(avatar_split_clause,[],[f4530,f8539]) ).
fof(f8539,plain,
( spl107_470
<=> ! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_470])]) ).
fof(f4530,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0),X0),
inference(cnf_transformation,[],[f1431]) ).
fof(f1431,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0),X0),
inference(rectify,[],[f963]) ).
fof(f963,axiom,
! [X4,X5] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5,X4),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8537,plain,
spl107_469,
inference(avatar_split_clause,[],[f4508,f8535]) ).
fof(f8535,plain,
( spl107_469
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealDef_Oreal(tc_Nat_Onat,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_469])]) ).
fof(f4508,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealDef_Oreal(tc_Nat_Onat,X0) ),
inference(cnf_transformation,[],[f3665]) ).
fof(f3665,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealDef_Oreal(tc_Nat_Onat,X0) ) ),
inference(nnf_transformation,[],[f1415]) ).
fof(f1415,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,X0)
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(rectify,[],[f662]) ).
fof(f662,axiom,
! [X65] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,X65)
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X65 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8533,plain,
spl107_468,
inference(avatar_split_clause,[],[f4492,f8531]) ).
fof(f8531,plain,
( spl107_468
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_468])]) ).
fof(f4492,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(cnf_transformation,[],[f2398]) ).
fof(f2398,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(ennf_transformation,[],[f1404]) ).
fof(f1404,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(X0) ),
inference(rectify,[],[f631]) ).
fof(f631,axiom,
! [X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8529,plain,
spl107_467,
inference(avatar_split_clause,[],[f4491,f8527]) ).
fof(f8527,plain,
( spl107_467
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_467])]) ).
fof(f4491,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(cnf_transformation,[],[f2397]) ).
fof(f2397,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(ennf_transformation,[],[f1403]) ).
fof(f1403,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(X0) ),
inference(rectify,[],[f632]) ).
fof(f632,axiom,
! [X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8525,plain,
( spl107_466
| ~ spl107_237
| ~ spl107_392 ),
inference(avatar_split_clause,[],[f8073,f8019,f7351,f8522]) ).
fof(f8522,plain,
( spl107_466
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_466])]) ).
fof(f7351,plain,
( spl107_237
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK52) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_237])]) ).
fof(f8073,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK52)
| ~ spl107_237
| ~ spl107_392 ),
inference(resolution,[],[f8020,f7353]) ).
fof(f7353,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK52)
| ~ spl107_237 ),
inference(avatar_component_clause,[],[f7351]) ).
fof(f8520,plain,
spl107_465,
inference(avatar_split_clause,[],[f4489,f8518]) ).
fof(f8518,plain,
( spl107_465
<=> ! [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,[spl107_465])]) ).
fof(f4489,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,[],[f2395]) ).
fof(f2395,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,[],[f1401]) ).
fof(f1401,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,[],[f471]) ).
fof(f471,axiom,
! [X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(X3,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8516,plain,
spl107_464,
inference(avatar_split_clause,[],[f4471,f8514]) ).
fof(f8514,plain,
( spl107_464
<=> ! [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,[spl107_464])]) ).
fof(f4471,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,[],[f2377]) ).
fof(f2377,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,[],[f1383]) ).
fof(f1383,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,[],[f467]) ).
fof(f467,axiom,
! [X3] :
( class_Groups_Ozero(X3)
=> c_Polynomial_Odegree(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8512,plain,
spl107_463,
inference(avatar_split_clause,[],[f4403,f8510]) ).
fof(f8510,plain,
( spl107_463
<=> ! [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,[spl107_463])]) ).
fof(f4403,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,[],[f1318]) ).
fof(f1318,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,[],[f500]) ).
fof(f500,axiom,
! [X41] : 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)),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8508,plain,
spl107_462,
inference(avatar_split_clause,[],[f4402,f8506]) ).
fof(f8506,plain,
( spl107_462
<=> ! [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,[spl107_462])]) ).
fof(f4402,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,[],[f1317]) ).
fof(f1317,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,[],[f499]) ).
fof(f499,axiom,
! [X42] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8504,plain,
spl107_461,
inference(avatar_split_clause,[],[f4361,f8501]) ).
fof(f8501,plain,
( spl107_461
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_d____),v_m____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_461])]) ).
fof(f4361,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_d____),v_m____)),
inference(cnf_transformation,[],[f215]) ).
fof(f215,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_d____),v_m____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8478,plain,
( spl107_460
| ~ spl107_235
| ~ spl107_392 ),
inference(avatar_split_clause,[],[f8072,f8019,f7341,f8475]) ).
fof(f8475,plain,
( spl107_460
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_460])]) ).
fof(f7341,plain,
( spl107_235
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK51) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_235])]) ).
fof(f8072,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK51)
| ~ spl107_235
| ~ spl107_392 ),
inference(resolution,[],[f8020,f7343]) ).
fof(f7343,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK51)
| ~ spl107_235 ),
inference(avatar_component_clause,[],[f7341]) ).
fof(f8439,plain,
( spl107_459
| ~ spl107_234
| ~ spl107_392 ),
inference(avatar_split_clause,[],[f8066,f8019,f7336,f8436]) ).
fof(f8436,plain,
( spl107_459
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_459])]) ).
fof(f7336,plain,
( spl107_234
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_234])]) ).
fof(f8066,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| ~ spl107_234
| ~ spl107_392 ),
inference(resolution,[],[f8020,f7338]) ).
fof(f7338,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| ~ spl107_234 ),
inference(avatar_component_clause,[],[f7336]) ).
fof(f8402,plain,
( spl107_458
| ~ spl107_233
| ~ spl107_392 ),
inference(avatar_split_clause,[],[f8065,f8019,f7331,f8399]) ).
fof(f8399,plain,
( spl107_458
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_e) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_458])]) ).
fof(f7331,plain,
( spl107_233
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_e) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_233])]) ).
fof(f8065,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_e)
| ~ spl107_233
| ~ spl107_392 ),
inference(resolution,[],[f8020,f7333]) ).
fof(f7333,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_e)
| ~ spl107_233 ),
inference(avatar_component_clause,[],[f7331]) ).
fof(f8386,plain,
( spl107_457
| ~ spl107_232
| ~ spl107_392 ),
inference(avatar_split_clause,[],[f8064,f8019,f7326,f8383]) ).
fof(f8383,plain,
( spl107_457
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_457])]) ).
fof(f7326,plain,
( spl107_232
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_232])]) ).
fof(f8064,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____)
| ~ spl107_232
| ~ spl107_392 ),
inference(resolution,[],[f8020,f7328]) ).
fof(f7328,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____)
| ~ spl107_232 ),
inference(avatar_component_clause,[],[f7326]) ).
fof(f8327,plain,
( spl107_456
| ~ spl107_303
| ~ spl107_392 ),
inference(avatar_split_clause,[],[f8063,f8019,f7617,f8324]) ).
fof(f8324,plain,
( spl107_456
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sK104,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_456])]) ).
fof(f7617,plain,
( spl107_303
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK104,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_303])]) ).
fof(f8063,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sK104,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl107_303
| ~ spl107_392 ),
inference(resolution,[],[f8020,f7619]) ).
fof(f7619,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK104,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl107_303 ),
inference(avatar_component_clause,[],[f7617]) ).
fof(f8315,plain,
spl107_455,
inference(avatar_split_clause,[],[f6156,f8312]) ).
fof(f8312,plain,
( spl107_455
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_455])]) ).
fof(f6156,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_demodulation,[],[f6155,f4403]) ).
fof(f6155,plain,
! [X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_demodulation,[],[f5995,f4403]) ).
fof(f5995,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)),
inference(equality_resolution,[],[f4920]) ).
fof(f4920,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(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_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ),
inference(cnf_transformation,[],[f2660]) ).
fof(f2660,plain,
! [X0,X1,X2] :
( ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0) = c_Divides_Odiv__class_Odiv(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_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(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_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) ),
inference(ennf_transformation,[],[f1720]) ).
fof(f1720,plain,
! [X0,X1,X2] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0) = c_Divides_Odiv__class_Odiv(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_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(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,[],[f693]) ).
fof(f693,axiom,
! [X41,X42,X13] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X13
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13),X41)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X42,X41) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X13
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13),X41)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8310,plain,
spl107_454,
inference(avatar_split_clause,[],[f6051,f8308]) ).
fof(f8308,plain,
( spl107_454
<=> ! [X2,X1] :
( hBOOL(hAPP(X2,X1))
| ~ sP24(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_454])]) ).
fof(f6051,plain,
! [X2,X1] :
( hBOOL(hAPP(X2,X1))
| ~ sP24(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1,X2) ),
inference(equality_resolution,[],[f5365]) ).
fof(f5365,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| ~ sP24(X0,X1,X2) ),
inference(cnf_transformation,[],[f3921]) ).
fof(f3921,plain,
! [X0,X1,X2] :
( ( sP24(X0,X1,X2)
| ~ sP23(X2,X1,X0)
| ~ sP22(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,X1))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP23(X2,X1,X0)
& sP22(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP24(X0,X1,X2) ) ),
inference(flattening,[],[f3920]) ).
fof(f3920,plain,
! [X0,X1,X2] :
( ( sP24(X0,X1,X2)
| ~ sP23(X2,X1,X0)
| ~ sP22(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,X1))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP23(X2,X1,X0)
& sP22(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP24(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f3609]) ).
fof(f8306,plain,
spl107_453,
inference(avatar_split_clause,[],[f6016,f8304]) ).
fof(f8304,plain,
( spl107_453
<=> ! [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,[spl107_453])]) ).
fof(f6016,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,[],[f5148]) ).
fof(f5148,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,[],[f3844]) ).
fof(f8302,plain,
spl107_452,
inference(avatar_split_clause,[],[f6006,f8300]) ).
fof(f8300,plain,
( spl107_452
<=> ! [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,[spl107_452])]) ).
fof(f6006,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,[],[f5087]) ).
fof(f5087,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,[],[f3830]) ).
fof(f8298,plain,
( spl107_451
| ~ spl107_236
| ~ spl107_392 ),
inference(avatar_split_clause,[],[f8062,f8019,f7346,f8295]) ).
fof(f8295,plain,
( spl107_451
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sK51,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_451])]) ).
fof(f7346,plain,
( spl107_236
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK51,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_236])]) ).
fof(f8062,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sK51,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl107_236
| ~ spl107_392 ),
inference(resolution,[],[f8020,f7348]) ).
fof(f7348,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK51,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl107_236 ),
inference(avatar_component_clause,[],[f7346]) ).
fof(f8293,plain,
spl107_450,
inference(avatar_split_clause,[],[f5377,f8291]) ).
fof(f8291,plain,
( spl107_450
<=> ! [X2,X0,X1] :
( sP22(X0,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,[spl107_450])]) ).
fof(f5377,plain,
! [X2,X0,X1] :
( sP22(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(cnf_transformation,[],[f3931]) ).
fof(f8289,plain,
spl107_449,
inference(avatar_split_clause,[],[f5371,f8287]) ).
fof(f8287,plain,
( spl107_449
<=> ! [X2,X0,X1] :
( sP23(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_449])]) ).
fof(f5371,plain,
! [X2,X0,X1] :
( sP23(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3926]) ).
fof(f8285,plain,
spl107_448,
inference(avatar_split_clause,[],[f5349,f8283]) ).
fof(f8283,plain,
( spl107_448
<=> ! [X2,X0,X1] :
( sP18(X0,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,[spl107_448])]) ).
fof(f5349,plain,
! [X2,X0,X1] :
( sP18(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(cnf_transformation,[],[f3911]) ).
fof(f8281,plain,
spl107_447,
inference(avatar_split_clause,[],[f5343,f8279]) ).
fof(f8279,plain,
( spl107_447
<=> ! [X2,X0,X1] :
( sP19(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_447])]) ).
fof(f5343,plain,
! [X2,X0,X1] :
( sP19(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3905]) ).
fof(f8277,plain,
spl107_446,
inference(avatar_split_clause,[],[f5283,f8275]) ).
fof(f8275,plain,
( spl107_446
<=> ! [X2,X0,X1] :
( sP16(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_446])]) ).
fof(f5283,plain,
! [X2,X0,X1] :
( sP16(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(cnf_transformation,[],[f3598]) ).
fof(f3598,plain,
! [X0,X1,X2] :
( sP16(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(definition_folding,[],[f3020,f3597,f3596]) ).
fof(f3597,plain,
! [X2,X0,X1] :
( ( hBOOL(hAPP(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X2)))
<=> sP15(X1,X0,X2) )
| ~ sP16(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f3020,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X2)))
<=> ! [X3,X4] :
( hBOOL(hAPP(hAPP(X1,X3),X4))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) != X0
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(flattening,[],[f3019]) ).
fof(f3019,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X2)))
<=> ! [X3,X4] :
( hBOOL(hAPP(hAPP(X1,X3),X4))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) != X0
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(ennf_transformation,[],[f1955]) ).
fof(f1955,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
=> ( hBOOL(hAPP(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X2)))
<=> ! [X3,X4] :
( ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) = X0
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4) )
=> hBOOL(hAPP(hAPP(X1,X3),X4)) ) ) ),
inference(rectify,[],[f969]) ).
fof(f969,axiom,
! [X65,X70,X63] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X63)
=> ( hBOOL(hAPP(hAPP(X70,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X65,X63)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X65,X63)))
<=> ! [X80,X81] :
( ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X63),X80),X81) = X65
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X81,X63)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X81) )
=> hBOOL(hAPP(hAPP(X70,X80),X81)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8273,plain,
spl107_445,
inference(avatar_split_clause,[],[f5273,f8271]) ).
fof(f8271,plain,
( spl107_445
<=> ! [X2,X0,X1] :
( sP14(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_445])]) ).
fof(f5273,plain,
! [X2,X0,X1] :
( sP14(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3595]) ).
fof(f3595,plain,
! [X0,X1,X2] :
( sP14(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(definition_folding,[],[f3016,f3594,f3593]) ).
fof(f3594,plain,
! [X2,X0,X1] :
( ( hBOOL(hAPP(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X2)))
<=> sP13(X1,X0,X2) )
| ~ sP14(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f3016,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X2)))
<=> ! [X3,X4] :
( hBOOL(hAPP(hAPP(X1,X3),X4))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) != X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(flattening,[],[f3015]) ).
fof(f3015,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X2)))
<=> ! [X3,X4] :
( hBOOL(hAPP(hAPP(X1,X3),X4))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) != X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(ennf_transformation,[],[f1952]) ).
fof(f1952,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( hBOOL(hAPP(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X2)))
<=> ! [X3,X4] :
( ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4) = X0
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) )
=> hBOOL(hAPP(hAPP(X1,X3),X4)) ) ) ),
inference(rectify,[],[f970]) ).
fof(f970,axiom,
! [X65,X70,X63] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X63,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( hBOOL(hAPP(hAPP(X70,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X65,X63)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X65,X63)))
<=> ! [X80,X81] :
( ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X63),X80),X81) = X65
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X81,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X63,X81) )
=> hBOOL(hAPP(hAPP(X70,X80),X81)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8269,plain,
spl107_444,
inference(avatar_split_clause,[],[f4825,f8267]) ).
fof(f8267,plain,
( spl107_444
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| ~ c_RealDef_Opositive(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_444])]) ).
fof(f4825,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| ~ c_RealDef_Opositive(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1)) ),
inference(cnf_transformation,[],[f3736]) ).
fof(f3736,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| ~ c_RealDef_Opositive(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1)) )
& ( c_RealDef_Opositive(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) ),
inference(nnf_transformation,[],[f1667]) ).
fof(f1667,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
<=> c_RealDef_Opositive(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1)) ),
inference(rectify,[],[f83]) ).
fof(f83,axiom,
! [X20,X16] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X16,X20)
<=> c_RealDef_Opositive(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X20,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8265,plain,
spl107_443,
inference(avatar_split_clause,[],[f4824,f8263]) ).
fof(f8263,plain,
( spl107_443
<=> ! [X0,X1] :
( c_RealDef_Opositive(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_443])]) ).
fof(f4824,plain,
! [X0,X1] :
( c_RealDef_Opositive(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f3736]) ).
fof(f8261,plain,
spl107_442,
inference(avatar_split_clause,[],[f4668,f8259]) ).
fof(f8259,plain,
( spl107_442
<=> ! [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,[spl107_442])]) ).
fof(f4668,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,[],[f2500]) ).
fof(f2500,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,[],[f1545]) ).
fof(f1545,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,[],[f420]) ).
fof(f420,axiom,
! [X5,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Ozero__class_Ozero(X3),X5) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8257,plain,
spl107_441,
inference(avatar_split_clause,[],[f4667,f8255]) ).
fof(f8255,plain,
( spl107_441
<=> ! [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,[spl107_441])]) ).
fof(f4667,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,[],[f2499]) ).
fof(f2499,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,[],[f1544]) ).
fof(f1544,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,[],[f421]) ).
fof(f421,axiom,
! [X5,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,X5,c_Groups_Ozero__class_Ozero(X3)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8253,plain,
( spl107_440
| ~ spl107_230
| ~ spl107_392 ),
inference(avatar_split_clause,[],[f8060,f8019,f7316,f8250]) ).
fof(f8250,plain,
( spl107_440
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_d____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_440])]) ).
fof(f7316,plain,
( spl107_230
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_230])]) ).
fof(f8060,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_d____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl107_230
| ~ spl107_392 ),
inference(resolution,[],[f8020,f7318]) ).
fof(f7318,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl107_230 ),
inference(avatar_component_clause,[],[f7316]) ).
fof(f8248,plain,
spl107_439,
inference(avatar_split_clause,[],[f4656,f8246]) ).
fof(f8246,plain,
( spl107_439
<=> ! [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,[spl107_439])]) ).
fof(f4656,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,[],[f2488]) ).
fof(f2488,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,[],[f1533]) ).
fof(f1533,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,[],[f103]) ).
fof(f103,axiom,
! [X5,X3] :
( class_Groups_Ocomm__monoid__add(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Ozero__class_Ozero(X3),X5) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8244,plain,
spl107_438,
inference(avatar_split_clause,[],[f4655,f8242]) ).
fof(f8242,plain,
( spl107_438
<=> ! [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,[spl107_438])]) ).
fof(f4655,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,[],[f2487]) ).
fof(f2487,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,[],[f1532]) ).
fof(f1532,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,[],[f107]) ).
fof(f107,axiom,
! [X5,X3] :
( class_Groups_Ocomm__monoid__add(X3)
=> c_Groups_Oplus__class_Oplus(X3,X5,c_Groups_Ozero__class_Ozero(X3)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8240,plain,
spl107_437,
inference(avatar_split_clause,[],[f4641,f8238]) ).
fof(f8238,plain,
( spl107_437
<=> ! [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,[spl107_437])]) ).
fof(f4641,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,[],[f2475]) ).
fof(f2475,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,[],[f1520]) ).
fof(f1520,plain,
! [X0,X1] :
( class_Groups_Omonoid__add(X1)
=> c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 ),
inference(rectify,[],[f102]) ).
fof(f102,axiom,
! [X5,X3] :
( class_Groups_Omonoid__add(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Ozero__class_Ozero(X3),X5) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8236,plain,
spl107_436,
inference(avatar_split_clause,[],[f4640,f8234]) ).
fof(f8234,plain,
( spl107_436
<=> ! [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,[spl107_436])]) ).
fof(f4640,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,[],[f2474]) ).
fof(f2474,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,[],[f1519]) ).
fof(f1519,plain,
! [X0,X1] :
( class_Groups_Omonoid__add(X1)
=> c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f106]) ).
fof(f106,axiom,
! [X5,X3] :
( class_Groups_Omonoid__add(X3)
=> c_Groups_Oplus__class_Oplus(X3,X5,c_Groups_Ozero__class_Ozero(X3)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8232,plain,
spl107_435,
inference(avatar_split_clause,[],[f4635,f8230]) ).
fof(f8230,plain,
( spl107_435
<=> ! [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,[spl107_435])]) ).
fof(f4635,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,[],[f2470]) ).
fof(f2470,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,[],[f1515]) ).
fof(f1515,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f191]) ).
fof(f191,axiom,
! [X5,X3] :
( class_Groups_Ogroup__add(X3)
=> c_Groups_Ominus__class_Ominus(X3,X5,c_Groups_Ozero__class_Ozero(X3)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8228,plain,
spl107_434,
inference(avatar_split_clause,[],[f4634,f8226]) ).
fof(f8226,plain,
( spl107_434
<=> ! [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,[spl107_434])]) ).
fof(f4634,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,[],[f2469]) ).
fof(f2469,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,[],[f1514]) ).
fof(f1514,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ominus__class_Ominus(X1,X0,X0) ),
inference(rectify,[],[f192]) ).
fof(f192,axiom,
! [X5,X3] :
( class_Groups_Ogroup__add(X3)
=> c_Groups_Ozero__class_Ozero(X3) = c_Groups_Ominus__class_Ominus(X3,X5,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8224,plain,
spl107_433,
inference(avatar_split_clause,[],[f4627,f8222]) ).
fof(f8222,plain,
( spl107_433
<=> ! [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,[spl107_433])]) ).
fof(f4627,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,[],[f2461]) ).
fof(f2461,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,[],[f1507]) ).
fof(f1507,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f753]) ).
fof(f753,axiom,
! [X5,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,X5,c_Groups_Ozero__class_Ozero(X3)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8220,plain,
spl107_432,
inference(avatar_split_clause,[],[f4626,f8218]) ).
fof(f8218,plain,
( spl107_432
<=> ! [X0,X1] :
( c_Divides_Odiv__class_Odiv(X1,X0,c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Divides_Osemiring__div(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_432])]) ).
fof(f4626,plain,
! [X0,X1] :
( c_Divides_Odiv__class_Odiv(X1,X0,c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Divides_Osemiring__div(X1) ),
inference(cnf_transformation,[],[f2460]) ).
fof(f2460,plain,
! [X0,X1] :
( c_Divides_Odiv__class_Odiv(X1,X0,c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Divides_Osemiring__div(X1) ),
inference(ennf_transformation,[],[f1506]) ).
fof(f1506,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Divides_Odiv__class_Odiv(X1,X0,c_Groups_Oone__class_Oone(X1)) = X0 ),
inference(rectify,[],[f703]) ).
fof(f703,axiom,
! [X5,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Odiv(X3,X5,c_Groups_Oone__class_Oone(X3)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8216,plain,
spl107_431,
inference(avatar_split_clause,[],[f4625,f8214]) ).
fof(f8214,plain,
( spl107_431
<=> ! [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,[spl107_431])]) ).
fof(f4625,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,[],[f2459]) ).
fof(f2459,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,[],[f1505]) ).
fof(f1505,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,X0) ),
inference(rectify,[],[f752]) ).
fof(f752,axiom,
! [X5,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Groups_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(X3,X5,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8212,plain,
spl107_430,
inference(avatar_split_clause,[],[f4612,f8210]) ).
fof(f8210,plain,
( spl107_430
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_430])]) ).
fof(f4612,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f2448]) ).
fof(f2448,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f1496]) ).
fof(f1496,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0)) ),
inference(rectify,[],[f129]) ).
fof(f129,axiom,
! [X5,X3] :
( class_Groups_Oordered__ab__group__add__abs(X3)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oabs__class_Oabs(X3,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8208,plain,
( spl107_429
| ~ spl107_229
| ~ spl107_392 ),
inference(avatar_split_clause,[],[f8059,f8019,f7311,f8205]) ).
fof(f8205,plain,
( spl107_429
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_429])]) ).
fof(f8059,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl107_229
| ~ spl107_392 ),
inference(resolution,[],[f8020,f7313]) ).
fof(f7313,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl107_229 ),
inference(avatar_component_clause,[],[f7311]) ).
fof(f8203,plain,
spl107_428,
inference(avatar_split_clause,[],[f4611,f8201]) ).
fof(f8201,plain,
( spl107_428
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_428])]) ).
fof(f4611,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f2447]) ).
fof(f2447,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f1495]) ).
fof(f1495,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X0),c_Groups_Ozero__class_Ozero(X1)) ),
inference(rectify,[],[f132]) ).
fof(f132,axiom,
! [X5,X3] :
( class_Groups_Oordered__ab__group__add__abs(X3)
=> ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oabs__class_Oabs(X3,X5),c_Groups_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8199,plain,
spl107_427,
inference(avatar_split_clause,[],[f4592,f8197]) ).
fof(f8197,plain,
( spl107_427
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK62(X0,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_427])]) ).
fof(f4592,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK62(X0,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(cnf_transformation,[],[f3685]) ).
fof(f3685,plain,
! [X0,X1] :
( ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),sK62(X0,X1)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK62(X0,X1)) )
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK62])],[f2435,f3684]) ).
fof(f3684,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
=> ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),sK62(X0,X1)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK62(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2435,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(ennf_transformation,[],[f1483]) ).
fof(f1483,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__algebra(X1)
=> ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ) ),
inference(rectify,[],[f435]) ).
fof(f435,axiom,
! [X6,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> ? [X51] :
( ! [X2] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X6),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X2)),X51))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X51) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8195,plain,
spl107_426,
inference(avatar_split_clause,[],[f4590,f8193]) ).
fof(f8193,plain,
( spl107_426
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK61(X0,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_426])]) ).
fof(f4590,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK61(X0,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(cnf_transformation,[],[f3683]) ).
fof(f3683,plain,
! [X0,X1] :
( ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),sK61(X0,X1)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK61(X0,X1)) )
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK61])],[f2434,f3682]) ).
fof(f3682,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
=> ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),sK61(X0,X1)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK61(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2434,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(ennf_transformation,[],[f1482]) ).
fof(f1482,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__algebra(X1)
=> ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ) ),
inference(rectify,[],[f439]) ).
fof(f439,axiom,
! [X21,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> ? [X51] :
( ! [X2] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X2)),X51))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X51) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8191,plain,
spl107_425,
inference(avatar_split_clause,[],[f4588,f8189]) ).
fof(f8189,plain,
( spl107_425
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK60(X0,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_425])]) ).
fof(f4588,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK60(X0,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(cnf_transformation,[],[f3681]) ).
fof(f3681,plain,
! [X0,X1] :
( ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),sK60(X0,X1)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK60(X0,X1)) )
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK60])],[f2433,f3680]) ).
fof(f3680,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
=> ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),sK60(X0,X1)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK60(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2433,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(ennf_transformation,[],[f1481]) ).
fof(f1481,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__algebra(X1)
=> ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ) ),
inference(rectify,[],[f692]) ).
fof(f692,axiom,
! [X21,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> ? [X51] :
( ! [X2] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X2)),X51))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X51) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8187,plain,
spl107_424,
inference(avatar_split_clause,[],[f4586,f8185]) ).
fof(f8185,plain,
( spl107_424
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK59(X0,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_424])]) ).
fof(f4586,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK59(X0,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(cnf_transformation,[],[f3679]) ).
fof(f3679,plain,
! [X0,X1] :
( ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),sK59(X0,X1)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK59(X0,X1)) )
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK59])],[f2432,f3678]) ).
fof(f3678,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
=> ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),sK59(X0,X1)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK59(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2432,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(ennf_transformation,[],[f1480]) ).
fof(f1480,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__algebra(X1)
=> ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ) ),
inference(rectify,[],[f656]) ).
fof(f656,axiom,
! [X6,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> ? [X51] :
( ! [X2] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X6),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X2)),X51))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X51) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8183,plain,
spl107_423,
inference(avatar_split_clause,[],[f4574,f8181]) ).
fof(f8181,plain,
( spl107_423
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
| ~ class_RealVector_Oreal__normed__vector(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_423])]) ).
fof(f4574,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(cnf_transformation,[],[f2423]) ).
fof(f2423,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(ennf_transformation,[],[f1471]) ).
fof(f1471,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__vector(X1)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0)) ),
inference(rectify,[],[f209]) ).
fof(f209,axiom,
! [X6,X3] :
( class_RealVector_Oreal__normed__vector(X3)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8179,plain,
spl107_422,
inference(avatar_split_clause,[],[f4573,f8177]) ).
fof(f8177,plain,
( spl107_422
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_422])]) ).
fof(f4573,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(cnf_transformation,[],[f2422]) ).
fof(f2422,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(ennf_transformation,[],[f1470]) ).
fof(f1470,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__vector(X1)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(rectify,[],[f210]) ).
fof(f210,axiom,
! [X6,X3] :
( class_RealVector_Oreal__normed__vector(X3)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3,X6),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8175,plain,
spl107_421,
inference(avatar_split_clause,[],[f4570,f8173]) ).
fof(f4570,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,[],[f2418]) ).
fof(f2418,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,[],[f1467]) ).
fof(f1467,plain,
! [X0,X1] :
( class_Rings_Odivision__ring(X1)
=> c_Rings_Oinverse__class_Odivide(X1,X0,c_Groups_Oone__class_Oone(X1)) = X0 ),
inference(rectify,[],[f148]) ).
fof(f148,axiom,
! [X5,X3] :
( class_Rings_Odivision__ring(X3)
=> c_Rings_Oinverse__class_Odivide(X3,X5,c_Groups_Oone__class_Oone(X3)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8171,plain,
spl107_420,
inference(avatar_split_clause,[],[f4568,f8169]) ).
fof(f8169,plain,
( spl107_420
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK58(X0,X1))
| ~ class_RealVector_Oreal__normed__field(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_420])]) ).
fof(f4568,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK58(X0,X1))
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(cnf_transformation,[],[f3674]) ).
fof(f3674,plain,
! [X0,X1] :
( ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),sK58(X0,X1)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK58(X0,X1)) )
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK58])],[f2417,f3673]) ).
fof(f3673,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
=> ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),sK58(X0,X1)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK58(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2417,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(ennf_transformation,[],[f1466]) ).
fof(f1466,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__field(X1)
=> ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ) ),
inference(rectify,[],[f432]) ).
fof(f432,axiom,
! [X21,X3] :
( class_RealVector_Oreal__normed__field(X3)
=> ? [X51] :
( ! [X2] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X2)),X51))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X51) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8167,plain,
spl107_419,
inference(avatar_split_clause,[],[f4566,f8165]) ).
fof(f8165,plain,
( spl107_419
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK57(X0,X1))
| ~ class_RealVector_Oreal__normed__field(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_419])]) ).
fof(f4566,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK57(X0,X1))
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(cnf_transformation,[],[f3672]) ).
fof(f3672,plain,
! [X0,X1] :
( ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),sK57(X0,X1)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK57(X0,X1)) )
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK57])],[f2416,f3671]) ).
fof(f3671,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
=> ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),sK57(X0,X1)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK57(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2416,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(ennf_transformation,[],[f1465]) ).
fof(f1465,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__field(X1)
=> ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ) ),
inference(rectify,[],[f477]) ).
fof(f477,axiom,
! [X21,X3] :
( class_RealVector_Oreal__normed__field(X3)
=> ? [X51] :
( ! [X2] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X2)),X51))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X51) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8163,plain,
( spl107_418
| ~ spl107_231
| ~ spl107_392 ),
inference(avatar_split_clause,[],[f8058,f8019,f7321,f8160]) ).
fof(f8160,plain,
( spl107_418
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_da____) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_418])]) ).
fof(f7321,plain,
( spl107_231
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_da____) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_231])]) ).
fof(f8058,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_da____)
| ~ spl107_231
| ~ spl107_392 ),
inference(resolution,[],[f8020,f7323]) ).
fof(f7323,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_da____)
| ~ spl107_231 ),
inference(avatar_component_clause,[],[f7321]) ).
fof(f8158,plain,
spl107_417,
inference(avatar_split_clause,[],[f4563,f8156]) ).
fof(f8156,plain,
( spl107_417
<=> ! [X0,X1] :
( c_RealDef_Opositive(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0))
| ~ c_RealDef_Opositive(X0)
| ~ c_RealDef_Opositive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_417])]) ).
fof(f4563,plain,
! [X0,X1] :
( c_RealDef_Opositive(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0))
| ~ c_RealDef_Opositive(X0)
| ~ c_RealDef_Opositive(X1) ),
inference(cnf_transformation,[],[f2412]) ).
fof(f2412,plain,
! [X0,X1] :
( c_RealDef_Opositive(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0))
| ~ c_RealDef_Opositive(X0)
| ~ c_RealDef_Opositive(X1) ),
inference(flattening,[],[f2411]) ).
fof(f2411,plain,
! [X0,X1] :
( c_RealDef_Opositive(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0))
| ~ c_RealDef_Opositive(X0)
| ~ c_RealDef_Opositive(X1) ),
inference(ennf_transformation,[],[f1462]) ).
fof(f1462,plain,
! [X0,X1] :
( c_RealDef_Opositive(X1)
=> ( c_RealDef_Opositive(X0)
=> c_RealDef_Opositive(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)) ) ),
inference(rectify,[],[f115]) ).
fof(f115,axiom,
! [X21,X6] :
( c_RealDef_Opositive(X6)
=> ( c_RealDef_Opositive(X21)
=> c_RealDef_Opositive(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X6,X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8154,plain,
spl107_416,
inference(avatar_split_clause,[],[f4529,f8152]) ).
fof(f8152,plain,
( spl107_416
<=> ! [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,[spl107_416])]) ).
fof(f4529,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,[],[f1430]) ).
fof(f1430,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,[],[f514]) ).
fof(f514,axiom,
! [X41,X42] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X41),X41) = X42,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8150,plain,
spl107_415,
inference(avatar_split_clause,[],[f4528,f8148]) ).
fof(f8148,plain,
( spl107_415
<=> ! [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,[spl107_415])]) ).
fof(f4528,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,[],[f1429]) ).
fof(f1429,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,[],[f515]) ).
fof(f515,axiom,
! [X42,X41] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X42),X41) = X42,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8146,plain,
spl107_414,
inference(avatar_split_clause,[],[f4527,f8144]) ).
fof(f8144,plain,
( spl107_414
<=> ! [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,[spl107_414])]) ).
fof(f4527,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,[],[f1428]) ).
fof(f1428,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,[],[f523]) ).
fof(f523,axiom,
! [X41,X42] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X41) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8142,plain,
spl107_413,
inference(avatar_split_clause,[],[f4506,f8140]) ).
fof(f8140,plain,
( spl107_413
<=> ! [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,[spl107_413])]) ).
fof(f4506,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,[],[f3664]) ).
fof(f3664,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,[],[f1414]) ).
fof(f1414,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,[],[f564]) ).
fof(f564,axiom,
! [X65] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X65,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X65 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8138,plain,
spl107_412,
inference(avatar_split_clause,[],[f4504,f8136]) ).
fof(f8136,plain,
( spl107_412
<=> ! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_412])]) ).
fof(f4504,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(cnf_transformation,[],[f3663]) ).
fof(f3663,plain,
! [X0] :
( ( 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
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(nnf_transformation,[],[f1413]) ).
fof(f1413,plain,
! [X0] :
( 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,[],[f815]) ).
fof(f815,axiom,
! [X66] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X66,c_Groups_Oone__class_Oone(tc_Nat_Onat))
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = X66 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8134,plain,
spl107_411,
inference(avatar_split_clause,[],[f4490,f8132]) ).
fof(f8132,plain,
( spl107_411
<=> ! [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,[spl107_411])]) ).
fof(f4490,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,[],[f2396]) ).
fof(f2396,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,[],[f1402]) ).
fof(f1402,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,[],[f548]) ).
fof(f548,axiom,
! [X41] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X41
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8130,plain,
spl107_410,
inference(avatar_split_clause,[],[f4447,f8128]) ).
fof(f4447,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = c_Groups_Oabs__class_Oabs(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2353]) ).
fof(f2353,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = c_Groups_Oabs__class_Oabs(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1359]) ).
fof(f1359,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> c_Groups_Oone__class_Oone(X0) = c_Groups_Oabs__class_Oabs(X0,c_Groups_Oone__class_Oone(X0)) ),
inference(rectify,[],[f146]) ).
fof(f146,axiom,
! [X3] :
( class_Rings_Olinordered__idom(X3)
=> c_Groups_Oone__class_Oone(X3) = c_Groups_Oabs__class_Oabs(X3,c_Groups_Oone__class_Oone(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8126,plain,
spl107_409,
inference(avatar_split_clause,[],[f4420,f8124]) ).
fof(f4420,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Oabs__class_Oabs(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X0) ),
inference(cnf_transformation,[],[f2326]) ).
fof(f2326,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Oabs__class_Oabs(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X0) ),
inference(ennf_transformation,[],[f1332]) ).
fof(f1332,plain,
! [X0] :
( class_Groups_Oordered__ab__group__add__abs(X0)
=> c_Groups_Ozero__class_Ozero(X0) = c_Groups_Oabs__class_Oabs(X0,c_Groups_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f97]) ).
fof(f97,axiom,
! [X3] :
( class_Groups_Oordered__ab__group__add__abs(X3)
=> c_Groups_Ozero__class_Ozero(X3) = c_Groups_Oabs__class_Oabs(X3,c_Groups_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8122,plain,
spl107_408,
inference(avatar_split_clause,[],[f4413,f8120]) ).
fof(f4413,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(cnf_transformation,[],[f2321]) ).
fof(f2321,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(ennf_transformation,[],[f1327]) ).
fof(f1327,plain,
! [X0] :
( class_RealVector_Oreal__normed__vector(X0)
=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f150]) ).
fof(f150,axiom,
! [X3] :
( class_RealVector_Oreal__normed__vector(X3)
=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X3,c_Groups_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8118,plain,
spl107_407,
inference(avatar_split_clause,[],[f4412,f8116]) ).
fof(f4412,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_RealVector_Oreal__normed__algebra__1(X0) ),
inference(cnf_transformation,[],[f2320]) ).
fof(f2320,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_RealVector_Oreal__normed__algebra__1(X0) ),
inference(ennf_transformation,[],[f1326]) ).
fof(f1326,plain,
! [X0] :
( class_RealVector_Oreal__normed__algebra__1(X0)
=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Oone__class_Oone(X0)) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X3] :
( class_RealVector_Oreal__normed__algebra__1(X3)
=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X3,c_Groups_Oone__class_Oone(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8114,plain,
spl107_406,
inference(avatar_split_clause,[],[f4400,f8112]) ).
fof(f8112,plain,
( spl107_406
<=> ! [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,[spl107_406])]) ).
fof(f4400,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,[],[f1315]) ).
fof(f1315,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,[],[f543]) ).
fof(f543,axiom,
! [X42] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8110,plain,
spl107_405,
inference(avatar_split_clause,[],[f4399,f8108]) ).
fof(f8108,plain,
( spl107_405
<=> ! [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,[spl107_405])]) ).
fof(f4399,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,[],[f1314]) ).
fof(f1314,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f493]) ).
fof(f493,axiom,
! [X41] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X41) = X41,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8106,plain,
spl107_404,
inference(avatar_split_clause,[],[f4398,f8104]) ).
fof(f8104,plain,
( spl107_404
<=> ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl107_404])]) ).
fof(f4398,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0) = X0,
inference(cnf_transformation,[],[f1313]) ).
fof(f1313,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0) = X0,
inference(rectify,[],[f260]) ).
fof(f260,axiom,
! [X12] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X12) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8102,plain,
spl107_403,
inference(avatar_split_clause,[],[f4397,f8100]) ).
fof(f8100,plain,
( spl107_403
<=> ! [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,[spl107_403])]) ).
fof(f4397,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,[],[f1312]) ).
fof(f1312,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(rectify,[],[f491]) ).
fof(f491,axiom,
! [X41] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X41),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X41,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8098,plain,
spl107_402,
inference(avatar_split_clause,[],[f4396,f8096]) ).
fof(f4396,plain,
! [X0] : c_RealDef_Oreal(tc_Nat_Onat,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0)),
inference(cnf_transformation,[],[f1311]) ).
fof(f1311,plain,
! [X0] : c_RealDef_Oreal(tc_Nat_Onat,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0)),
inference(rectify,[],[f659]) ).
fof(f659,axiom,
! [X6] : c_RealDef_Oreal(tc_Nat_Onat,X6) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8094,plain,
spl107_401,
inference(avatar_split_clause,[],[f4360,f8091]) ).
fof(f8091,plain,
( spl107_401
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_d____),v_m____),v_e) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_401])]) ).
fof(f4360,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_d____),v_m____),v_e),
inference(cnf_transformation,[],[f214]) ).
fof(f214,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_d____),v_m____),v_e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8089,plain,
spl107_400,
inference(avatar_split_clause,[],[f4359,f8086]) ).
fof(f4359,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),v_da____),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),v_da____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8084,plain,
( spl107_399
| spl107_218
| ~ spl107_388 ),
inference(avatar_split_clause,[],[f8047,f8003,f7261,f8081]) ).
fof(f7261,plain,
( spl107_218
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_218])]) ).
fof(f8047,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))
| spl107_218
| ~ spl107_388 ),
inference(resolution,[],[f8004,f7263]) ).
fof(f7263,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| spl107_218 ),
inference(avatar_component_clause,[],[f7261]) ).
fof(f8045,plain,
spl107_398,
inference(avatar_split_clause,[],[f5839,f8043]) ).
fof(f8043,plain,
( spl107_398
<=> ! [X4,X0,X3,X2,X1] :
( sP50(X3,X1,X2,X4,X0)
| ~ class_Fields_Ofield(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_398])]) ).
fof(f5839,plain,
! [X2,X3,X0,X1,X4] :
( sP50(X3,X1,X2,X4,X0)
| ~ class_Fields_Ofield(X4) ),
inference(cnf_transformation,[],[f3648]) ).
fof(f3648,plain,
! [X0,X1,X2,X3,X4] :
( sP50(X3,X1,X2,X4,X0)
| ~ class_Fields_Ofield(X4) ),
inference(definition_folding,[],[f3476,f3647,f3646,f3645]) ).
fof(f3647,plain,
! [X3,X1,X2,X4,X0] :
( ( c_Polynomial_Opdivmod__rel(X4,X3,X2,X1,X0)
<=> sP49(X0,X4,X2,X1,X3) )
| ~ sP50(X3,X1,X2,X4,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP50])]) ).
fof(f3476,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,[],[f3475]) ).
fof(f3475,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,[],[f2249]) ).
fof(f2249,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,[],[f638]) ).
fof(f638,axiom,
! [X31,X59,X20,X16,X3] :
( class_Fields_Ofield(X3)
=> ( c_Polynomial_Opdivmod__rel(X3,X16,X20,X59,X31)
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != X20
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X3,X31),c_Polynomial_Odegree(X3,X20))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X31 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X20
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X59 )
& c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X59),X20),X31) = X16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8041,plain,
spl107_397,
inference(avatar_split_clause,[],[f5367,f8039]) ).
fof(f8039,plain,
( spl107_397
<=> ! [X2,X0,X1] :
( sP23(X2,X1,X0)
| ~ sP24(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_397])]) ).
fof(f5367,plain,
! [X2,X0,X1] :
( sP23(X2,X1,X0)
| ~ sP24(X0,X1,X2) ),
inference(cnf_transformation,[],[f3921]) ).
fof(f8037,plain,
spl107_396,
inference(avatar_split_clause,[],[f5366,f8035]) ).
fof(f8035,plain,
( spl107_396
<=> ! [X2,X0,X1] :
( sP22(X2,X1,X0)
| ~ sP24(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_396])]) ).
fof(f5366,plain,
! [X2,X0,X1] :
( sP22(X2,X1,X0)
| ~ sP24(X0,X1,X2) ),
inference(cnf_transformation,[],[f3921]) ).
fof(f8033,plain,
spl107_395,
inference(avatar_split_clause,[],[f5339,f8031]) ).
fof(f8031,plain,
( spl107_395
<=> ! [X2,X0,X1] :
( sP19(X2,X1,X0)
| ~ sP20(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_395])]) ).
fof(f5339,plain,
! [X2,X0,X1] :
( sP19(X2,X1,X0)
| ~ sP20(X0,X1,X2) ),
inference(cnf_transformation,[],[f3899]) ).
fof(f8029,plain,
spl107_394,
inference(avatar_split_clause,[],[f5338,f8027]) ).
fof(f8027,plain,
( spl107_394
<=> ! [X2,X0,X1] :
( sP18(X2,X1,X0)
| ~ sP20(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_394])]) ).
fof(f5338,plain,
! [X2,X0,X1] :
( sP18(X2,X1,X0)
| ~ sP20(X0,X1,X2) ),
inference(cnf_transformation,[],[f3899]) ).
fof(f8025,plain,
spl107_393,
inference(avatar_split_clause,[],[f5331,f8023]) ).
fof(f8023,plain,
( spl107_393
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ sP17(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_393])]) ).
fof(f5331,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ sP17(X0,X1,X2) ),
inference(cnf_transformation,[],[f3897]) ).
fof(f8021,plain,
spl107_392,
inference(avatar_split_clause,[],[f4813,f8019]) ).
fof(f4813,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f3724]) ).
fof(f8017,plain,
spl107_391,
inference(avatar_split_clause,[],[f4727,f8015]) ).
fof(f8015,plain,
( spl107_391
<=> ! [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,[spl107_391])]) ).
fof(f4727,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,[],[f2567]) ).
fof(f2567,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,[],[f1597]) ).
fof(f1597,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,[],[f580]) ).
fof(f580,axiom,
! [X41,X42] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X41)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8013,plain,
spl107_390,
inference(avatar_split_clause,[],[f4610,f8011]) ).
fof(f4610,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oabs__class_Oabs(X1,X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f2446]) ).
fof(f2446,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oabs__class_Oabs(X1,X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f1494]) ).
fof(f1494,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oabs__class_Oabs(X1,X0)) ),
inference(rectify,[],[f166]) ).
fof(f166,axiom,
! [X5,X3] :
( class_Groups_Oordered__ab__group__add__abs(X3)
=> c_Orderings_Oord__class_Oless__eq(X3,X5,c_Groups_Oabs__class_Oabs(X3,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8009,plain,
spl107_389,
inference(avatar_split_clause,[],[f4559,f8007]) ).
fof(f4559,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,[],[f1457]) ).
fof(f1457,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,[],[f528]) ).
fof(f528,axiom,
! [X41,X42] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,X42)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8005,plain,
spl107_388,
inference(avatar_split_clause,[],[f4558,f8003]) ).
fof(f4558,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f1456]) ).
fof(f1456,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X11,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11,X12)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f8001,plain,
spl107_387,
inference(avatar_split_clause,[],[f4463,f7999]) ).
fof(f7999,plain,
( spl107_387
<=> ! [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,[spl107_387])]) ).
fof(f4463,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,[],[f2369]) ).
fof(f2369,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,[],[f1375]) ).
fof(f1375,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,[],[f199]) ).
fof(f199,axiom,
! [X3] :
( class_Rings_Olinordered__semidom(X3)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oone__class_Oone(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7997,plain,
spl107_386,
inference(avatar_split_clause,[],[f4462,f7995]) ).
fof(f7995,plain,
( spl107_386
<=> ! [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,[spl107_386])]) ).
fof(f4462,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,[],[f2368]) ).
fof(f2368,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,[],[f1374]) ).
fof(f1374,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,[],[f198]) ).
fof(f198,axiom,
! [X3] :
( class_Rings_Olinordered__semidom(X3)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oone__class_Oone(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7993,plain,
spl107_385,
inference(avatar_split_clause,[],[f4461,f7991]) ).
fof(f7991,plain,
( spl107_385
<=> ! [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,[spl107_385])]) ).
fof(f4461,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,[],[f2367]) ).
fof(f2367,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,[],[f1373]) ).
fof(f1373,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,[],[f200]) ).
fof(f200,axiom,
! [X3] :
( class_Rings_Olinordered__semidom(X3)
=> ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7989,plain,
spl107_384,
inference(avatar_split_clause,[],[f4460,f7987]) ).
fof(f7987,plain,
( spl107_384
<=> ! [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,[spl107_384])]) ).
fof(f4460,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,[],[f2366]) ).
fof(f2366,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,[],[f1372]) ).
fof(f1372,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,[],[f197]) ).
fof(f197,axiom,
! [X3] :
( class_Rings_Olinordered__semidom(X3)
=> ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7985,plain,
spl107_383,
inference(avatar_split_clause,[],[f4416,f7983]) ).
fof(f7983,plain,
( spl107_383
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK55(X0))
| ~ class_RealVector_Oreal__normed__algebra(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_383])]) ).
fof(f4416,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK55(X0))
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(cnf_transformation,[],[f3658]) ).
fof(f3658,plain,
! [X0] :
( ( ! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X2)),c_RealVector_Onorm__class_Onorm(X0,X3))),sK55(X0)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK55(X0)) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK55])],[f2323,f3657]) ).
fof(f3657,plain,
! [X0] :
( ? [X1] :
( ! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X2)),c_RealVector_Onorm__class_Onorm(X0,X3))),X1))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) )
=> ( ! [X3,X2] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X2)),c_RealVector_Onorm__class_Onorm(X0,X3))),sK55(X0)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK55(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f2323,plain,
! [X0] :
( ? [X1] :
( ! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X2)),c_RealVector_Onorm__class_Onorm(X0,X3))),X1))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(ennf_transformation,[],[f1329]) ).
fof(f1329,plain,
! [X0] :
( class_RealVector_Oreal__normed__algebra(X0)
=> ? [X1] :
( ! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X2)),c_RealVector_Onorm__class_Onorm(X0,X3))),X1))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ) ),
inference(rectify,[],[f434]) ).
fof(f434,axiom,
! [X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> ? [X51] :
( ! [X52,X53] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X52),X53)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X52)),c_RealVector_Onorm__class_Onorm(X3,X53))),X51))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X51) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7981,plain,
spl107_382,
inference(avatar_split_clause,[],[f4414,f7979]) ).
fof(f7979,plain,
( spl107_382
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK54(X0))
| ~ class_RealVector_Oreal__normed__algebra(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_382])]) ).
fof(f4414,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK54(X0))
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(cnf_transformation,[],[f3656]) ).
fof(f3656,plain,
! [X0] :
( ( ! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X2)),c_RealVector_Onorm__class_Onorm(X0,X3))),sK54(X0)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK54(X0)) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54])],[f2322,f3655]) ).
fof(f3655,plain,
! [X0] :
( ? [X1] :
( ! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X2)),c_RealVector_Onorm__class_Onorm(X0,X3))),X1))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) )
=> ( ! [X3,X2] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X2)),c_RealVector_Onorm__class_Onorm(X0,X3))),sK54(X0)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK54(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f2322,plain,
! [X0] :
( ? [X1] :
( ! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X2)),c_RealVector_Onorm__class_Onorm(X0,X3))),X1))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(ennf_transformation,[],[f1328]) ).
fof(f1328,plain,
! [X0] :
( class_RealVector_Oreal__normed__algebra(X0)
=> ? [X1] :
( ! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X2)),c_RealVector_Onorm__class_Onorm(X0,X3))),X1))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ) ),
inference(rectify,[],[f478]) ).
fof(f478,axiom,
! [X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> ? [X51] :
( ! [X52,X53] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X52),X53)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X52)),c_RealVector_Onorm__class_Onorm(X3,X53))),X51))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X51) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7977,plain,
spl107_381,
inference(avatar_split_clause,[],[f4410,f7975]) ).
fof(f7975,plain,
( spl107_381
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_381])]) ).
fof(f4410,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f1325]) ).
fof(f1325,plain,
! [X0] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(rectify,[],[f962]) ).
fof(f962,axiom,
! [X5] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X5
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7973,plain,
spl107_380,
inference(avatar_split_clause,[],[f4395,f7971]) ).
fof(f7971,plain,
( spl107_380
<=> ! [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,[spl107_380])]) ).
fof(f4395,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,[],[f1310]) ).
fof(f1310,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,[],[f504]) ).
fof(f504,axiom,
! [X41] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7969,plain,
spl107_379,
inference(avatar_split_clause,[],[f4394,f7967]) ).
fof(f7967,plain,
( spl107_379
<=> ! [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,[spl107_379])]) ).
fof(f4394,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),
inference(cnf_transformation,[],[f1309]) ).
fof(f1309,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),
inference(rectify,[],[f996]) ).
fof(f996,axiom,
! [X4] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7965,plain,
spl107_378,
inference(avatar_split_clause,[],[f4358,f7962]) ).
fof(f7962,plain,
( spl107_378
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_378])]) ).
fof(f4358,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
inference(cnf_transformation,[],[f95]) ).
fof(f95,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7960,plain,
( spl107_377
| ~ spl107_336
| ~ spl107_351 ),
inference(avatar_split_clause,[],[f7939,f7828,f7760,f7957]) ).
fof(f7957,plain,
( spl107_377
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_377])]) ).
fof(f7828,plain,
( spl107_351
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_351])]) ).
fof(f7939,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl107_336
| ~ spl107_351 ),
inference(superposition,[],[f7829,f7762]) ).
fof(f7829,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X0))
| ~ spl107_351 ),
inference(avatar_component_clause,[],[f7828]) ).
fof(f7945,plain,
( ~ spl107_376
| ~ spl107_336
| ~ spl107_343 ),
inference(avatar_split_clause,[],[f7933,f7796,f7760,f7942]) ).
fof(f7942,plain,
( spl107_376
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_376])]) ).
fof(f7796,plain,
( spl107_343
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_343])]) ).
fof(f7933,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl107_336
| ~ spl107_343 ),
inference(superposition,[],[f7797,f7762]) ).
fof(f7797,plain,
( ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl107_343 ),
inference(avatar_component_clause,[],[f7796]) ).
fof(f7932,plain,
( spl107_375
| ~ spl107_338 ),
inference(avatar_split_clause,[],[f7774,f7770,f7929]) ).
fof(f7929,plain,
( spl107_375
<=> c_Polynomial_Odegree(tc_Complex_Ocomplex,v_q____) = c_Polynomial_Odegree(tc_Complex_Ocomplex,sK53) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_375])]) ).
fof(f7770,plain,
( spl107_338
<=> c_Polynomial_Odegree(tc_Complex_Ocomplex,v_q____) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_338])]) ).
fof(f7774,plain,
( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_q____) = c_Polynomial_Odegree(tc_Complex_Ocomplex,sK53)
| ~ spl107_338 ),
inference(forward_demodulation,[],[f7772,f4367]) ).
fof(f4367,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Polynomial_Odegree(tc_Complex_Ocomplex,sK53),
inference(cnf_transformation,[],[f3654]) ).
fof(f7772,plain,
( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_q____) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)
| ~ spl107_338 ),
inference(avatar_component_clause,[],[f7770]) ).
fof(f7923,plain,
spl107_374,
inference(avatar_split_clause,[],[f6080,f7921]) ).
fof(f7921,plain,
( spl107_374
<=> ! [X1,X3] : sP42(c_Groups_Ozero__class_Ozero(X1),X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_374])]) ).
fof(f6080,plain,
! [X3,X1] : sP42(c_Groups_Ozero__class_Ozero(X1),X1,c_Groups_Ozero__class_Ozero(X1),X3),
inference(equality_resolution,[],[f6079]) ).
fof(f6079,plain,
! [X2,X3,X1] :
( sP42(c_Groups_Ozero__class_Ozero(X1),X1,X2,X3)
| c_Groups_Ozero__class_Ozero(X1) != X2 ),
inference(equality_resolution,[],[f5566]) ).
fof(f5566,plain,
! [X2,X3,X0,X1] :
( sP42(X0,X1,X2,X3)
| c_Groups_Ozero__class_Ozero(X1) != X0
| c_Groups_Ozero__class_Ozero(X1) != X2 ),
inference(cnf_transformation,[],[f4027]) ).
fof(f7919,plain,
spl107_373,
inference(avatar_split_clause,[],[f6072,f7917]) ).
fof(f7917,plain,
( spl107_373
<=> ! [X1,X3] : sP40(c_Groups_Ozero__class_Ozero(X1),X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_373])]) ).
fof(f6072,plain,
! [X3,X1] : sP40(c_Groups_Ozero__class_Ozero(X1),X1,c_Groups_Ozero__class_Ozero(X1),X3),
inference(equality_resolution,[],[f6071]) ).
fof(f6071,plain,
! [X2,X3,X1] :
( sP40(c_Groups_Ozero__class_Ozero(X1),X1,X2,X3)
| c_Groups_Ozero__class_Ozero(X1) != X2 ),
inference(equality_resolution,[],[f5557]) ).
fof(f5557,plain,
! [X2,X3,X0,X1] :
( sP40(X0,X1,X2,X3)
| c_Groups_Ozero__class_Ozero(X1) != X0
| c_Groups_Ozero__class_Ozero(X1) != X2 ),
inference(cnf_transformation,[],[f4022]) ).
fof(f7915,plain,
spl107_372,
inference(avatar_split_clause,[],[f5926,f7912]) ).
fof(f5926,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK104,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
inference(cnf_transformation,[],[f4112]) ).
fof(f4112,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK104,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK104,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK104) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK104])],[f2310,f4111]) ).
fof(f4111,plain,
( ? [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) )
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK104,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK104,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK104) ) ),
introduced(choice_axiom,[]) ).
fof(f2310,plain,
? [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(rectify,[],[f213]) ).
fof(f213,axiom,
? [X30] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X30,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X30,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7910,plain,
spl107_371,
inference(avatar_split_clause,[],[f5630,f7908]) ).
fof(f7908,plain,
( spl107_371
<=> ! [X0,X3,X2,X1] :
( sP47(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_371])]) ).
fof(f5630,plain,
! [X2,X3,X0,X1] :
( sP47(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f3644]) ).
fof(f3644,plain,
! [X0,X1,X2,X3] :
( sP47(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(definition_folding,[],[f3200,f3643,f3642]) ).
fof(f3643,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))
<=> sP46(X2,X0,X3,X1) )
| ~ sP47(X1,X3,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP47])]) ).
fof(f3200,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,[],[f2083]) ).
fof(f2083,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,[],[f310]) ).
fof(f310,axiom,
! [X9,X8,X10,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X10),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X9),X8))
<=> ( ( c_Orderings_Oord__class_Oless(X3,X9,X10)
& c_Orderings_Oord__class_Oless(X3,X8,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X10,X9)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X8) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7906,plain,
spl107_370,
inference(avatar_split_clause,[],[f5621,f7904]) ).
fof(f7904,plain,
( spl107_370
<=> ! [X0,X3,X2,X1] :
( sP45(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_370])]) ).
fof(f5621,plain,
! [X2,X3,X0,X1] :
( sP45(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f3641]) ).
fof(f3641,plain,
! [X0,X1,X2,X3] :
( sP45(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(definition_folding,[],[f3199,f3640,f3639]) ).
fof(f3640,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))
<=> sP44(X1,X0,X3,X2) )
| ~ sP45(X2,X3,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP45])]) ).
fof(f3199,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,[],[f2082]) ).
fof(f2082,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,[],[f309]) ).
fof(f309,axiom,
! [X9,X10,X8,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X8),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X8),X9))
<=> ( ( c_Orderings_Oord__class_Oless(X3,X9,X10)
& c_Orderings_Oord__class_Oless(X3,X8,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X10,X9)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X8) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7902,plain,
spl107_369,
inference(avatar_split_clause,[],[f5568,f7900]) ).
fof(f7900,plain,
( spl107_369
<=> ! [X0,X3,X2,X1] :
( sP43(X1,X0,X3,X2)
| ~ class_Fields_Ofield__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_369])]) ).
fof(f5568,plain,
! [X2,X3,X0,X1] :
( sP43(X1,X0,X3,X2)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(cnf_transformation,[],[f3638]) ).
fof(f3638,plain,
! [X0,X1,X2,X3] :
( sP43(X1,X0,X3,X2)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(definition_folding,[],[f3145,f3637,f3636]) ).
fof(f3637,plain,
! [X1,X0,X3,X2] :
( ( c_Rings_Oinverse__class_Odivide(X3,X1,X0) = X2
<=> sP42(X2,X3,X0,X1) )
| ~ sP43(X1,X0,X3,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP43])]) ).
fof(f3145,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,[],[f2047]) ).
fof(f2047,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,[],[f262]) ).
fof(f262,axiom,
! [X8,X9,X10,X3] :
( class_Fields_Ofield__inverse__zero(X3)
=> ( c_Rings_Oinverse__class_Odivide(X3,X9,X8) = X10
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = X8
=> c_Groups_Ozero__class_Ozero(X3) = X10 )
& ( c_Groups_Ozero__class_Ozero(X3) != X8
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X10),X8) = X9 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7898,plain,
spl107_368,
inference(avatar_split_clause,[],[f5559,f7896]) ).
fof(f7896,plain,
( spl107_368
<=> ! [X0,X3,X2,X1] :
( sP41(X2,X1,X3,X0)
| ~ class_Fields_Ofield__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_368])]) ).
fof(f5559,plain,
! [X2,X3,X0,X1] :
( sP41(X2,X1,X3,X0)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(cnf_transformation,[],[f3635]) ).
fof(f3635,plain,
! [X0,X1,X2,X3] :
( sP41(X2,X1,X3,X0)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(definition_folding,[],[f3144,f3634,f3633]) ).
fof(f3634,plain,
! [X2,X1,X3,X0] :
( ( c_Rings_Oinverse__class_Odivide(X3,X2,X1) = X0
<=> sP40(X0,X3,X1,X2) )
| ~ sP41(X2,X1,X3,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP41])]) ).
fof(f3144,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,[],[f2046]) ).
fof(f2046,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,[],[f263]) ).
fof(f263,axiom,
! [X10,X8,X9,X3] :
( class_Fields_Ofield__inverse__zero(X3)
=> ( c_Rings_Oinverse__class_Odivide(X3,X9,X8) = X10
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = X8
=> c_Groups_Ozero__class_Ozero(X3) = X10 )
& ( c_Groups_Ozero__class_Ozero(X3) != X8
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X10),X8) = X9 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7894,plain,
spl107_367,
inference(avatar_split_clause,[],[f5515,f7892]) ).
fof(f7892,plain,
( spl107_367
<=> ! [X0,X3,X2,X1] :
( sP39(X0,X3,X1,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_367])]) ).
fof(f5515,plain,
! [X2,X3,X0,X1] :
( sP39(X0,X3,X1,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(cnf_transformation,[],[f3632]) ).
fof(f3632,plain,
! [X0,X1,X2,X3] :
( sP39(X0,X3,X1,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(definition_folding,[],[f3095,f3631,f3630,f3629]) ).
fof(f3631,plain,
! [X0,X3,X1,X2] :
( ( c_Orderings_Oord__class_Oless(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X1),X0)
<=> sP38(X2,X1,X3,X0) )
| ~ sP39(X0,X3,X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP39])]) ).
fof(f3095,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X1),X0)
<=> ( ( ( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
& ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),X2)
| ~ c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) ) )
| c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) )
& ( c_Orderings_Oord__class_Oless(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(ennf_transformation,[],[f2018]) ).
fof(f2018,plain,
! [X0,X1,X2,X3] :
( class_Fields_Olinordered__field__inverse__zero(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X1),X0)
<=> ( ( ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1)
=> ( ( ~ c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0) )
& ( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),X2) ) ) )
& ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1)
=> c_Orderings_Oord__class_Oless(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ) ) ) ),
inference(rectify,[],[f293]) ).
fof(f293,axiom,
! [X10,X8,X9,X3] :
( class_Fields_Olinordered__field__inverse__zero(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Rings_Oinverse__class_Odivide(X3,X9,X8),X10)
<=> ( ( ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X8)
=> ( ( ~ c_Orderings_Oord__class_Oless(X3,X8,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X10) )
& ( c_Orderings_Oord__class_Oless(X3,X8,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X10),X8),X9) ) ) )
& ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X8)
=> c_Orderings_Oord__class_Oless(X3,X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X10),X8)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7890,plain,
spl107_366,
inference(avatar_split_clause,[],[f5500,f7888]) ).
fof(f7888,plain,
( spl107_366
<=> ! [X0,X3,X2,X1] :
( sP36(X3,X2,X0,X1)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_366])]) ).
fof(f5500,plain,
! [X2,X3,X0,X1] :
( sP36(X3,X2,X0,X1)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(cnf_transformation,[],[f3628]) ).
fof(f3628,plain,
! [X0,X1,X2,X3] :
( sP36(X3,X2,X0,X1)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(definition_folding,[],[f3094,f3627,f3626,f3625]) ).
fof(f3627,plain,
! [X3,X2,X0,X1] :
( ( c_Orderings_Oord__class_Oless(X3,X2,c_Rings_Oinverse__class_Odivide(X3,X1,X0))
<=> sP35(X1,X0,X2,X3) )
| ~ sP36(X3,X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP36])]) ).
fof(f3094,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless(X3,X2,c_Rings_Oinverse__class_Odivide(X3,X1,X0))
<=> ( ( ( ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3)) )
& ( c_Orderings_Oord__class_Oless(X3,X1,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,c_Groups_Ozero__class_Ozero(X3),X0) )
& ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0) ) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(ennf_transformation,[],[f2017]) ).
fof(f2017,plain,
! [X0,X1,X2,X3] :
( class_Fields_Olinordered__field__inverse__zero(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,c_Rings_Oinverse__class_Odivide(X3,X1,X0))
<=> ( ( ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> ( ( ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
& ( c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ) ) )
& ( 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),X1) ) ) ) ),
inference(rectify,[],[f294]) ).
fof(f294,axiom,
! [X8,X9,X10,X3] :
( class_Fields_Olinordered__field__inverse__zero(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X10,c_Rings_Oinverse__class_Odivide(X3,X9,X8))
<=> ( ( ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X8)
=> ( ( ~ c_Orderings_Oord__class_Oless(X3,X8,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless(X3,X10,c_Groups_Ozero__class_Ozero(X3)) )
& ( c_Orderings_Oord__class_Oless(X3,X8,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless(X3,X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X10),X8)) ) ) )
& ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X8)
=> c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X10),X8),X9) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7886,plain,
spl107_365,
inference(avatar_split_clause,[],[f5485,f7884]) ).
fof(f7884,plain,
( spl107_365
<=> ! [X0,X3,X2,X1] :
( sP33(X0,X3,X1,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_365])]) ).
fof(f5485,plain,
! [X2,X3,X0,X1] :
( sP33(X0,X3,X1,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(cnf_transformation,[],[f3624]) ).
fof(f3624,plain,
! [X0,X1,X2,X3] :
( sP33(X0,X3,X1,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(definition_folding,[],[f3093,f3623,f3622,f3621]) ).
fof(f3623,plain,
! [X0,X3,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X1),X0)
<=> sP32(X2,X1,X3,X0) )
| ~ sP33(X0,X3,X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP33])]) ).
fof(f3093,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X1),X0)
<=> ( ( ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0)
| c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
& ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),X2)
| ~ c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) ) )
| c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) )
& ( c_Orderings_Oord__class_Oless__eq(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(ennf_transformation,[],[f2016]) ).
fof(f2016,plain,
! [X0,X1,X2,X3] :
( class_Fields_Olinordered__field__inverse__zero(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Rings_Oinverse__class_Odivide(X3,X2,X1),X0)
<=> ( ( ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1)
=> ( ( ~ c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X0) )
& ( c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1),X2) ) ) )
& ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1)
=> c_Orderings_Oord__class_Oless__eq(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)) ) ) ) ),
inference(rectify,[],[f342]) ).
fof(f342,axiom,
! [X10,X8,X9,X3] :
( class_Fields_Olinordered__field__inverse__zero(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Rings_Oinverse__class_Odivide(X3,X9,X8),X10)
<=> ( ( ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X8)
=> ( ( ~ c_Orderings_Oord__class_Oless(X3,X8,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X10) )
& ( c_Orderings_Oord__class_Oless(X3,X8,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X10),X8),X9) ) ) )
& ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X8)
=> c_Orderings_Oord__class_Oless__eq(X3,X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X10),X8)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7882,plain,
spl107_364,
inference(avatar_split_clause,[],[f5470,f7880]) ).
fof(f7880,plain,
( spl107_364
<=> ! [X0,X3,X2,X1] :
( sP30(X3,X2,X0,X1)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_364])]) ).
fof(f5470,plain,
! [X2,X3,X0,X1] :
( sP30(X3,X2,X0,X1)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(cnf_transformation,[],[f3620]) ).
fof(f3620,plain,
! [X0,X1,X2,X3] :
( sP30(X3,X2,X0,X1)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(definition_folding,[],[f3092,f3619,f3618,f3617]) ).
fof(f3619,plain,
! [X3,X2,X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Rings_Oinverse__class_Odivide(X3,X1,X0))
<=> sP29(X1,X0,X2,X3) )
| ~ sP30(X3,X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP30])]) ).
fof(f3092,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Rings_Oinverse__class_Odivide(X3,X1,X0))
<=> ( ( ( ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3))
| c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3)) )
& ( c_Orderings_Oord__class_Oless__eq(X3,X1,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,c_Groups_Ozero__class_Ozero(X3),X0) )
& ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),X1)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0) ) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(ennf_transformation,[],[f2015]) ).
fof(f2015,plain,
! [X0,X1,X2,X3] :
( class_Fields_Olinordered__field__inverse__zero(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Rings_Oinverse__class_Odivide(X3,X1,X0))
<=> ( ( ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X0)
=> ( ( ~ c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
& ( c_Orderings_Oord__class_Oless(X3,X0,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ) ) )
& ( c_Orderings_Oord__class_Oless(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),X1) ) ) ) ),
inference(rectify,[],[f343]) ).
fof(f343,axiom,
! [X8,X9,X10,X3] :
( class_Fields_Olinordered__field__inverse__zero(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X10,c_Rings_Oinverse__class_Odivide(X3,X9,X8))
<=> ( ( ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X8)
=> ( ( ~ c_Orderings_Oord__class_Oless(X3,X8,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,X10,c_Groups_Ozero__class_Ozero(X3)) )
& ( c_Orderings_Oord__class_Oless(X3,X8,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X10),X8)) ) ) )
& ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X8)
=> c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X10),X8),X9) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7878,plain,
spl107_363,
inference(avatar_split_clause,[],[f4889,f7876]) ).
fof(f4889,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK72(X0,X1)),
inference(cnf_transformation,[],[f3780]) ).
fof(f3780,plain,
! [X0,X1] :
( ! [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X3)),sK72(X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3),X1) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK72(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK72])],[f2659,f3779]) ).
fof(f3779,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X3)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3),X1) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
=> ( ! [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X3)),sK72(X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3),X1) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK72(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2659,plain,
! [X0,X1] :
? [X2] :
( ! [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X3)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3),X1) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(ennf_transformation,[],[f1690]) ).
fof(f1690,plain,
! [X0,X1] :
? [X2] :
( ! [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3),X1)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X3)),X2) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(rectify,[],[f476]) ).
fof(f476,axiom,
! [X58,X25] :
? [X54] :
( ! [X55] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X55),X25)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X58),X55)),X54) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X54) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7874,plain,
spl107_362,
inference(avatar_split_clause,[],[f4666,f7872]) ).
fof(f7872,plain,
( spl107_362
<=> ! [X0,X1] :
( 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,[spl107_362])]) ).
fof(f4666,plain,
! [X0,X1] :
( c_Rings_Odvd__class_Odvd(X1,c_Groups_Oone__class_Oone(X1),X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2498]) ).
fof(f2498,plain,
! [X0,X1] :
( c_Rings_Odvd__class_Odvd(X1,c_Groups_Oone__class_Oone(X1),X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1543]) ).
fof(f1543,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Rings_Odvd__class_Odvd(X1,c_Groups_Oone__class_Oone(X1),X0) ),
inference(rectify,[],[f816]) ).
fof(f816,axiom,
! [X5,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Rings_Odvd__class_Odvd(X3,c_Groups_Oone__class_Oone(X3),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7870,plain,
spl107_361,
inference(avatar_split_clause,[],[f4665,f7868]) ).
fof(f7868,plain,
( spl107_361
<=> ! [X0,X1] :
( 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,[spl107_361])]) ).
fof(f4665,plain,
! [X0,X1] :
( c_Rings_Odvd__class_Odvd(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2497]) ).
fof(f2497,plain,
! [X0,X1] :
( c_Rings_Odvd__class_Odvd(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1542]) ).
fof(f1542,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Rings_Odvd__class_Odvd(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ),
inference(rectify,[],[f792]) ).
fof(f792,axiom,
! [X5,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Rings_Odvd__class_Odvd(X3,X5,c_Groups_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7866,plain,
spl107_360,
inference(avatar_split_clause,[],[f4526,f7864]) ).
fof(f7864,plain,
( spl107_360
<=> ! [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,[spl107_360])]) ).
fof(f4526,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,[],[f1427]) ).
fof(f1427,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,[],[f538]) ).
fof(f538,axiom,
! [X41,X42] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X42,X41),X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7862,plain,
spl107_359,
inference(avatar_split_clause,[],[f4525,f7860]) ).
fof(f7860,plain,
( spl107_359
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_359])]) ).
fof(f4525,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0),X1),
inference(cnf_transformation,[],[f1426]) ).
fof(f1426,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0),X1),
inference(rectify,[],[f749]) ).
fof(f749,axiom,
! [X41,X42] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X42,X41),X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7858,plain,
spl107_358,
inference(avatar_split_clause,[],[f4524,f7856]) ).
fof(f7856,plain,
( spl107_358
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_358])]) ).
fof(f4524,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0),X1),
inference(cnf_transformation,[],[f1425]) ).
fof(f1425,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0),X1),
inference(rectify,[],[f704]) ).
fof(f704,axiom,
! [X41,X42] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X42,X41),X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7854,plain,
spl107_357,
inference(avatar_split_clause,[],[f4523,f7852]) ).
fof(f4523,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,[],[f1424]) ).
fof(f1424,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,[],[f585]) ).
fof(f585,axiom,
! [X42,X41] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X41)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7850,plain,
spl107_356,
inference(avatar_split_clause,[],[f4522,f7848]) ).
fof(f4522,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,[],[f1423]) ).
fof(f1423,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,[],[f586]) ).
fof(f586,axiom,
! [X42,X41] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7846,plain,
spl107_355,
inference(avatar_split_clause,[],[f4521,f7844]) ).
fof(f7844,plain,
( spl107_355
<=> ! [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,[spl107_355])]) ).
fof(f4521,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,[],[f1422]) ).
fof(f1422,plain,
! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1),
inference(rectify,[],[f567]) ).
fof(f567,axiom,
! [X14,X15] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X14),X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7842,plain,
spl107_354,
inference(avatar_split_clause,[],[f4520,f7840]) ).
fof(f7840,plain,
( spl107_354
<=> ! [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,[spl107_354])]) ).
fof(f4520,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,[],[f1421]) ).
fof(f1421,plain,
! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0),
inference(rectify,[],[f568]) ).
fof(f568,axiom,
! [X15,X14] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X15),X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7838,plain,
spl107_353,
inference(avatar_split_clause,[],[f4468,f7836]) ).
fof(f7836,plain,
( spl107_353
<=> ! [X0] :
( c_Groups_Oone__class_Oone(X0) != c_Groups_Ozero__class_Ozero(X0)
| ~ class_Rings_Ozero__neq__one(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_353])]) ).
fof(f4468,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) != c_Groups_Ozero__class_Ozero(X0)
| ~ class_Rings_Ozero__neq__one(X0) ),
inference(cnf_transformation,[],[f2374]) ).
fof(f2374,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) != c_Groups_Ozero__class_Ozero(X0)
| ~ class_Rings_Ozero__neq__one(X0) ),
inference(ennf_transformation,[],[f1380]) ).
fof(f1380,plain,
! [X0] :
( class_Rings_Ozero__neq__one(X0)
=> c_Groups_Oone__class_Oone(X0) != c_Groups_Ozero__class_Ozero(X0) ),
inference(rectify,[],[f152]) ).
fof(f152,axiom,
! [X3] :
( class_Rings_Ozero__neq__one(X3)
=> c_Groups_Oone__class_Oone(X3) != c_Groups_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7834,plain,
spl107_352,
inference(avatar_split_clause,[],[f4411,f7832]) ).
fof(f7832,plain,
( spl107_352
<=> ! [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,[spl107_352])]) ).
fof(f4411,plain,
! [X0] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
inference(cnf_transformation,[],[f1325]) ).
fof(f7830,plain,
spl107_351,
inference(avatar_split_clause,[],[f4393,f7828]) ).
fof(f4393,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X0)),
inference(cnf_transformation,[],[f1308]) ).
fof(f1308,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X0)),
inference(rectify,[],[f657]) ).
fof(f657,axiom,
! [X41] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X41)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7826,plain,
spl107_350,
inference(avatar_split_clause,[],[f4392,f7824]) ).
fof(f4392,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X0))),
inference(cnf_transformation,[],[f1307]) ).
fof(f1307,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X0))),
inference(rectify,[],[f670]) ).
fof(f670,axiom,
! [X6] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X6))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7822,plain,
spl107_349,
inference(avatar_split_clause,[],[f4391,f7820]) ).
fof(f7820,plain,
( spl107_349
<=> ! [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,[spl107_349])]) ).
fof(f4391,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
inference(cnf_transformation,[],[f1306]) ).
fof(f1306,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
inference(rectify,[],[f558]) ).
fof(f558,axiom,
! [X41] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X41) = X41,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7818,plain,
spl107_348,
inference(avatar_split_clause,[],[f4390,f7816]) ).
fof(f7816,plain,
( spl107_348
<=> ! [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,[spl107_348])]) ).
fof(f4390,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f1305]) ).
fof(f1305,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f559]) ).
fof(f559,axiom,
! [X42] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X42,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7814,plain,
spl107_347,
inference(avatar_split_clause,[],[f4389,f7812]) ).
fof(f7812,plain,
( spl107_347
<=> ! [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,[spl107_347])]) ).
fof(f4389,plain,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f1304]) ).
fof(f1304,plain,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f503]) ).
fof(f503,axiom,
! [X42] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X42,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X42,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7810,plain,
spl107_346,
inference(avatar_split_clause,[],[f4388,f7808]) ).
fof(f7808,plain,
( spl107_346
<=> ! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_346])]) ).
fof(f7806,plain,
spl107_345,
inference(avatar_split_clause,[],[f4387,f7804]) ).
fof(f7804,plain,
( spl107_345
<=> ! [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,[spl107_345])]) ).
fof(f4387,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0),
inference(cnf_transformation,[],[f1302]) ).
fof(f1302,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0),
inference(rectify,[],[f502]) ).
fof(f502,axiom,
! [X42] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X42,X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7802,plain,
spl107_344,
inference(avatar_split_clause,[],[f4386,f7800]) ).
fof(f7800,plain,
( spl107_344
<=> ! [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,[spl107_344])]) ).
fof(f4386,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f1301]) ).
fof(f1301,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0),
inference(rectify,[],[f995]) ).
fof(f995,axiom,
! [X5] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X5,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7798,plain,
spl107_343,
inference(avatar_split_clause,[],[f4385,f7796]) ).
fof(f4385,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f1300]) ).
fof(f1300,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(rectify,[],[f664]) ).
fof(f664,axiom,
! [X41] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X41),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7794,plain,
spl107_342,
inference(avatar_split_clause,[],[f4367,f7791]) ).
fof(f7791,plain,
( spl107_342
<=> c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Polynomial_Odegree(tc_Complex_Ocomplex,sK53) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_342])]) ).
fof(f7789,plain,
spl107_341,
inference(avatar_split_clause,[],[f4364,f7786]) ).
fof(f4364,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK51,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
inference(cnf_transformation,[],[f3650]) ).
fof(f3650,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK51,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK51,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK51) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK51])],[f2317,f3649]) ).
fof(f3649,plain,
( ? [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) )
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK51,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK51,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK51) ) ),
introduced(choice_axiom,[]) ).
fof(f2317,plain,
? [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(flattening,[],[f2316]) ).
fof(f2316,plain,
? [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(ennf_transformation,[],[f1281]) ).
fof(f1281,plain,
~ ! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ) ),
inference(rectify,[],[f212]) ).
fof(f212,axiom,
~ ! [X29] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X29)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X29,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X29,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7784,plain,
spl107_340,
inference(avatar_split_clause,[],[f4357,f7781]) ).
fof(f4357,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
inference(cnf_transformation,[],[f94]) ).
fof(f94,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7779,plain,
spl107_339,
inference(avatar_split_clause,[],[f4356,f7776]) ).
fof(f4356,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
inference(cnf_transformation,[],[f81]) ).
fof(f81,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7773,plain,
spl107_338,
inference(avatar_split_clause,[],[f4355,f7770]) ).
fof(f4355,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_q____) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),
inference(cnf_transformation,[],[f451]) ).
fof(f451,axiom,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_q____) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7768,plain,
spl107_337,
inference(avatar_split_clause,[],[f4354,f7765]) ).
fof(f4354,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f663]) ).
fof(f663,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7763,plain,
spl107_336,
inference(avatar_split_clause,[],[f4353,f7760]) ).
fof(f4353,plain,
c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f669]) ).
fof(f669,axiom,
c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7758,plain,
spl107_335,
inference(avatar_split_clause,[],[f6151,f7755]) ).
fof(f7755,plain,
( spl107_335
<=> 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,[spl107_335])]) ).
fof(f6151,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,[],[f5989,f5937]) ).
fof(f5989,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,[],[f4875]) ).
fof(f4875,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,[],[f3770]) ).
fof(f7753,plain,
spl107_334,
inference(avatar_split_clause,[],[f6124,f7751]) ).
fof(f7751,plain,
( spl107_334
<=> ! [X2,X1] : sP48(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_334])]) ).
fof(f6124,plain,
! [X2,X1] : sP48(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1,X2),
inference(equality_resolution,[],[f5836]) ).
fof(f5836,plain,
! [X2,X0,X1] :
( sP48(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X0 ),
inference(cnf_transformation,[],[f4085]) ).
fof(f7749,plain,
spl107_333,
inference(avatar_split_clause,[],[f6123,f7747]) ).
fof(f7747,plain,
( spl107_333
<=> ! [X0,X1] : sP48(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_333])]) ).
fof(f6123,plain,
! [X0,X1] : sP48(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),
inference(equality_resolution,[],[f5837]) ).
fof(f5837,plain,
! [X2,X0,X1] :
( sP48(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X2 ),
inference(cnf_transformation,[],[f4085]) ).
fof(f7745,plain,
spl107_332,
inference(avatar_split_clause,[],[f6024,f7743]) ).
fof(f7743,plain,
( spl107_332
<=> ! [X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X1)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_332])]) ).
fof(f6024,plain,
! [X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X1)
| ~ class_Orderings_Oorder(X2) ),
inference(equality_resolution,[],[f5192]) ).
fof(f5192,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| X0 != X1
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f3850]) ).
fof(f3850,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,[],[f3849]) ).
fof(f3849,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,[],[f2942]) ).
fof(f2942,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,[],[f1899]) ).
fof(f1899,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,[],[f76]) ).
fof(f76,axiom,
! [X20,X16,X3] :
( class_Orderings_Oorder(X3)
=> ( X16 = X20
<=> ( c_Orderings_Oord__class_Oless__eq(X3,X20,X16)
& c_Orderings_Oord__class_Oless__eq(X3,X16,X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7741,plain,
spl107_331,
inference(avatar_split_clause,[],[f6021,f7739]) ).
fof(f7739,plain,
( spl107_331
<=> ! [X2,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_331])]) ).
fof(f6021,plain,
! [X2,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
| ~ class_Orderings_Oorder(X2) ),
inference(equality_resolution,[],[f5187]) ).
fof(f5187,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f2935]) ).
fof(f2935,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f2934]) ).
fof(f2934,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f1895]) ).
fof(f1895,plain,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X0)
=> X0 != X1 ) ),
inference(rectify,[],[f28]) ).
fof(f28,axiom,
! [X21,X6,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X6,X21)
=> X6 != X21 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7737,plain,
spl107_330,
inference(avatar_split_clause,[],[f6013,f7735]) ).
fof(f7735,plain,
( spl107_330
<=> ! [X2,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_330])]) ).
fof(f6013,plain,
! [X2,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(equality_resolution,[],[f5129]) ).
fof(f5129,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f3839]) ).
fof(f3839,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,[],[f3838]) ).
fof(f3838,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,[],[f2859]) ).
fof(f2859,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,[],[f1848]) ).
fof(f1848,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,[],[f19]) ).
fof(f19,axiom,
! [X20,X16,X3] :
( class_Orderings_Olinorder(X3)
=> ( X16 != X20
<=> ( c_Orderings_Oord__class_Oless(X3,X20,X16)
| c_Orderings_Oord__class_Oless(X3,X16,X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7733,plain,
spl107_329,
inference(avatar_split_clause,[],[f5025,f7731]) ).
fof(f7731,plain,
( spl107_329
<=> ! [X2,X0,X1] :
( sP12(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_329])]) ).
fof(f5025,plain,
! [X2,X0,X1] :
( sP12(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f3592]) ).
fof(f3592,plain,
! [X0,X1,X2] :
( sP12(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(definition_folding,[],[f2729,f3591,f3590]) ).
fof(f3591,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))
<=> sP11(X0,X2,X1) )
| ~ sP12(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f2729,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,[],[f1767]) ).
fof(f1767,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,[],[f282]) ).
fof(f282,axiom,
! [X9,X10,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X10),X9),c_Groups_Ozero__class_Ozero(X3))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X9)
& c_Orderings_Oord__class_Oless__eq(X3,X10,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless__eq(X3,X9,c_Groups_Ozero__class_Ozero(X3))
& c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X10) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7729,plain,
spl107_328,
inference(avatar_split_clause,[],[f5016,f7727]) ).
fof(f7727,plain,
( spl107_328
<=> ! [X2,X0,X1] :
( sP10(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_328])]) ).
fof(f5016,plain,
! [X2,X0,X1] :
( sP10(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f3589]) ).
fof(f3589,plain,
! [X0,X1,X2] :
( sP10(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(definition_folding,[],[f2728,f3588,f3587]) ).
fof(f3588,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))
<=> sP9(X2,X0,X1) )
| ~ sP10(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f2728,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,[],[f1766]) ).
fof(f1766,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,[],[f283]) ).
fof(f283,axiom,
! [X9,X10,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X10),X9))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X3,X9,c_Groups_Ozero__class_Ozero(X3))
& c_Orderings_Oord__class_Oless__eq(X3,X10,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X9)
& c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X10) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7725,plain,
spl107_327,
inference(avatar_split_clause,[],[f4964,f7723]) ).
fof(f7723,plain,
( spl107_327
<=> ! [X2,X0,X1] :
( sP8(X1,X2,X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_327])]) ).
fof(f4964,plain,
! [X2,X0,X1] :
( sP8(X1,X2,X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(cnf_transformation,[],[f3586]) ).
fof(f3586,plain,
! [X0,X1,X2] :
( sP8(X1,X2,X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(definition_folding,[],[f2671,f3585,f3584]) ).
fof(f3585,plain,
! [X1,X2,X0] :
( ( c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
<=> sP7(X0,X2,X1) )
| ~ sP8(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f2671,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Odivide(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)) )
| ( 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_Fields_Olinordered__field__inverse__zero(X2) ),
inference(ennf_transformation,[],[f1729]) ).
fof(f1729,plain,
! [X0,X1,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Odivide(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)) )
| ( 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) ) ) ) ),
inference(rectify,[],[f380]) ).
fof(f380,axiom,
! [X9,X10,X3] :
( class_Fields_Olinordered__field__inverse__zero(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Rings_Oinverse__class_Odivide(X3,X10,X9),c_Groups_Ozero__class_Ozero(X3))
<=> ( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X9)
& c_Orderings_Oord__class_Oless(X3,X10,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X9,c_Groups_Ozero__class_Ozero(X3))
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X10) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7721,plain,
spl107_326,
inference(avatar_split_clause,[],[f4955,f7719]) ).
fof(f7719,plain,
( spl107_326
<=> ! [X2,X0,X1] :
( sP6(X1,X0,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_326])]) ).
fof(f4955,plain,
! [X2,X0,X1] :
( sP6(X1,X0,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(cnf_transformation,[],[f3583]) ).
fof(f3583,plain,
! [X0,X1,X2] :
( sP6(X1,X0,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(definition_folding,[],[f2670,f3582,f3581]) ).
fof(f3582,plain,
! [X1,X0,X2] :
( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Rings_Oinverse__class_Odivide(X2,X1,X0))
<=> sP5(X2,X0,X1) )
| ~ sP6(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f2670,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Rings_Oinverse__class_Odivide(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)) )
| ( 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_Fields_Olinordered__field__inverse__zero(X2) ),
inference(ennf_transformation,[],[f1728]) ).
fof(f1728,plain,
! [X0,X1,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Rings_Oinverse__class_Odivide(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)) )
| ( 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,[],[f381]) ).
fof(f381,axiom,
! [X9,X10,X3] :
( class_Fields_Olinordered__field__inverse__zero(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Rings_Oinverse__class_Odivide(X3,X10,X9))
<=> ( ( c_Orderings_Oord__class_Oless(X3,X9,c_Groups_Ozero__class_Ozero(X3))
& c_Orderings_Oord__class_Oless(X3,X10,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X9)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X10) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7717,plain,
spl107_325,
inference(avatar_split_clause,[],[f4946,f7715]) ).
fof(f7715,plain,
( spl107_325
<=> ! [X2,X0,X1] :
( sP4(X1,X2,X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_325])]) ).
fof(f4946,plain,
! [X2,X0,X1] :
( sP4(X1,X2,X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(cnf_transformation,[],[f3580]) ).
fof(f3580,plain,
! [X0,X1,X2] :
( sP4(X1,X2,X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(definition_folding,[],[f2669,f3579,f3578]) ).
fof(f3579,plain,
! [X1,X2,X0] :
( ( c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X0),c_Groups_Ozero__class_Ozero(X2))
<=> sP3(X0,X2,X1) )
| ~ sP4(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f2669,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Odivide(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_Fields_Olinordered__field__inverse__zero(X2) ),
inference(ennf_transformation,[],[f1727]) ).
fof(f1727,plain,
! [X0,X1,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Odivide(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,[],[f372]) ).
fof(f372,axiom,
! [X9,X10,X3] :
( class_Fields_Olinordered__field__inverse__zero(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Rings_Oinverse__class_Odivide(X3,X10,X9),c_Groups_Ozero__class_Ozero(X3))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X9)
& c_Orderings_Oord__class_Oless__eq(X3,X10,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless__eq(X3,X9,c_Groups_Ozero__class_Ozero(X3))
& c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X10) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7713,plain,
spl107_324,
inference(avatar_split_clause,[],[f4937,f7711]) ).
fof(f7711,plain,
( spl107_324
<=> ! [X2,X0,X1] :
( sP2(X1,X0,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_324])]) ).
fof(f4937,plain,
! [X2,X0,X1] :
( sP2(X1,X0,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(cnf_transformation,[],[f3577]) ).
fof(f3577,plain,
! [X0,X1,X2] :
( sP2(X1,X0,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(definition_folding,[],[f2668,f3576,f3575]) ).
fof(f3576,plain,
! [X1,X0,X2] :
( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Rings_Oinverse__class_Odivide(X2,X1,X0))
<=> sP1(X2,X0,X1) )
| ~ sP2(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f2668,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Rings_Oinverse__class_Odivide(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_Fields_Olinordered__field__inverse__zero(X2) ),
inference(ennf_transformation,[],[f1726]) ).
fof(f1726,plain,
! [X0,X1,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Rings_Oinverse__class_Odivide(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,[],[f373]) ).
fof(f373,axiom,
! [X9,X10,X3] :
( class_Fields_Olinordered__field__inverse__zero(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Rings_Oinverse__class_Odivide(X3,X10,X9))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X3,X9,c_Groups_Ozero__class_Ozero(X3))
& c_Orderings_Oord__class_Oless__eq(X3,X10,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X9)
& c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X10) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7709,plain,
spl107_323,
inference(avatar_split_clause,[],[f4686,f7707]) ).
fof(f7707,plain,
( spl107_323
<=> ! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_323])]) ).
fof(f4686,plain,
! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ),
inference(cnf_transformation,[],[f2517]) ).
fof(f2517,plain,
! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ),
inference(ennf_transformation,[],[f1561]) ).
fof(f1561,plain,
! [X0,X1] :
( class_Groups_Ominus(X1)
=> class_Groups_Ominus(tc_fun(X0,X1)) ),
inference(rectify,[],[f1005]) ).
fof(f1005,axiom,
! [X93,X92] :
( class_Groups_Ominus(X92)
=> class_Groups_Ominus(tc_fun(X93,X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7705,plain,
spl107_322,
inference(avatar_split_clause,[],[f4682,f7703]) ).
fof(f7703,plain,
( spl107_322
<=> ! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_322])]) ).
fof(f4682,plain,
! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(cnf_transformation,[],[f2515]) ).
fof(f2515,plain,
! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(ennf_transformation,[],[f1559]) ).
fof(f1559,plain,
! [X0,X1] :
( class_Orderings_Oorder(X1)
=> class_Orderings_Oorder(tc_fun(X0,X1)) ),
inference(rectify,[],[f1003]) ).
fof(f1003,axiom,
! [X93,X92] :
( class_Orderings_Oorder(X92)
=> class_Orderings_Oorder(tc_fun(X93,X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7701,plain,
spl107_321,
inference(avatar_split_clause,[],[f4681,f7699]) ).
fof(f7699,plain,
( spl107_321
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_321])]) ).
fof(f4681,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f2514]) ).
fof(f2514,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f1558]) ).
fof(f1558,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> c_Orderings_Oord__class_Oless__eq(X1,X0,X0) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X6,X3] :
( class_Orderings_Opreorder(X3)
=> c_Orderings_Oord__class_Oless__eq(X3,X6,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7697,plain,
spl107_320,
inference(avatar_split_clause,[],[f4680,f7695]) ).
fof(f7695,plain,
( spl107_320
<=> ! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_320])]) ).
fof(f4680,plain,
! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f2513]) ).
fof(f2513,plain,
! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f1557]) ).
fof(f1557,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> class_Orderings_Opreorder(tc_fun(X0,X1)) ),
inference(rectify,[],[f1002]) ).
fof(f1002,axiom,
! [X93,X92] :
( class_Orderings_Opreorder(X92)
=> class_Orderings_Opreorder(tc_fun(X93,X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7693,plain,
spl107_319,
inference(avatar_split_clause,[],[f4679,f7691]) ).
fof(f7691,plain,
( spl107_319
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_319])]) ).
fof(f4679,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f2512]) ).
fof(f2512,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f1556]) ).
fof(f1556,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> ~ c_Orderings_Oord__class_Oless(X1,X0,X0) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X6,X3] :
( class_Orderings_Opreorder(X3)
=> ~ c_Orderings_Oord__class_Oless(X3,X6,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7689,plain,
spl107_318,
inference(avatar_split_clause,[],[f4678,f7687]) ).
fof(f7687,plain,
( spl107_318
<=> ! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_318])]) ).
fof(f4678,plain,
! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ),
inference(cnf_transformation,[],[f2511]) ).
fof(f2511,plain,
! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ),
inference(ennf_transformation,[],[f1555]) ).
fof(f1555,plain,
! [X0,X1] :
( class_Orderings_Oord(X1)
=> class_Orderings_Oord(tc_fun(X0,X1)) ),
inference(rectify,[],[f1004]) ).
fof(f1004,axiom,
! [X93,X92] :
( class_Orderings_Oord(X92)
=> class_Orderings_Oord(tc_fun(X93,X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7685,plain,
spl107_317,
inference(avatar_split_clause,[],[f4664,f7683]) ).
fof(f7683,plain,
( spl107_317
<=> ! [X0,X1] :
( c_Rings_Odvd__class_Odvd(X1,X0,X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_317])]) ).
fof(f4664,plain,
! [X0,X1] :
( c_Rings_Odvd__class_Odvd(X1,X0,X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2496]) ).
fof(f2496,plain,
! [X0,X1] :
( c_Rings_Odvd__class_Odvd(X1,X0,X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1541]) ).
fof(f1541,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Rings_Odvd__class_Odvd(X1,X0,X0) ),
inference(rectify,[],[f814]) ).
fof(f814,axiom,
! [X5,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Rings_Odvd__class_Odvd(X3,X5,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7681,plain,
spl107_316,
inference(avatar_split_clause,[],[f4382,f7679]) ).
fof(f7679,plain,
( spl107_316
<=> ! [X0] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl107_316])]) ).
fof(f4382,plain,
! [X0] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X0)) = X0,
inference(cnf_transformation,[],[f1297]) ).
fof(f1297,plain,
! [X0] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X0)) = X0,
inference(rectify,[],[f661]) ).
fof(f661,axiom,
! [X41] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X41)) = X41,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7677,plain,
spl107_315,
inference(avatar_split_clause,[],[f4381,f7675]) ).
fof(f4381,plain,
! [X0] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X0)) = X0,
inference(cnf_transformation,[],[f1296]) ).
fof(f1296,plain,
! [X0] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X0)) = X0,
inference(rectify,[],[f660]) ).
fof(f660,axiom,
! [X41] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X41)) = X41,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7673,plain,
spl107_314,
inference(avatar_split_clause,[],[f4352,f7670]) ).
fof(f7670,plain,
( spl107_314
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_314])]) ).
fof(f4352,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f80]) ).
fof(f80,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7668,plain,
spl107_313,
inference(avatar_split_clause,[],[f4351,f7665]) ).
fof(f7665,plain,
( spl107_313
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_313])]) ).
fof(f4351,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f623]) ).
fof(f623,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7663,plain,
spl107_312,
inference(avatar_split_clause,[],[f4350,f7660]) ).
fof(f7660,plain,
( spl107_312
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_312])]) ).
fof(f4350,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f627]) ).
fof(f627,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7658,plain,
spl107_311,
inference(avatar_split_clause,[],[f4349,f7655]) ).
fof(f7655,plain,
( spl107_311
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Oarctan(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_311])]) ).
fof(f4349,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Oarctan(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f445]) ).
fof(f445,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Oarctan(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7653,plain,
spl107_310,
inference(avatar_split_clause,[],[f4348,f7650]) ).
fof(f7650,plain,
( spl107_310
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_310])]) ).
fof(f4348,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f626]) ).
fof(f626,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7648,plain,
spl107_309,
inference(avatar_split_clause,[],[f4347,f7645]) ).
fof(f4347,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f630]) ).
fof(f630,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7643,plain,
spl107_308,
inference(avatar_split_clause,[],[f4346,f7640]) ).
fof(f7640,plain,
( spl107_308
<=> c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_308])]) ).
fof(f4346,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(cnf_transformation,[],[f781]) ).
fof(f781,axiom,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7638,plain,
spl107_307,
inference(avatar_split_clause,[],[f6054,f7636]) ).
fof(f7636,plain,
( spl107_307
<=> ! [X0,X1] : sP25(X0,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_307])]) ).
fof(f6054,plain,
! [X0,X1] : sP25(X0,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f5385]) ).
fof(f5385,plain,
! [X2,X0,X1] :
( sP25(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ),
inference(cnf_transformation,[],[f3937]) ).
fof(f7634,plain,
spl107_306,
inference(avatar_split_clause,[],[f6048,f7632]) ).
fof(f7632,plain,
( spl107_306
<=> ! [X0,X1] : sP21(X0,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_306])]) ).
fof(f6048,plain,
! [X0,X1] : sP21(X0,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f5357]) ).
fof(f5357,plain,
! [X2,X0,X1] :
( sP21(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ),
inference(cnf_transformation,[],[f3917]) ).
fof(f7630,plain,
spl107_305,
inference(avatar_split_clause,[],[f5929,f7627]) ).
fof(f5929,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK106),
inference(cnf_transformation,[],[f4116]) ).
fof(f4116,plain,
( ! [X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z,v_z)))),v_e)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z)),sK106)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z))) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK106) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK106])],[f3572,f4115]) ).
fof(f4115,plain,
( ? [X0] :
( ! [X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z,v_z)))),v_e)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z))) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) )
=> ( ! [X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z,v_z)))),v_e)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z)),sK106)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z))) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK106) ) ),
introduced(choice_axiom,[]) ).
fof(f3572,plain,
? [X0] :
( ! [X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z,v_z)))),v_e)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z))) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(flattening,[],[f3571]) ).
fof(f3571,plain,
? [X0] :
( ! [X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z,v_z)))),v_e)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z))) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(ennf_transformation,[],[f2312]) ).
fof(f2312,plain,
? [X0] :
( ! [X1] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z)),X0)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z))) )
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z,v_z)))),v_e) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(rectify,[],[f441]) ).
fof(f441,axiom,
? [X29] :
( ! [X23] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X23,v_z)),X29)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X23,v_z))) )
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X23,v_z)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z,v_z)))),v_e) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X29) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7625,plain,
spl107_304,
inference(avatar_split_clause,[],[f5927,f7622]) ).
fof(f5927,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK105),
inference(cnf_transformation,[],[f4114]) ).
fof(f4114,plain,
( ! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),X1)),sK105)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK105) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK105])],[f3570,f4113]) ).
fof(f4113,plain,
( ? [X0] :
( ! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),X1)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) )
=> ( ! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),X1)),sK105)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK105) ) ),
introduced(choice_axiom,[]) ).
fof(f3570,plain,
? [X0] :
( ! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),X1)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(ennf_transformation,[],[f2311]) ).
fof(f2311,plain,
? [X0] :
( ! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),X1)),X0) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(rectify,[],[f447]) ).
fof(f447,axiom,
? [X54] :
( ! [X55] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X55),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),X55)),X54) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X54) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7620,plain,
spl107_303,
inference(avatar_split_clause,[],[f5925,f7617]) ).
fof(f5925,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK104,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f4112]) ).
fof(f7615,plain,
spl107_302,
inference(avatar_split_clause,[],[f5924,f7612]) ).
fof(f5924,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK104),
inference(cnf_transformation,[],[f4112]) ).
fof(f7610,plain,
spl107_301,
inference(avatar_split_clause,[],[f4488,f7608]) ).
fof(f7608,plain,
( spl107_301
<=> ! [X0] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_301])]) ).
fof(f4488,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2394]) ).
fof(f2394,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1400]) ).
fof(f1400,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1249]) ).
fof(f1249,axiom,
! [X92] :
( class_Rings_Ocomm__semiring__1(X92)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7606,plain,
spl107_300,
inference(avatar_split_clause,[],[f4487,f7604]) ).
fof(f7604,plain,
( spl107_300
<=> ! [X0] :
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_300])]) ).
fof(f4487,plain,
! [X0] :
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2393]) ).
fof(f2393,plain,
! [X0] :
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1399]) ).
fof(f1399,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1258]) ).
fof(f1258,axiom,
! [X92] :
( class_Rings_Ocomm__semiring__1(X92)
=> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7602,plain,
spl107_299,
inference(avatar_split_clause,[],[f4486,f7600]) ).
fof(f7600,plain,
( spl107_299
<=> ! [X0] :
( class_Power_Opower(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_299])]) ).
fof(f4486,plain,
! [X0] :
( class_Power_Opower(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2392]) ).
fof(f2392,plain,
! [X0] :
( class_Power_Opower(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1398]) ).
fof(f1398,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Power_Opower(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1272]) ).
fof(f1272,axiom,
! [X92] :
( class_Rings_Ocomm__semiring__1(X92)
=> class_Power_Opower(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7598,plain,
spl107_298,
inference(avatar_split_clause,[],[f4485,f7596]) ).
fof(f7596,plain,
( spl107_298
<=> ! [X0] :
( class_Rings_Odvd(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_298])]) ).
fof(f4485,plain,
! [X0] :
( class_Rings_Odvd(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2391]) ).
fof(f2391,plain,
! [X0] :
( class_Rings_Odvd(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1397]) ).
fof(f1397,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Rings_Odvd(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1277]) ).
fof(f1277,axiom,
! [X92] :
( class_Rings_Ocomm__semiring__1(X92)
=> class_Rings_Odvd(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7594,plain,
spl107_297,
inference(avatar_split_clause,[],[f4484,f7592]) ).
fof(f7592,plain,
( spl107_297
<=> ! [X0] :
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_297])]) ).
fof(f4484,plain,
! [X0] :
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2390]) ).
fof(f2390,plain,
! [X0] :
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1396]) ).
fof(f1396,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1241]) ).
fof(f1241,axiom,
! [X92] :
( class_Rings_Ocomm__semiring__1(X92)
=> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7590,plain,
spl107_296,
inference(avatar_split_clause,[],[f4483,f7588]) ).
fof(f7588,plain,
( spl107_296
<=> ! [X0] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_296])]) ).
fof(f4483,plain,
! [X0] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2389]) ).
fof(f2389,plain,
! [X0] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1395]) ).
fof(f1395,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1254]) ).
fof(f1254,axiom,
! [X92] :
( class_Rings_Ocomm__semiring__1(X92)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7586,plain,
spl107_295,
inference(avatar_split_clause,[],[f4482,f7584]) ).
fof(f7584,plain,
( spl107_295
<=> ! [X0] :
( class_Groups_Oone(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_295])]) ).
fof(f4482,plain,
! [X0] :
( class_Groups_Oone(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2388]) ).
fof(f2388,plain,
! [X0] :
( class_Groups_Oone(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1394]) ).
fof(f1394,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Groups_Oone(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1276]) ).
fof(f1276,axiom,
! [X92] :
( class_Rings_Ocomm__semiring__1(X92)
=> class_Groups_Oone(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7582,plain,
spl107_294,
inference(avatar_split_clause,[],[f4481,f7580]) ).
fof(f7580,plain,
( spl107_294
<=> ! [X0] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_294])]) ).
fof(f4481,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2387]) ).
fof(f2387,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1393]) ).
fof(f1393,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1250]) ).
fof(f1250,axiom,
! [X92] :
( class_Rings_Ocomm__semiring__0(X92)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7578,plain,
spl107_293,
inference(avatar_split_clause,[],[f4480,f7576]) ).
fof(f7576,plain,
( spl107_293
<=> ! [X0] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_293])]) ).
fof(f4480,plain,
! [X0] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2386]) ).
fof(f2386,plain,
! [X0] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1392]) ).
fof(f1392,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1264]) ).
fof(f1264,axiom,
! [X92] :
( class_Rings_Ocomm__semiring__0(X92)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7574,plain,
spl107_292,
inference(avatar_split_clause,[],[f4479,f7572]) ).
fof(f7572,plain,
( spl107_292
<=> ! [X0] :
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_292])]) ).
fof(f4479,plain,
! [X0] :
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2385]) ).
fof(f2385,plain,
! [X0] :
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1391]) ).
fof(f1391,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1261]) ).
fof(f1261,axiom,
! [X92] :
( class_Rings_Ocomm__semiring__0(X92)
=> class_Rings_Osemiring__0(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7570,plain,
spl107_291,
inference(avatar_split_clause,[],[f4478,f7568]) ).
fof(f7568,plain,
( spl107_291
<=> ! [X0] :
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_291])]) ).
fof(f4478,plain,
! [X0] :
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2384]) ).
fof(f2384,plain,
! [X0] :
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1390]) ).
fof(f1390,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1240]) ).
fof(f1240,axiom,
! [X92] :
( class_Rings_Ocomm__semiring__0(X92)
=> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7566,plain,
spl107_290,
inference(avatar_split_clause,[],[f4477,f7564]) ).
fof(f7564,plain,
( spl107_290
<=> ! [X0] :
( class_Rings_Osemiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_290])]) ).
fof(f4477,plain,
! [X0] :
( class_Rings_Osemiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2383]) ).
fof(f2383,plain,
! [X0] :
( class_Rings_Osemiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1389]) ).
fof(f1389,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Rings_Osemiring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1268]) ).
fof(f1268,axiom,
! [X92] :
( class_Rings_Ocomm__semiring__0(X92)
=> class_Rings_Osemiring(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7562,plain,
spl107_289,
inference(avatar_split_clause,[],[f4476,f7560]) ).
fof(f7560,plain,
( spl107_289
<=> ! [X0] :
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_289])]) ).
fof(f4476,plain,
! [X0] :
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2382]) ).
fof(f2382,plain,
! [X0] :
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1388]) ).
fof(f1388,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1252]) ).
fof(f1252,axiom,
! [X92] :
( class_Rings_Ocomm__semiring__0(X92)
=> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7558,plain,
spl107_288,
inference(avatar_split_clause,[],[f4475,f7556]) ).
fof(f7556,plain,
( spl107_288
<=> ! [X0] :
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_288])]) ).
fof(f4475,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2381]) ).
fof(f2381,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(ennf_transformation,[],[f1387]) ).
fof(f1387,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(X0)
=> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1246]) ).
fof(f1246,axiom,
! [X92] :
( class_Groups_Ocomm__monoid__add(X92)
=> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7554,plain,
spl107_287,
inference(avatar_split_clause,[],[f4474,f7552]) ).
fof(f7552,plain,
( spl107_287
<=> ! [X0] :
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_287])]) ).
fof(f4474,plain,
! [X0] :
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2380]) ).
fof(f2380,plain,
! [X0] :
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(ennf_transformation,[],[f1386]) ).
fof(f1386,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(X0)
=> class_Groups_Omonoid__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1260]) ).
fof(f1260,axiom,
! [X92] :
( class_Groups_Ocomm__monoid__add(X92)
=> class_Groups_Omonoid__add(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7550,plain,
spl107_286,
inference(avatar_split_clause,[],[f4473,f7548]) ).
fof(f7548,plain,
( spl107_286
<=> ! [X0] :
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_286])]) ).
fof(f4473,plain,
! [X0] :
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2379]) ).
fof(f2379,plain,
! [X0] :
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(ennf_transformation,[],[f1385]) ).
fof(f1385,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(X0)
=> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1242]) ).
fof(f1242,axiom,
! [X92] :
( class_Groups_Ocomm__monoid__add(X92)
=> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7546,plain,
spl107_285,
inference(avatar_split_clause,[],[f4470,f7544]) ).
fof(f7544,plain,
( spl107_285
<=> ! [X0] :
( class_Groups_Ozero(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_285])]) ).
fof(f4470,plain,
! [X0] :
( class_Groups_Ozero(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f2376]) ).
fof(f2376,plain,
! [X0] :
( class_Groups_Ozero(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ozero(X0) ),
inference(ennf_transformation,[],[f1382]) ).
fof(f1382,plain,
! [X0] :
( class_Groups_Ozero(X0)
=> class_Groups_Ozero(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1273]) ).
fof(f1273,axiom,
! [X92] :
( class_Groups_Ozero(X92)
=> class_Groups_Ozero(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7542,plain,
spl107_284,
inference(avatar_split_clause,[],[f4467,f7540]) ).
fof(f7540,plain,
( spl107_284
<=> ! [X0] :
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_284])]) ).
fof(f4467,plain,
! [X0] :
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2373]) ).
fof(f2373,plain,
! [X0] :
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(ennf_transformation,[],[f1379]) ).
fof(f1379,plain,
! [X0] :
( class_Groups_Ocancel__comm__monoid__add(X0)
=> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1237]) ).
fof(f1237,axiom,
! [X92] :
( class_Groups_Ocancel__comm__monoid__add(X92)
=> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7538,plain,
spl107_283,
inference(avatar_split_clause,[],[f4466,f7536]) ).
fof(f7536,plain,
( spl107_283
<=> ! [X0] :
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_283])]) ).
fof(f4466,plain,
! [X0] :
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2372]) ).
fof(f2372,plain,
! [X0] :
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(ennf_transformation,[],[f1378]) ).
fof(f1378,plain,
! [X0] :
( class_Groups_Ocancel__comm__monoid__add(X0)
=> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f997]) ).
fof(f997,axiom,
! [X92] :
( class_Groups_Ocancel__comm__monoid__add(X92)
=> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7534,plain,
spl107_282,
inference(avatar_split_clause,[],[f4465,f7532]) ).
fof(f7532,plain,
( spl107_282
<=> ! [X0] :
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_282])]) ).
fof(f4465,plain,
! [X0] :
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2371]) ).
fof(f2371,plain,
! [X0] :
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(ennf_transformation,[],[f1377]) ).
fof(f1377,plain,
! [X0] :
( class_Groups_Ocancel__comm__monoid__add(X0)
=> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1229]) ).
fof(f1229,axiom,
! [X92] :
( class_Groups_Ocancel__comm__monoid__add(X92)
=> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7530,plain,
spl107_281,
inference(avatar_split_clause,[],[f4459,f7528]) ).
fof(f7528,plain,
( spl107_281
<=> ! [X0] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_281])]) ).
fof(f4459,plain,
! [X0] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f2365]) ).
fof(f2365,plain,
! [X0] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(ennf_transformation,[],[f1371]) ).
fof(f1371,plain,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1219]) ).
fof(f1219,axiom,
! [X92] :
( class_Rings_Oidom(X92)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7526,plain,
spl107_280,
inference(avatar_split_clause,[],[f4458,f7524]) ).
fof(f7524,plain,
( spl107_280
<=> ! [X0] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_280])]) ).
fof(f4458,plain,
! [X0] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f2364]) ).
fof(f2364,plain,
! [X0] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(ennf_transformation,[],[f1370]) ).
fof(f1370,plain,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1245]) ).
fof(f1245,axiom,
! [X92] :
( class_Rings_Oidom(X92)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7522,plain,
spl107_279,
inference(avatar_split_clause,[],[f4457,f7520]) ).
fof(f7520,plain,
( spl107_279
<=> ! [X0] :
( class_Rings_Oidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_279])]) ).
fof(f4457,plain,
! [X0] :
( class_Rings_Oidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f2363]) ).
fof(f2363,plain,
! [X0] :
( class_Rings_Oidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(ennf_transformation,[],[f1369]) ).
fof(f1369,plain,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Rings_Oidom(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1275]) ).
fof(f1275,axiom,
! [X92] :
( class_Rings_Oidom(X92)
=> class_Rings_Oidom(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7518,plain,
spl107_278,
inference(avatar_split_clause,[],[f4456,f7516]) ).
fof(f7516,plain,
( spl107_278
<=> ! [X0] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_278])]) ).
fof(f4456,plain,
! [X0] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f2362]) ).
fof(f2362,plain,
! [X0] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(ennf_transformation,[],[f1368]) ).
fof(f1368,plain,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1230]) ).
fof(f1230,axiom,
! [X92] :
( class_Rings_Oidom(X92)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7514,plain,
spl107_277,
inference(avatar_split_clause,[],[f4455,f7512]) ).
fof(f7512,plain,
( spl107_277
<=> ! [X0] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_277])]) ).
fof(f4455,plain,
! [X0] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f2361]) ).
fof(f2361,plain,
! [X0] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(ennf_transformation,[],[f1367]) ).
fof(f1367,plain,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1233]) ).
fof(f1233,axiom,
! [X92] :
( class_Rings_Oidom(X92)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7510,plain,
spl107_276,
inference(avatar_split_clause,[],[f4454,f7508]) ).
fof(f7508,plain,
( spl107_276
<=> ! [X0] :
( class_Groups_Ominus(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_276])]) ).
fof(f4454,plain,
! [X0] :
( class_Groups_Ominus(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f2360]) ).
fof(f2360,plain,
! [X0] :
( class_Groups_Ominus(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(ennf_transformation,[],[f1366]) ).
fof(f1366,plain,
! [X0] :
( class_Groups_Oab__group__add(X0)
=> class_Groups_Ominus(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1271]) ).
fof(f1271,axiom,
! [X92] :
( class_Groups_Oab__group__add(X92)
=> class_Groups_Ominus(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7506,plain,
spl107_275,
inference(avatar_split_clause,[],[f4453,f7504]) ).
fof(f7504,plain,
( spl107_275
<=> ! [X0] :
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_275])]) ).
fof(f4453,plain,
! [X0] :
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f2359]) ).
fof(f2359,plain,
! [X0] :
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(ennf_transformation,[],[f1365]) ).
fof(f1365,plain,
! [X0] :
( class_Groups_Oab__group__add(X0)
=> class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1253]) ).
fof(f1253,axiom,
! [X92] :
( class_Groups_Oab__group__add(X92)
=> class_Groups_Oab__group__add(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7502,plain,
spl107_274,
inference(avatar_split_clause,[],[f4452,f7500]) ).
fof(f7500,plain,
( spl107_274
<=> ! [X0] :
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_274])]) ).
fof(f4452,plain,
! [X0] :
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f2358]) ).
fof(f2358,plain,
! [X0] :
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(ennf_transformation,[],[f1364]) ).
fof(f1364,plain,
! [X0] :
( class_Groups_Oab__group__add(X0)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1262]) ).
fof(f1262,axiom,
! [X92] :
( class_Groups_Oab__group__add(X92)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7498,plain,
spl107_273,
inference(avatar_split_clause,[],[f4451,f7496]) ).
fof(f7496,plain,
( spl107_273
<=> ! [X0] :
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_273])]) ).
fof(f4451,plain,
! [X0] :
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ),
inference(cnf_transformation,[],[f2357]) ).
fof(f2357,plain,
! [X0] :
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ),
inference(ennf_transformation,[],[f1363]) ).
fof(f1363,plain,
! [X0] :
( class_Rings_Ocomm__ring(X0)
=> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1265]) ).
fof(f1265,axiom,
! [X92] :
( class_Rings_Ocomm__ring(X92)
=> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7494,plain,
spl107_272,
inference(avatar_split_clause,[],[f4450,f7492]) ).
fof(f7492,plain,
( spl107_272
<=> ! [X0] :
( class_Rings_Oring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_272])]) ).
fof(f4450,plain,
! [X0] :
( class_Rings_Oring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ),
inference(cnf_transformation,[],[f2356]) ).
fof(f2356,plain,
! [X0] :
( class_Rings_Oring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ),
inference(ennf_transformation,[],[f1362]) ).
fof(f1362,plain,
! [X0] :
( class_Rings_Ocomm__ring(X0)
=> class_Rings_Oring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1274]) ).
fof(f1274,axiom,
! [X92] :
( class_Rings_Ocomm__ring(X92)
=> class_Rings_Oring(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7490,plain,
spl107_271,
inference(avatar_split_clause,[],[f4449,f7488]) ).
fof(f7488,plain,
( spl107_271
<=> ! [X0] :
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_271])]) ).
fof(f4449,plain,
! [X0] :
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(cnf_transformation,[],[f2355]) ).
fof(f2355,plain,
! [X0] :
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(ennf_transformation,[],[f1361]) ).
fof(f1361,plain,
! [X0] :
( class_Rings_Ocomm__ring__1(X0)
=> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1259]) ).
fof(f1259,axiom,
! [X92] :
( class_Rings_Ocomm__ring__1(X92)
=> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7486,plain,
spl107_270,
inference(avatar_split_clause,[],[f4448,f7484]) ).
fof(f7484,plain,
( spl107_270
<=> ! [X0] :
( class_Rings_Oring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_270])]) ).
fof(f4448,plain,
! [X0] :
( class_Rings_Oring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(cnf_transformation,[],[f2354]) ).
fof(f2354,plain,
! [X0] :
( class_Rings_Oring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(ennf_transformation,[],[f1360]) ).
fof(f1360,plain,
! [X0] :
( class_Rings_Ocomm__ring__1(X0)
=> class_Rings_Oring__1(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1270]) ).
fof(f1270,axiom,
! [X92] :
( class_Rings_Ocomm__ring__1(X92)
=> class_Rings_Oring__1(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7482,plain,
spl107_269,
inference(avatar_split_clause,[],[f4446,f7480]) ).
fof(f7480,plain,
( spl107_269
<=> ! [X0] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_269])]) ).
fof(f4446,plain,
! [X0] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2352]) ).
fof(f2352,plain,
! [X0] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1358]) ).
fof(f1358,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Orderings_Oorder(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1266]) ).
fof(f1266,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Orderings_Oorder(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7478,plain,
spl107_268,
inference(avatar_split_clause,[],[f4445,f7476]) ).
fof(f7476,plain,
( spl107_268
<=> ! [X0] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_268])]) ).
fof(f4445,plain,
! [X0] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2351]) ).
fof(f2351,plain,
! [X0] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1357]) ).
fof(f1357,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Orderings_Opreorder(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1256]) ).
fof(f1256,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Orderings_Opreorder(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7474,plain,
spl107_267,
inference(avatar_split_clause,[],[f4444,f7472]) ).
fof(f7472,plain,
( spl107_267
<=> ! [X0] :
( class_Orderings_Oord(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_267])]) ).
fof(f4444,plain,
! [X0] :
( class_Orderings_Oord(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2350]) ).
fof(f2350,plain,
! [X0] :
( class_Orderings_Oord(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1356]) ).
fof(f1356,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Orderings_Oord(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1269]) ).
fof(f1269,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Orderings_Oord(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7470,plain,
spl107_266,
inference(avatar_split_clause,[],[f4443,f7468]) ).
fof(f7468,plain,
( spl107_266
<=> ! [X0] :
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_266])]) ).
fof(f4443,plain,
! [X0] :
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2349]) ).
fof(f2349,plain,
! [X0] :
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1355]) ).
fof(f1355,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1239]) ).
fof(f1239,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7466,plain,
spl107_265,
inference(avatar_split_clause,[],[f4442,f7464]) ).
fof(f7464,plain,
( spl107_265
<=> ! [X0] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_265])]) ).
fof(f4442,plain,
! [X0] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2348]) ).
fof(f2348,plain,
! [X0] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1354]) ).
fof(f1354,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Orderings_Olinorder(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1257]) ).
fof(f1257,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Orderings_Olinorder(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7462,plain,
spl107_264,
inference(avatar_split_clause,[],[f4441,f7460]) ).
fof(f7460,plain,
( spl107_264
<=> ! [X0] :
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_264])]) ).
fof(f4441,plain,
! [X0] :
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2347]) ).
fof(f2347,plain,
! [X0] :
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1353]) ).
fof(f1353,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1224]) ).
fof(f1224,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7458,plain,
spl107_263,
inference(avatar_split_clause,[],[f4440,f7456]) ).
fof(f7456,plain,
( spl107_263
<=> ! [X0] :
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_263])]) ).
fof(f4440,plain,
! [X0] :
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2346]) ).
fof(f2346,plain,
! [X0] :
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1352]) ).
fof(f1352,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1227]) ).
fof(f1227,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7454,plain,
spl107_262,
inference(avatar_split_clause,[],[f4439,f7452]) ).
fof(f7452,plain,
( spl107_262
<=> ! [X0] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_262])]) ).
fof(f4439,plain,
! [X0] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2345]) ).
fof(f2345,plain,
! [X0] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1351]) ).
fof(f1351,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1221]) ).
fof(f1221,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7450,plain,
spl107_261,
inference(avatar_split_clause,[],[f4438,f7448]) ).
fof(f7448,plain,
( spl107_261
<=> ! [X0] :
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_261])]) ).
fof(f4438,plain,
! [X0] :
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2344]) ).
fof(f2344,plain,
! [X0] :
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1350]) ).
fof(f1350,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1231]) ).
fof(f1231,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7446,plain,
spl107_260,
inference(avatar_split_clause,[],[f4437,f7444]) ).
fof(f7444,plain,
( spl107_260
<=> ! [X0] :
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_260])]) ).
fof(f4437,plain,
! [X0] :
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2343]) ).
fof(f2343,plain,
! [X0] :
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1349]) ).
fof(f1349,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1220]) ).
fof(f1220,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7442,plain,
spl107_259,
inference(avatar_split_clause,[],[f4436,f7440]) ).
fof(f7440,plain,
( spl107_259
<=> ! [X0] :
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_259])]) ).
fof(f4436,plain,
! [X0] :
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2342]) ).
fof(f2342,plain,
! [X0] :
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1348]) ).
fof(f1348,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1243]) ).
fof(f1243,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7438,plain,
spl107_258,
inference(avatar_split_clause,[],[f4435,f7436]) ).
fof(f7436,plain,
( spl107_258
<=> ! [X0] :
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_258])]) ).
fof(f4435,plain,
! [X0] :
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2341]) ).
fof(f2341,plain,
! [X0] :
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1347]) ).
fof(f1347,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1225]) ).
fof(f1225,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7434,plain,
spl107_257,
inference(avatar_split_clause,[],[f4434,f7432]) ).
fof(f7432,plain,
( spl107_257
<=> ! [X0] :
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_257])]) ).
fof(f4434,plain,
! [X0] :
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2340]) ).
fof(f2340,plain,
! [X0] :
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1346]) ).
fof(f1346,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1238]) ).
fof(f1238,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7430,plain,
spl107_256,
inference(avatar_split_clause,[],[f4433,f7428]) ).
fof(f7428,plain,
( spl107_256
<=> ! [X0] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_256])]) ).
fof(f4433,plain,
! [X0] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2339]) ).
fof(f2339,plain,
! [X0] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1345]) ).
fof(f1345,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Int_Oring__char__0(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1267]) ).
fof(f1267,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Int_Oring__char__0(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7426,plain,
spl107_255,
inference(avatar_split_clause,[],[f4432,f7424]) ).
fof(f7424,plain,
( spl107_255
<=> ! [X0] :
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_255])]) ).
fof(f4432,plain,
! [X0] :
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2338]) ).
fof(f2338,plain,
! [X0] :
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1344]) ).
fof(f1344,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1234]) ).
fof(f1234,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7422,plain,
spl107_254,
inference(avatar_split_clause,[],[f4431,f7420]) ).
fof(f7420,plain,
( spl107_254
<=> ! [X0] :
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_254])]) ).
fof(f4431,plain,
! [X0] :
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2337]) ).
fof(f2337,plain,
! [X0] :
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1343]) ).
fof(f1343,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1222]) ).
fof(f1222,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7418,plain,
spl107_253,
inference(avatar_split_clause,[],[f4430,f7416]) ).
fof(f7416,plain,
( spl107_253
<=> ! [X0] :
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_253])]) ).
fof(f4430,plain,
! [X0] :
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2336]) ).
fof(f2336,plain,
! [X0] :
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1342]) ).
fof(f1342,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1248]) ).
fof(f1248,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7414,plain,
spl107_252,
inference(avatar_split_clause,[],[f4429,f7412]) ).
fof(f7412,plain,
( spl107_252
<=> ! [X0] :
( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_252])]) ).
fof(f4429,plain,
! [X0] :
( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2335]) ).
fof(f2335,plain,
! [X0] :
( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1341]) ).
fof(f1341,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1226]) ).
fof(f1226,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7410,plain,
spl107_251,
inference(avatar_split_clause,[],[f4428,f7408]) ).
fof(f7408,plain,
( spl107_251
<=> ! [X0] :
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_251])]) ).
fof(f4428,plain,
! [X0] :
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2334]) ).
fof(f2334,plain,
! [X0] :
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1340]) ).
fof(f1340,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1232]) ).
fof(f1232,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7406,plain,
spl107_250,
inference(avatar_split_clause,[],[f4427,f7404]) ).
fof(f7404,plain,
( spl107_250
<=> ! [X0] :
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_250])]) ).
fof(f4427,plain,
! [X0] :
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2333]) ).
fof(f2333,plain,
! [X0] :
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1339]) ).
fof(f1339,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1255]) ).
fof(f1255,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Rings_Oordered__ring(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7402,plain,
spl107_249,
inference(avatar_split_clause,[],[f4426,f7400]) ).
fof(f7400,plain,
( spl107_249
<=> ! [X0] :
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_249])]) ).
fof(f4426,plain,
! [X0] :
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2332]) ).
fof(f2332,plain,
! [X0] :
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1338]) ).
fof(f1338,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1228]) ).
fof(f1228,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7398,plain,
spl107_248,
inference(avatar_split_clause,[],[f4425,f7396]) ).
fof(f7396,plain,
( spl107_248
<=> ! [X0] :
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_248])]) ).
fof(f4425,plain,
! [X0] :
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2331]) ).
fof(f2331,plain,
! [X0] :
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1337]) ).
fof(f1337,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1247]) ).
fof(f1247,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7394,plain,
spl107_247,
inference(avatar_split_clause,[],[f4424,f7392]) ).
fof(f7392,plain,
( spl107_247
<=> ! [X0] :
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_247])]) ).
fof(f4424,plain,
! [X0] :
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2330]) ).
fof(f2330,plain,
! [X0] :
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1336]) ).
fof(f1336,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1236]) ).
fof(f1236,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7390,plain,
spl107_246,
inference(avatar_split_clause,[],[f4423,f7388]) ).
fof(f7388,plain,
( spl107_246
<=> ! [X0] :
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_246])]) ).
fof(f4423,plain,
! [X0] :
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2329]) ).
fof(f2329,plain,
! [X0] :
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1335]) ).
fof(f1335,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1235]) ).
fof(f1235,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7386,plain,
spl107_245,
inference(avatar_split_clause,[],[f4422,f7384]) ).
fof(f7384,plain,
( spl107_245
<=> ! [X0] :
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_245])]) ).
fof(f4422,plain,
! [X0] :
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2328]) ).
fof(f2328,plain,
! [X0] :
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1334]) ).
fof(f1334,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1223]) ).
fof(f1223,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7382,plain,
spl107_244,
inference(avatar_split_clause,[],[f4421,f7380]) ).
fof(f7380,plain,
( spl107_244
<=> ! [X0] :
( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_244])]) ).
fof(f4421,plain,
! [X0] :
( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2327]) ).
fof(f2327,plain,
! [X0] :
( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1333]) ).
fof(f1333,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1244]) ).
fof(f1244,axiom,
! [X92] :
( class_Rings_Olinordered__idom(X92)
=> class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7378,plain,
spl107_243,
inference(avatar_split_clause,[],[f4419,f7376]) ).
fof(f7376,plain,
( spl107_243
<=> ! [X0] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0))
| ~ class_Fields_Ofield(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_243])]) ).
fof(f4419,plain,
! [X0] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0))
| ~ class_Fields_Ofield(X0) ),
inference(cnf_transformation,[],[f2325]) ).
fof(f2325,plain,
! [X0] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0))
| ~ class_Fields_Ofield(X0) ),
inference(ennf_transformation,[],[f1331]) ).
fof(f1331,plain,
! [X0] :
( class_Fields_Ofield(X0)
=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1251]) ).
fof(f1251,axiom,
! [X92] :
( class_Fields_Ofield(X92)
=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7374,plain,
spl107_242,
inference(avatar_split_clause,[],[f4418,f7372]) ).
fof(f7372,plain,
( spl107_242
<=> ! [X0] :
( class_Divides_Oring__div(tc_Polynomial_Opoly(X0))
| ~ class_Fields_Ofield(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_242])]) ).
fof(f4418,plain,
! [X0] :
( class_Divides_Oring__div(tc_Polynomial_Opoly(X0))
| ~ class_Fields_Ofield(X0) ),
inference(cnf_transformation,[],[f2324]) ).
fof(f2324,plain,
! [X0] :
( class_Divides_Oring__div(tc_Polynomial_Opoly(X0))
| ~ class_Fields_Ofield(X0) ),
inference(ennf_transformation,[],[f1330]) ).
fof(f1330,plain,
! [X0] :
( class_Fields_Ofield(X0)
=> class_Divides_Oring__div(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1263]) ).
fof(f1263,axiom,
! [X92] :
( class_Fields_Ofield(X92)
=> class_Divides_Oring__div(tc_Polynomial_Opoly(X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7370,plain,
spl107_241,
inference(avatar_split_clause,[],[f4379,f7368]) ).
fof(f7368,plain,
( spl107_241
<=> ! [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,[spl107_241])]) ).
fof(f4379,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f1294]) ).
fof(f1294,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
inference(rectify,[],[f481]) ).
fof(f481,axiom,
! [X41] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7366,plain,
spl107_240,
inference(avatar_split_clause,[],[f4378,f7364]) ).
fof(f7364,plain,
( spl107_240
<=> ! [X0] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_240])]) ).
fof(f4378,plain,
! [X0] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f1293]) ).
fof(f1293,plain,
! [X0] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(rectify,[],[f870]) ).
fof(f870,axiom,
! [X6] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7362,plain,
spl107_239,
inference(avatar_split_clause,[],[f4377,f7360]) ).
fof(f7360,plain,
( spl107_239
<=> ! [X0] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_239])]) ).
fof(f4377,plain,
! [X0] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f1292]) ).
fof(f1292,plain,
! [X0] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rectify,[],[f871]) ).
fof(f871,axiom,
! [X6] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X6,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7358,plain,
spl107_238,
inference(avatar_split_clause,[],[f4374,f7356]) ).
fof(f7356,plain,
( spl107_238
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_238])]) ).
fof(f4374,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f1289]) ).
fof(f1289,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rectify,[],[f546]) ).
fof(f546,axiom,
! [X41] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7354,plain,
spl107_237,
inference(avatar_split_clause,[],[f4365,f7351]) ).
fof(f4365,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK52),
inference(cnf_transformation,[],[f3652]) ).
fof(f3652,plain,
( ! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),X1)),sK52)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK52) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f2318,f3651]) ).
fof(f3651,plain,
( ? [X0] :
( ! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),X1)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) )
=> ( ! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),X1)),sK52)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK52) ) ),
introduced(choice_axiom,[]) ).
fof(f2318,plain,
? [X0] :
( ! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),X1)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(ennf_transformation,[],[f1282]) ).
fof(f1282,plain,
~ ! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
=> ~ ! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),X1)),X0) ) ),
inference(rectify,[],[f450]) ).
fof(f450,axiom,
~ ! [X54] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X54)
=> ~ ! [X55] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X55),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),X55)),X54) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7349,plain,
spl107_236,
inference(avatar_split_clause,[],[f4363,f7346]) ).
fof(f4363,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK51,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f3650]) ).
fof(f7344,plain,
spl107_235,
inference(avatar_split_clause,[],[f4362,f7341]) ).
fof(f4362,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK51),
inference(cnf_transformation,[],[f3650]) ).
fof(f7339,plain,
spl107_234,
inference(avatar_split_clause,[],[f4345,f7336]) ).
fof(f4345,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
inference(cnf_transformation,[],[f92]) ).
fof(f92,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7334,plain,
spl107_233,
inference(avatar_split_clause,[],[f4344,f7331]) ).
fof(f4344,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_e),
inference(cnf_transformation,[],[f93]) ).
fof(f93,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7329,plain,
spl107_232,
inference(avatar_split_clause,[],[f4343,f7326]) ).
fof(f4343,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____),
inference(cnf_transformation,[],[f84]) ).
fof(f84,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7324,plain,
spl107_231,
inference(avatar_split_clause,[],[f4342,f7321]) ).
fof(f4342,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_da____),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_da____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7319,plain,
spl107_230,
inference(avatar_split_clause,[],[f4341,f7316]) ).
fof(f4341,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7314,plain,
spl107_229,
inference(avatar_split_clause,[],[f4340,f7311]) ).
fof(f4340,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7309,plain,
~ spl107_228,
inference(avatar_split_clause,[],[f4339,f7306]) ).
fof(f7306,plain,
( spl107_228
<=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_228])]) ).
fof(f4339,plain,
c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f196]) ).
fof(f196,axiom,
c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7304,plain,
spl107_227,
inference(avatar_split_clause,[],[f5976,f7302]) ).
fof(f7302,plain,
( spl107_227
<=> ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_227])]) ).
fof(f5976,plain,
! [X1] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(equality_resolution,[],[f4827]) ).
fof(f4827,plain,
! [X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f3738]) ).
fof(f3738,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) )
& ( ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) ),
inference(flattening,[],[f3737]) ).
fof(f3737,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) )
& ( ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) ),
inference(nnf_transformation,[],[f1668]) ).
fof(f1668,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
<=> ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
inference(rectify,[],[f62]) ).
fof(f62,axiom,
! [X20,X16] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X16,X20)
<=> ( X16 != X20
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7300,plain,
spl107_226,
inference(avatar_split_clause,[],[f4373,f7298]) ).
fof(f7298,plain,
( spl107_226
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_226])]) ).
fof(f4373,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0),
inference(cnf_transformation,[],[f1288]) ).
fof(f1288,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0),
inference(rectify,[],[f527]) ).
fof(f527,axiom,
! [X41] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7296,plain,
spl107_225,
inference(avatar_split_clause,[],[f4372,f7294]) ).
fof(f7294,plain,
( spl107_225
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_225])]) ).
fof(f4372,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0),
inference(cnf_transformation,[],[f1287]) ).
fof(f1287,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X11] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11,X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7292,plain,
spl107_224,
inference(avatar_split_clause,[],[f4371,f7290]) ).
fof(f7290,plain,
( spl107_224
<=> ! [X0] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_224])]) ).
fof(f4371,plain,
! [X0] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X0),
inference(cnf_transformation,[],[f1286]) ).
fof(f1286,plain,
! [X0] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X0),
inference(rectify,[],[f791]) ).
fof(f791,axiom,
! [X6] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X6,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7288,plain,
spl107_223,
inference(avatar_split_clause,[],[f4369,f7286]) ).
fof(f7286,plain,
( spl107_223
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_223])]) ).
fof(f4369,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0),
inference(cnf_transformation,[],[f1284]) ).
fof(f1284,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0),
inference(rectify,[],[f508]) ).
fof(f508,axiom,
! [X41] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7284,plain,
~ spl107_222,
inference(avatar_split_clause,[],[f4338,f7281]) ).
fof(f7281,plain,
( spl107_222
<=> c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Oii ),
introduced(avatar_definition,[new_symbols(naming,[spl107_222])]) ).
fof(f4338,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Complex_Oii,
inference(cnf_transformation,[],[f436]) ).
fof(f436,axiom,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Complex_Oii,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7279,plain,
~ spl107_221,
inference(avatar_split_clause,[],[f4337,f7276]) ).
fof(f7276,plain,
( spl107_221
<=> c_Complex_Oii = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_221])]) ).
fof(f4337,plain,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f437]) ).
fof(f437,axiom,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7274,plain,
~ spl107_220,
inference(avatar_split_clause,[],[f4336,f7271]) ).
fof(f7271,plain,
( spl107_220
<=> c_RealDef_Opositive(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_220])]) ).
fof(f4336,plain,
~ c_RealDef_Opositive(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f96]) ).
fof(f96,axiom,
~ c_RealDef_Opositive(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7269,plain,
~ spl107_219,
inference(avatar_split_clause,[],[f4335,f7266]) ).
fof(f7266,plain,
( spl107_219
<=> v_w____ = v_z ),
introduced(avatar_definition,[new_symbols(naming,[spl107_219])]) ).
fof(f4335,plain,
v_w____ != v_z,
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
v_w____ != v_z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7264,plain,
~ spl107_218,
inference(avatar_split_clause,[],[f4117,f7261]) ).
fof(f4117,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f1280]) ).
fof(f1280,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(flattening,[],[f1279]) ).
fof(f1279,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(negated_conjecture,[],[f1278]) ).
fof(f1278,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7259,plain,
spl107_217,
inference(avatar_split_clause,[],[f4334,f7256]) ).
fof(f7256,plain,
( spl107_217
<=> class_Groups_Ominus(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_217])]) ).
fof(f4334,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(cnf_transformation,[],[f1098]) ).
fof(f1098,axiom,
class_Groups_Ominus(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7254,plain,
spl107_216,
inference(avatar_split_clause,[],[f4333,f7251]) ).
fof(f7251,plain,
( spl107_216
<=> class_Groups_Ominus(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_216])]) ).
fof(f4333,plain,
class_Groups_Ominus(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1169]) ).
fof(f1169,axiom,
class_Groups_Ominus(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7249,plain,
spl107_215,
inference(avatar_split_clause,[],[f4332,f7246]) ).
fof(f7246,plain,
( spl107_215
<=> class_Groups_Ominus(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_215])]) ).
fof(f4332,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(cnf_transformation,[],[f1058]) ).
fof(f1058,axiom,
class_Groups_Ominus(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7244,plain,
spl107_214,
inference(avatar_split_clause,[],[f4331,f7241]) ).
fof(f7241,plain,
( spl107_214
<=> class_Groups_Ominus(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_214])]) ).
fof(f4331,plain,
class_Groups_Ominus(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1211]) ).
fof(f1211,axiom,
class_Groups_Ominus(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7239,plain,
spl107_213,
inference(avatar_split_clause,[],[f4330,f7236]) ).
fof(f7236,plain,
( spl107_213
<=> class_Groups_Ominus(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_213])]) ).
fof(f4330,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(cnf_transformation,[],[f1106]) ).
fof(f1106,axiom,
class_Groups_Ominus(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7234,plain,
spl107_212,
inference(avatar_split_clause,[],[f4329,f7231]) ).
fof(f7231,plain,
( spl107_212
<=> class_Orderings_Oorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_212])]) ).
fof(f4329,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f1095]) ).
fof(f1095,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7229,plain,
spl107_211,
inference(avatar_split_clause,[],[f4328,f7226]) ).
fof(f7226,plain,
( spl107_211
<=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_211])]) ).
fof(f4328,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1164]) ).
fof(f1164,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7224,plain,
spl107_210,
inference(avatar_split_clause,[],[f4327,f7221]) ).
fof(f7221,plain,
( spl107_210
<=> class_Orderings_Oorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_210])]) ).
fof(f4327,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(cnf_transformation,[],[f1053]) ).
fof(f1053,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7219,plain,
spl107_209,
inference(avatar_split_clause,[],[f4326,f7216]) ).
fof(f7216,plain,
( spl107_209
<=> class_Orderings_Oorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_209])]) ).
fof(f4326,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f1104]) ).
fof(f1104,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7214,plain,
spl107_208,
inference(avatar_split_clause,[],[f4325,f7211]) ).
fof(f4325,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f1089]) ).
fof(f1089,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7209,plain,
spl107_207,
inference(avatar_split_clause,[],[f4324,f7206]) ).
fof(f4324,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1155]) ).
fof(f1155,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7204,plain,
spl107_206,
inference(avatar_split_clause,[],[f4323,f7201]) ).
fof(f7201,plain,
( spl107_206
<=> class_Orderings_Opreorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_206])]) ).
fof(f4323,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(cnf_transformation,[],[f1043]) ).
fof(f1043,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7199,plain,
spl107_205,
inference(avatar_split_clause,[],[f4322,f7196]) ).
fof(f7196,plain,
( spl107_205
<=> class_Orderings_Opreorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_205])]) ).
fof(f4322,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f1103]) ).
fof(f1103,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7194,plain,
spl107_204,
inference(avatar_split_clause,[],[f4321,f7191]) ).
fof(f7191,plain,
( spl107_204
<=> class_Orderings_Oord(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_204])]) ).
fof(f4321,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(cnf_transformation,[],[f1097]) ).
fof(f1097,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7189,plain,
spl107_203,
inference(avatar_split_clause,[],[f4320,f7186]) ).
fof(f7186,plain,
( spl107_203
<=> class_Orderings_Oord(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_203])]) ).
fof(f4320,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1167]) ).
fof(f1167,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7184,plain,
spl107_202,
inference(avatar_split_clause,[],[f4319,f7181]) ).
fof(f7181,plain,
( spl107_202
<=> class_Orderings_Oord(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_202])]) ).
fof(f4319,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(cnf_transformation,[],[f1056]) ).
fof(f1056,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7179,plain,
spl107_201,
inference(avatar_split_clause,[],[f4318,f7176]) ).
fof(f7176,plain,
( spl107_201
<=> class_Orderings_Oord(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_201])]) ).
fof(f4318,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(cnf_transformation,[],[f1105]) ).
fof(f1105,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7174,plain,
spl107_200,
inference(avatar_split_clause,[],[f4317,f7171]) ).
fof(f7171,plain,
( spl107_200
<=> class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_200])]) ).
fof(f4317,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(cnf_transformation,[],[f1084]) ).
fof(f1084,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7169,plain,
spl107_199,
inference(avatar_split_clause,[],[f4316,f7166]) ).
fof(f7166,plain,
( spl107_199
<=> class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_199])]) ).
fof(f4316,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1147]) ).
fof(f1147,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7164,plain,
spl107_198,
inference(avatar_split_clause,[],[f4315,f7161]) ).
fof(f7161,plain,
( spl107_198
<=> class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_198])]) ).
fof(f4315,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f1036]) ).
fof(f1036,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7159,plain,
spl107_197,
inference(avatar_split_clause,[],[f4314,f7156]) ).
fof(f7156,plain,
( spl107_197
<=> class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_197])]) ).
fof(f4314,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1194]) ).
fof(f1194,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7154,plain,
spl107_196,
inference(avatar_split_clause,[],[f4313,f7151]) ).
fof(f7151,plain,
( spl107_196
<=> class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_196])]) ).
fof(f4313,plain,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f1085]) ).
fof(f1085,axiom,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7149,plain,
spl107_195,
inference(avatar_split_clause,[],[f4312,f7146]) ).
fof(f7146,plain,
( spl107_195
<=> class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_195])]) ).
fof(f4312,plain,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1148]) ).
fof(f1148,axiom,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7144,plain,
spl107_194,
inference(avatar_split_clause,[],[f4311,f7141]) ).
fof(f7141,plain,
( spl107_194
<=> class_Rings_Ocomm__semiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_194])]) ).
fof(f4311,plain,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
inference(cnf_transformation,[],[f1037]) ).
fof(f1037,axiom,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7139,plain,
spl107_193,
inference(avatar_split_clause,[],[f4310,f7136]) ).
fof(f7136,plain,
( spl107_193
<=> class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_193])]) ).
fof(f4310,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1195]) ).
fof(f1195,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7134,plain,
spl107_192,
inference(avatar_split_clause,[],[f4309,f7131]) ).
fof(f7131,plain,
( spl107_192
<=> class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_192])]) ).
fof(f4309,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1083]) ).
fof(f1083,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7129,plain,
spl107_191,
inference(avatar_split_clause,[],[f4308,f7126]) ).
fof(f7126,plain,
( spl107_191
<=> class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_191])]) ).
fof(f4308,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1144]) ).
fof(f1144,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7124,plain,
spl107_190,
inference(avatar_split_clause,[],[f4307,f7121]) ).
fof(f7121,plain,
( spl107_190
<=> class_Groups_Ocomm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_190])]) ).
fof(f4307,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1033]) ).
fof(f1033,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7119,plain,
spl107_189,
inference(avatar_split_clause,[],[f4306,f7116]) ).
fof(f7116,plain,
( spl107_189
<=> class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_189])]) ).
fof(f4306,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1193]) ).
fof(f1193,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7114,plain,
spl107_188,
inference(avatar_split_clause,[],[f4305,f7111]) ).
fof(f7111,plain,
( spl107_188
<=> class_Groups_Omonoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_188])]) ).
fof(f4305,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f1091]) ).
fof(f1091,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7109,plain,
spl107_187,
inference(avatar_split_clause,[],[f4304,f7106]) ).
fof(f7106,plain,
( spl107_187
<=> class_Groups_Omonoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_187])]) ).
fof(f4304,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1157]) ).
fof(f1157,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7104,plain,
spl107_186,
inference(avatar_split_clause,[],[f4303,f7101]) ).
fof(f7101,plain,
( spl107_186
<=> class_Groups_Omonoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_186])]) ).
fof(f4303,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f1045]) ).
fof(f1045,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7099,plain,
spl107_185,
inference(avatar_split_clause,[],[f4302,f7096]) ).
fof(f7096,plain,
( spl107_185
<=> class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_185])]) ).
fof(f4302,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1201]) ).
fof(f1201,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7094,plain,
spl107_184,
inference(avatar_split_clause,[],[f4301,f7091]) ).
fof(f7091,plain,
( spl107_184
<=> class_Power_Opower(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_184])]) ).
fof(f4301,plain,
class_Power_Opower(tc_Nat_Onat),
inference(cnf_transformation,[],[f1099]) ).
fof(f1099,axiom,
class_Power_Opower(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7089,plain,
spl107_183,
inference(avatar_split_clause,[],[f4300,f7086]) ).
fof(f7086,plain,
( spl107_183
<=> class_Power_Opower(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_183])]) ).
fof(f4300,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1171]) ).
fof(f1171,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7084,plain,
spl107_182,
inference(avatar_split_clause,[],[f4299,f7081]) ).
fof(f4299,plain,
class_Power_Opower(tc_Int_Oint),
inference(cnf_transformation,[],[f1059]) ).
fof(f1059,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7079,plain,
spl107_181,
inference(avatar_split_clause,[],[f4298,f7076]) ).
fof(f7076,plain,
( spl107_181
<=> class_Power_Opower(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_181])]) ).
fof(f4298,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1213]) ).
fof(f1213,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7074,plain,
spl107_180,
inference(avatar_split_clause,[],[f4297,f7071]) ).
fof(f7071,plain,
( spl107_180
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_180])]) ).
fof(f4297,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(cnf_transformation,[],[f1065]) ).
fof(f1065,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7069,plain,
spl107_179,
inference(avatar_split_clause,[],[f4296,f7066]) ).
fof(f7066,plain,
( spl107_179
<=> class_Groups_Ozero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_179])]) ).
fof(f4296,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f1100]) ).
fof(f1100,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7064,plain,
spl107_178,
inference(avatar_split_clause,[],[f4295,f7061]) ).
fof(f7061,plain,
( spl107_178
<=> class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_178])]) ).
fof(f4295,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1075]) ).
fof(f1075,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7059,plain,
spl107_177,
inference(avatar_split_clause,[],[f4294,f7056]) ).
fof(f7056,plain,
( spl107_177
<=> class_Rings_Odvd(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_177])]) ).
fof(f4294,plain,
class_Rings_Odvd(tc_Nat_Onat),
inference(cnf_transformation,[],[f1102]) ).
fof(f1102,axiom,
class_Rings_Odvd(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7054,plain,
spl107_176,
inference(avatar_split_clause,[],[f4293,f7051]) ).
fof(f7051,plain,
( spl107_176
<=> class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_176])]) ).
fof(f4293,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1132]) ).
fof(f1132,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7049,plain,
spl107_175,
inference(avatar_split_clause,[],[f4292,f7046]) ).
fof(f7046,plain,
( spl107_175
<=> class_Rings_Odvd(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_175])]) ).
fof(f4292,plain,
class_Rings_Odvd(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1176]) ).
fof(f1176,axiom,
class_Rings_Odvd(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7044,plain,
spl107_174,
inference(avatar_split_clause,[],[f4291,f7041]) ).
fof(f7041,plain,
( spl107_174
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_174])]) ).
fof(f4291,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1107]) ).
fof(f1107,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7039,plain,
spl107_173,
inference(avatar_split_clause,[],[f4290,f7036]) ).
fof(f7036,plain,
( spl107_173
<=> class_Groups_Ozero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_173])]) ).
fof(f4290,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1172]) ).
fof(f1172,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7034,plain,
spl107_172,
inference(avatar_split_clause,[],[f4289,f7031]) ).
fof(f7031,plain,
( spl107_172
<=> class_Rings_Odvd(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_172])]) ).
fof(f4289,plain,
class_Rings_Odvd(tc_Int_Oint),
inference(cnf_transformation,[],[f1064]) ).
fof(f1064,axiom,
class_Rings_Odvd(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7029,plain,
spl107_171,
inference(avatar_split_clause,[],[f4288,f7026]) ).
fof(f7026,plain,
( spl107_171
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_171])]) ).
fof(f4288,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/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7024,plain,
spl107_170,
inference(avatar_split_clause,[],[f4287,f7021]) ).
fof(f7021,plain,
( spl107_170
<=> class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_170])]) ).
fof(f4287,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1024]) ).
fof(f1024,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7019,plain,
spl107_169,
inference(avatar_split_clause,[],[f4286,f7016]) ).
fof(f7016,plain,
( spl107_169
<=> class_Groups_Ozero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_169])]) ).
fof(f4286,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(cnf_transformation,[],[f1060]) ).
fof(f1060,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7014,plain,
spl107_168,
inference(avatar_split_clause,[],[f4285,f7011]) ).
fof(f7011,plain,
( spl107_168
<=> class_Groups_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_168])]) ).
fof(f4285,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1214]) ).
fof(f1214,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7009,plain,
spl107_167,
inference(avatar_split_clause,[],[f4284,f7006]) ).
fof(f7006,plain,
( spl107_167
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_167])]) ).
fof(f4284,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1177]) ).
fof(f1177,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f7004,plain,
spl107_166,
inference(avatar_split_clause,[],[f4283,f7001]) ).
fof(f7001,plain,
( spl107_166
<=> class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_166])]) ).
fof(f4283,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1187]) ).
fof(f1187,axiom,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6999,plain,
spl107_165,
inference(avatar_split_clause,[],[f4282,f6996]) ).
fof(f6996,plain,
( spl107_165
<=> class_Rings_Odvd(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_165])]) ).
fof(f4282,plain,
class_Rings_Odvd(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1218]) ).
fof(f1218,axiom,
class_Rings_Odvd(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6994,plain,
spl107_164,
inference(avatar_split_clause,[],[f4281,f6991]) ).
fof(f6991,plain,
( spl107_164
<=> class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_164])]) ).
fof(f4281,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1000]) ).
fof(f1000,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6989,plain,
spl107_163,
inference(avatar_split_clause,[],[f4280,f6986]) ).
fof(f6986,plain,
( spl107_163
<=> class_Rings_Ozero__neq__one(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_163])]) ).
fof(f4280,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(cnf_transformation,[],[f1088]) ).
fof(f1088,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6984,plain,
spl107_162,
inference(avatar_split_clause,[],[f4279,f6981]) ).
fof(f6981,plain,
( spl107_162
<=> class_Rings_Ono__zero__divisors(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_162])]) ).
fof(f4279,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(cnf_transformation,[],[f1082]) ).
fof(f1082,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6979,plain,
spl107_161,
inference(avatar_split_clause,[],[f4278,f6976]) ).
fof(f6976,plain,
( spl107_161
<=> class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_161])]) ).
fof(f4278,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f1079]) ).
fof(f1079,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6974,plain,
spl107_160,
inference(avatar_split_clause,[],[f4277,f6971]) ).
fof(f6971,plain,
( spl107_160
<=> class_Rings_Omult__zero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_160])]) ).
fof(f4277,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(cnf_transformation,[],[f1094]) ).
fof(f1094,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6969,plain,
spl107_159,
inference(avatar_split_clause,[],[f4276,f6966]) ).
fof(f6966,plain,
( spl107_159
<=> class_Rings_Omult__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_159])]) ).
fof(f4276,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1162]) ).
fof(f1162,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6964,plain,
spl107_158,
inference(avatar_split_clause,[],[f4275,f6961]) ).
fof(f6961,plain,
( spl107_158
<=> class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_158])]) ).
fof(f4275,plain,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f999]) ).
fof(f999,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6959,plain,
spl107_157,
inference(avatar_split_clause,[],[f4274,f6956]) ).
fof(f6956,plain,
( spl107_157
<=> class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_157])]) ).
fof(f4274,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1153]) ).
fof(f1153,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6954,plain,
spl107_156,
inference(avatar_split_clause,[],[f4273,f6951]) ).
fof(f6951,plain,
( spl107_156
<=> class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_156])]) ).
fof(f4273,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1143]) ).
fof(f1143,axiom,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6949,plain,
spl107_155,
inference(avatar_split_clause,[],[f4272,f6946]) ).
fof(f6946,plain,
( spl107_155
<=> class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_155])]) ).
fof(f4272,plain,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1138]) ).
fof(f1138,axiom,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6944,plain,
spl107_154,
inference(avatar_split_clause,[],[f4271,f6941]) ).
fof(f6941,plain,
( spl107_154
<=> class_Rings_Omult__zero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_154])]) ).
fof(f4271,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(cnf_transformation,[],[f1051]) ).
fof(f1051,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6939,plain,
spl107_153,
inference(avatar_split_clause,[],[f4270,f6936]) ).
fof(f6936,plain,
( spl107_153
<=> class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_153])]) ).
fof(f4270,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f1028]) ).
fof(f1028,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6934,plain,
spl107_152,
inference(avatar_split_clause,[],[f4269,f6931]) ).
fof(f6931,plain,
( spl107_152
<=> class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_152])]) ).
fof(f4269,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1001]) ).
fof(f1001,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6929,plain,
spl107_151,
inference(avatar_split_clause,[],[f4268,f6926]) ).
fof(f6926,plain,
( spl107_151
<=> class_Rings_Ono__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_151])]) ).
fof(f4268,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f1032]) ).
fof(f1032,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6924,plain,
spl107_150,
inference(avatar_split_clause,[],[f4267,f6921]) ).
fof(f6921,plain,
( spl107_150
<=> class_Rings_Ozero__neq__one(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_150])]) ).
fof(f4267,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(cnf_transformation,[],[f1041]) ).
fof(f1041,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6919,plain,
spl107_149,
inference(avatar_split_clause,[],[f4266,f6916]) ).
fof(f6916,plain,
( spl107_149
<=> class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_149])]) ).
fof(f4266,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1192]) ).
fof(f1192,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6914,plain,
spl107_148,
inference(avatar_split_clause,[],[f4265,f6911]) ).
fof(f6911,plain,
( spl107_148
<=> class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_148])]) ).
fof(f4265,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1200]) ).
fof(f1200,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6909,plain,
spl107_147,
inference(avatar_split_clause,[],[f4264,f6906]) ).
fof(f6906,plain,
( spl107_147
<=> class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_147])]) ).
fof(f4264,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1190]) ).
fof(f1190,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6904,plain,
spl107_146,
inference(avatar_split_clause,[],[f4263,f6901]) ).
fof(f6901,plain,
( spl107_146
<=> class_Rings_Omult__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_146])]) ).
fof(f4263,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1206]) ).
fof(f1206,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6899,plain,
spl107_145,
inference(avatar_split_clause,[],[f4262,f6896]) ).
fof(f6896,plain,
( spl107_145
<=> class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_145])]) ).
fof(f4262,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f998]) ).
fof(f998,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6894,plain,
spl107_144,
inference(avatar_split_clause,[],[f4261,f6891]) ).
fof(f6891,plain,
( spl107_144
<=> class_Groups_Omonoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_144])]) ).
fof(f4261,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1092]) ).
fof(f1092,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6889,plain,
spl107_143,
inference(avatar_split_clause,[],[f4260,f6886]) ).
fof(f6886,plain,
( spl107_143
<=> class_Rings_Osemiring__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_143])]) ).
fof(f4260,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f1093]) ).
fof(f1093,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6884,plain,
spl107_142,
inference(avatar_split_clause,[],[f4259,f6881]) ).
fof(f6881,plain,
( spl107_142
<=> class_Rings_Osemiring__0(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_142])]) ).
fof(f4259,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1160]) ).
fof(f1160,axiom,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6879,plain,
spl107_141,
inference(avatar_split_clause,[],[f4258,f6876]) ).
fof(f6876,plain,
( spl107_141
<=> class_Groups_Omonoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_141])]) ).
fof(f4258,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1159]) ).
fof(f1159,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6874,plain,
spl107_140,
inference(avatar_split_clause,[],[f4257,f6871]) ).
fof(f6871,plain,
( spl107_140
<=> class_Groups_Omonoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_140])]) ).
fof(f4257,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1047]) ).
fof(f1047,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6869,plain,
spl107_139,
inference(avatar_split_clause,[],[f4256,f6866]) ).
fof(f6866,plain,
( spl107_139
<=> class_Rings_Osemiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_139])]) ).
fof(f4256,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(cnf_transformation,[],[f1048]) ).
fof(f1048,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6864,plain,
spl107_138,
inference(avatar_split_clause,[],[f4255,f6861]) ).
fof(f6861,plain,
( spl107_138
<=> class_Rings_Osemiring__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_138])]) ).
fof(f4255,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1204]) ).
fof(f1204,axiom,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6859,plain,
spl107_137,
inference(avatar_split_clause,[],[f4254,f6856]) ).
fof(f6856,plain,
( spl107_137
<=> class_Groups_Omonoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_137])]) ).
fof(f4254,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1203]) ).
fof(f1203,axiom,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6854,plain,
spl107_136,
inference(avatar_split_clause,[],[f4253,f6851]) ).
fof(f6851,plain,
( spl107_136
<=> class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_136])]) ).
fof(f4253,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1080]) ).
fof(f1080,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6849,plain,
spl107_135,
inference(avatar_split_clause,[],[f4252,f6846]) ).
fof(f6846,plain,
( spl107_135
<=> class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_135])]) ).
fof(f4252,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f1078]) ).
fof(f1078,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6844,plain,
spl107_134,
inference(avatar_split_clause,[],[f4251,f6841]) ).
fof(f6841,plain,
( spl107_134
<=> class_Rings_Ocomm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_134])]) ).
fof(f4251,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1087]) ).
fof(f1087,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6839,plain,
spl107_133,
inference(avatar_split_clause,[],[f4250,f6836]) ).
fof(f6836,plain,
( spl107_133
<=> class_Rings_Osemiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_133])]) ).
fof(f4250,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1096]) ).
fof(f1096,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6834,plain,
spl107_132,
inference(avatar_split_clause,[],[f4249,f6831]) ).
fof(f6831,plain,
( spl107_132
<=> class_Groups_Oone(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_132])]) ).
fof(f4249,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(cnf_transformation,[],[f1101]) ).
fof(f1101,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6829,plain,
spl107_131,
inference(avatar_split_clause,[],[f4248,f6826]) ).
fof(f6826,plain,
( spl107_131
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_131])]) ).
fof(f4248,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1072]) ).
fof(f1072,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6824,plain,
spl107_130,
inference(avatar_split_clause,[],[f4247,f6821]) ).
fof(f6821,plain,
( spl107_130
<=> class_Rings_Ocomm__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_130])]) ).
fof(f4247,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1151]) ).
fof(f1151,axiom,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6819,plain,
spl107_129,
inference(avatar_split_clause,[],[f4246,f6816]) ).
fof(f6816,plain,
( spl107_129
<=> class_Rings_Osemiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_129])]) ).
fof(f4246,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1166]) ).
fof(f1166,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6814,plain,
spl107_128,
inference(avatar_split_clause,[],[f4245,f6811]) ).
fof(f6811,plain,
( spl107_128
<=> class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_128])]) ).
fof(f4245,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1137]) ).
fof(f1137,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6809,plain,
spl107_127,
inference(avatar_split_clause,[],[f4244,f6806]) ).
fof(f6806,plain,
( spl107_127
<=> class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_127])]) ).
fof(f4244,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1122]) ).
fof(f1122,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6804,plain,
spl107_126,
inference(avatar_split_clause,[],[f4243,f6801]) ).
fof(f6801,plain,
( spl107_126
<=> class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_126])]) ).
fof(f4243,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1139]) ).
fof(f1139,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6799,plain,
spl107_125,
inference(avatar_split_clause,[],[f4242,f6796]) ).
fof(f6796,plain,
( spl107_125
<=> class_Groups_Oone(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_125])]) ).
fof(f4242,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1175]) ).
fof(f1175,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6794,plain,
spl107_124,
inference(avatar_split_clause,[],[f4241,f6791]) ).
fof(f6791,plain,
( spl107_124
<=> class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_124])]) ).
fof(f4241,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1029]) ).
fof(f1029,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6789,plain,
spl107_123,
inference(avatar_split_clause,[],[f4240,f6786]) ).
fof(f6786,plain,
( spl107_123
<=> class_Rings_Ocomm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_123])]) ).
fof(f4240,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1039]) ).
fof(f1039,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6784,plain,
spl107_122,
inference(avatar_split_clause,[],[f4239,f6781]) ).
fof(f6781,plain,
( spl107_122
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_122])]) ).
fof(f4239,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1016]) ).
fof(f1016,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6779,plain,
spl107_121,
inference(avatar_split_clause,[],[f4238,f6776]) ).
fof(f6776,plain,
( spl107_121
<=> class_Rings_Osemiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_121])]) ).
fof(f4238,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1055]) ).
fof(f1055,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6774,plain,
spl107_120,
inference(avatar_split_clause,[],[f4237,f6771]) ).
fof(f6771,plain,
( spl107_120
<=> class_Groups_Oab__semigroup__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_120])]) ).
fof(f4237,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f1027]) ).
fof(f1027,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6769,plain,
spl107_119,
inference(avatar_split_clause,[],[f4236,f6766]) ).
fof(f6766,plain,
( spl107_119
<=> class_Groups_Oone(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_119])]) ).
fof(f4236,plain,
class_Groups_Oone(tc_Int_Oint),
inference(cnf_transformation,[],[f1063]) ).
fof(f1063,axiom,
class_Groups_Oone(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6764,plain,
spl107_118,
inference(avatar_split_clause,[],[f4235,f6761]) ).
fof(f6761,plain,
( spl107_118
<=> class_Rings_Osemiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_118])]) ).
fof(f4235,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1209]) ).
fof(f1209,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6759,plain,
spl107_117,
inference(avatar_split_clause,[],[f4234,f6756]) ).
fof(f6756,plain,
( spl107_117
<=> class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_117])]) ).
fof(f4234,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1191]) ).
fof(f1191,axiom,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6754,plain,
spl107_116,
inference(avatar_split_clause,[],[f4233,f6751]) ).
fof(f6751,plain,
( spl107_116
<=> class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_116])]) ).
fof(f4233,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1198]) ).
fof(f1198,axiom,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6749,plain,
spl107_115,
inference(avatar_split_clause,[],[f4232,f6746]) ).
fof(f6746,plain,
( spl107_115
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_115])]) ).
fof(f4232,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1182]) ).
fof(f1182,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6744,plain,
spl107_114,
inference(avatar_split_clause,[],[f4231,f6741]) ).
fof(f6741,plain,
( spl107_114
<=> class_Groups_Oone(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_114])]) ).
fof(f4231,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1217]) ).
fof(f1217,axiom,
class_Groups_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6739,plain,
spl107_113,
inference(avatar_split_clause,[],[f4230,f6736]) ).
fof(f6736,plain,
( spl107_113
<=> class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_113])]) ).
fof(f4230,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1189]) ).
fof(f1189,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6734,plain,
spl107_112,
inference(avatar_split_clause,[],[f4229,f6731]) ).
fof(f6731,plain,
( spl107_112
<=> class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_112])]) ).
fof(f4229,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(cnf_transformation,[],[f1077]) ).
fof(f1077,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6729,plain,
spl107_111,
inference(avatar_split_clause,[],[f4228,f6726]) ).
fof(f6726,plain,
( spl107_111
<=> class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_111])]) ).
fof(f4228,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1135]) ).
fof(f1135,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6724,plain,
spl107_110,
inference(avatar_split_clause,[],[f4227,f6721]) ).
fof(f6721,plain,
( spl107_110
<=> class_Rings_Olinordered__semidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_110])]) ).
fof(f4227,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(cnf_transformation,[],[f1026]) ).
fof(f1026,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6719,plain,
spl107_109,
inference(avatar_split_clause,[],[f4226,f6716]) ).
fof(f6716,plain,
( spl107_109
<=> class_Orderings_Olinorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_109])]) ).
fof(f4226,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f1090]) ).
fof(f1090,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6714,plain,
spl107_108,
inference(avatar_split_clause,[],[f4225,f6711]) ).
fof(f6711,plain,
( spl107_108
<=> class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_108])]) ).
fof(f4225,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f1069]) ).
fof(f1069,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6709,plain,
spl107_107,
inference(avatar_split_clause,[],[f4224,f6706]) ).
fof(f4224,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1156]) ).
fof(f1156,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6704,plain,
spl107_106,
inference(avatar_split_clause,[],[f4223,f6701]) ).
fof(f6701,plain,
( spl107_106
<=> class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_106])]) ).
fof(f4223,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1114]) ).
fof(f1114,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6699,plain,
spl107_105,
inference(avatar_split_clause,[],[f4222,f6696]) ).
fof(f6696,plain,
( spl107_105
<=> class_Orderings_Olinorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_105])]) ).
fof(f4222,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(cnf_transformation,[],[f1044]) ).
fof(f1044,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6694,plain,
spl107_104,
inference(avatar_split_clause,[],[f4221,f6691]) ).
fof(f6691,plain,
( spl107_104
<=> class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_104])]) ).
fof(f4221,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/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6689,plain,
spl107_103,
inference(avatar_split_clause,[],[f4220,f6686]) ).
fof(f6686,plain,
( spl107_103
<=> class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_103])]) ).
fof(f4220,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1071]) ).
fof(f1071,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6684,plain,
spl107_102,
inference(avatar_split_clause,[],[f4219,f6681]) ).
fof(f6681,plain,
( spl107_102
<=> class_Rings_Oidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_102])]) ).
fof(f4219,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1174]) ).
fof(f1174,axiom,
class_Rings_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6679,plain,
spl107_101,
inference(avatar_split_clause,[],[f4218,f6676]) ).
fof(f6676,plain,
( spl107_101
<=> class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_101])]) ).
fof(f4218,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1120]) ).
fof(f1120,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6674,plain,
spl107_100,
inference(avatar_split_clause,[],[f4217,f6671]) ).
fof(f6671,plain,
( spl107_100
<=> class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_100])]) ).
fof(f4217,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1014]) ).
fof(f1014,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6669,plain,
spl107_99,
inference(avatar_split_clause,[],[f4216,f6666]) ).
fof(f6666,plain,
( spl107_99
<=> class_Rings_Oidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_99])]) ).
fof(f4216,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(cnf_transformation,[],[f1062]) ).
fof(f1062,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6664,plain,
spl107_98,
inference(avatar_split_clause,[],[f4215,f6661]) ).
fof(f6661,plain,
( spl107_98
<=> class_Rings_Oidom(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_98])]) ).
fof(f4215,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1216]) ).
fof(f1216,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6659,plain,
spl107_97,
inference(avatar_split_clause,[],[f4214,f6656]) ).
fof(f6656,plain,
( spl107_97
<=> class_Groups_Oab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_97])]) ).
fof(f4214,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1152]) ).
fof(f1152,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6654,plain,
spl107_96,
inference(avatar_split_clause,[],[f4213,f6651]) ).
fof(f6651,plain,
( spl107_96
<=> class_Groups_Oab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_96])]) ).
fof(f4213,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1040]) ).
fof(f1040,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6649,plain,
spl107_95,
inference(avatar_split_clause,[],[f4212,f6646]) ).
fof(f6646,plain,
( spl107_95
<=> class_Groups_Oab__group__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_95])]) ).
fof(f4212,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1199]) ).
fof(f1199,axiom,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6644,plain,
spl107_94,
inference(avatar_split_clause,[],[f4211,f6641]) ).
fof(f6641,plain,
( spl107_94
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_94])]) ).
fof(f4211,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(cnf_transformation,[],[f1067]) ).
fof(f1067,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6639,plain,
spl107_93,
inference(avatar_split_clause,[],[f4210,f6636]) ).
fof(f6636,plain,
( spl107_93
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_93])]) ).
fof(f4210,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1109]) ).
fof(f1109,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6634,plain,
spl107_92,
inference(avatar_split_clause,[],[f4209,f6631]) ).
fof(f6631,plain,
( spl107_92
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_92])]) ).
fof(f4209,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/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6629,plain,
spl107_91,
inference(avatar_split_clause,[],[f4208,f6626]) ).
fof(f6626,plain,
( spl107_91
<=> class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_91])]) ).
fof(f4208,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1073]) ).
fof(f1073,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6624,plain,
spl107_90,
inference(avatar_split_clause,[],[f4207,f6621]) ).
fof(f6621,plain,
( spl107_90
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_90])]) ).
fof(f4207,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1066]) ).
fof(f1066,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6619,plain,
spl107_89,
inference(avatar_split_clause,[],[f4206,f6616]) ).
fof(f6616,plain,
( spl107_89
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_89])]) ).
fof(f4206,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1108]) ).
fof(f1108,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6614,plain,
spl107_88,
inference(avatar_split_clause,[],[f4205,f6611]) ).
fof(f6611,plain,
( spl107_88
<=> class_Rings_Ocomm__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_88])]) ).
fof(f4205,plain,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1163]) ).
fof(f1163,axiom,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6609,plain,
spl107_87,
inference(avatar_split_clause,[],[f4204,f6606]) ).
fof(f6606,plain,
( spl107_87
<=> class_Groups_Ogroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_87])]) ).
fof(f4204,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1161]) ).
fof(f1161,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6604,plain,
spl107_86,
inference(avatar_split_clause,[],[f4203,f6601]) ).
fof(f6601,plain,
( spl107_86
<=> class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_86])]) ).
fof(f4203,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1124]) ).
fof(f1124,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6599,plain,
spl107_85,
inference(avatar_split_clause,[],[f4202,f6596]) ).
fof(f6596,plain,
( spl107_85
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_85])]) ).
fof(f4202,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/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6594,plain,
spl107_84,
inference(avatar_split_clause,[],[f4201,f6591]) ).
fof(f6591,plain,
( spl107_84
<=> class_Rings_Ocomm__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_84])]) ).
fof(f4201,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f1052]) ).
fof(f1052,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6589,plain,
spl107_83,
inference(avatar_split_clause,[],[f4200,f6586]) ).
fof(f6586,plain,
( spl107_83
<=> class_Groups_Ogroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_83])]) ).
fof(f4200,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1049]) ).
fof(f1049,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6584,plain,
spl107_82,
inference(avatar_split_clause,[],[f4199,f6581]) ).
fof(f6581,plain,
( spl107_82
<=> class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_82])]) ).
fof(f4199,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1018]) ).
fof(f1018,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6579,plain,
spl107_81,
inference(avatar_split_clause,[],[f4198,f6576]) ).
fof(f6576,plain,
( spl107_81
<=> class_Groups_Ogroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_81])]) ).
fof(f4198,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1205]) ).
fof(f1205,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6574,plain,
spl107_80,
inference(avatar_split_clause,[],[f4197,f6571]) ).
fof(f6571,plain,
( spl107_80
<=> class_Rings_Ocomm__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_80])]) ).
fof(f4197,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1207]) ).
fof(f1207,axiom,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6569,plain,
spl107_79,
inference(avatar_split_clause,[],[f4196,f6566]) ).
fof(f6566,plain,
( spl107_79
<=> class_Rings_Oordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_79])]) ).
fof(f4196,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1081]) ).
fof(f1081,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6564,plain,
spl107_78,
inference(avatar_split_clause,[],[f4195,f6561]) ).
fof(f6561,plain,
( spl107_78
<=> class_Rings_Oordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_78])]) ).
fof(f4195,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1141]) ).
fof(f1141,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6559,plain,
spl107_77,
inference(avatar_split_clause,[],[f4194,f6556]) ).
fof(f6556,plain,
( spl107_77
<=> class_Rings_Oordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_77])]) ).
fof(f4194,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1030]) ).
fof(f1030,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6554,plain,
spl107_76,
inference(avatar_split_clause,[],[f4193,f6551]) ).
fof(f6551,plain,
( spl107_76
<=> class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_76])]) ).
fof(f4193,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1070]) ).
fof(f1070,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6549,plain,
spl107_75,
inference(avatar_split_clause,[],[f4192,f6546]) ).
fof(f6546,plain,
( spl107_75
<=> class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_75])]) ).
fof(f4192,plain,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1117]) ).
fof(f1117,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6544,plain,
spl107_74,
inference(avatar_split_clause,[],[f4191,f6541]) ).
fof(f6541,plain,
( spl107_74
<=> class_Rings_Ocomm__ring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_74])]) ).
fof(f4191,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1158]) ).
fof(f1158,axiom,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6539,plain,
spl107_73,
inference(avatar_split_clause,[],[f4190,f6536]) ).
fof(f6536,plain,
( spl107_73
<=> class_Rings_Oring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_73])]) ).
fof(f4190,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1173]) ).
fof(f1173,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6534,plain,
spl107_72,
inference(avatar_split_clause,[],[f4189,f6531]) ).
fof(f6531,plain,
( spl107_72
<=> class_Rings_Ocomm__ring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_72])]) ).
fof(f4189,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f1046]) ).
fof(f1046,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6529,plain,
spl107_71,
inference(avatar_split_clause,[],[f4188,f6526]) ).
fof(f6526,plain,
( spl107_71
<=> class_Rings_Oring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_71])]) ).
fof(f4188,plain,
class_Rings_Oring(tc_Int_Oint),
inference(cnf_transformation,[],[f1061]) ).
fof(f1061,axiom,
class_Rings_Oring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6524,plain,
spl107_70,
inference(avatar_split_clause,[],[f4187,f6521]) ).
fof(f6521,plain,
( spl107_70
<=> class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_70])]) ).
fof(f4187,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/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6519,plain,
spl107_69,
inference(avatar_split_clause,[],[f4186,f6516]) ).
fof(f6516,plain,
( spl107_69
<=> class_Rings_Oring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_69])]) ).
fof(f4186,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1215]) ).
fof(f1215,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6514,plain,
spl107_68,
inference(avatar_split_clause,[],[f4185,f6511]) ).
fof(f6511,plain,
( spl107_68
<=> class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_68])]) ).
fof(f4185,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1202]) ).
fof(f1202,axiom,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6509,plain,
spl107_67,
inference(avatar_split_clause,[],[f4184,f6506]) ).
fof(f6506,plain,
( spl107_67
<=> class_Rings_Olinordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_67])]) ).
fof(f4184,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1076]) ).
fof(f1076,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6504,plain,
spl107_66,
inference(avatar_split_clause,[],[f4183,f6501]) ).
fof(f6501,plain,
( spl107_66
<=> class_Rings_Olinordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_66])]) ).
fof(f4183,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1133]) ).
fof(f1133,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6499,plain,
spl107_65,
inference(avatar_split_clause,[],[f4182,f6496]) ).
fof(f6496,plain,
( spl107_65
<=> class_Int_Oring__char__0(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_65])]) ).
fof(f4182,plain,
class_Int_Oring__char__0(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1165]) ).
fof(f1165,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6494,plain,
spl107_64,
inference(avatar_split_clause,[],[f4181,f6491]) ).
fof(f6491,plain,
( spl107_64
<=> class_Rings_Olinordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_64])]) ).
fof(f4181,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1025]) ).
fof(f1025,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6489,plain,
spl107_63,
inference(avatar_split_clause,[],[f4180,f6486]) ).
fof(f6486,plain,
( spl107_63
<=> class_Int_Oring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_63])]) ).
fof(f4180,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(cnf_transformation,[],[f1054]) ).
fof(f1054,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6484,plain,
spl107_62,
inference(avatar_split_clause,[],[f4179,f6481]) ).
fof(f6481,plain,
( spl107_62
<=> class_Int_Oring__char__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_62])]) ).
fof(f4179,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1208]) ).
fof(f1208,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6479,plain,
spl107_61,
inference(avatar_split_clause,[],[f4178,f6476]) ).
fof(f6476,plain,
( spl107_61
<=> class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_61])]) ).
fof(f4178,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1074]) ).
fof(f1074,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6474,plain,
spl107_60,
inference(avatar_split_clause,[],[f4177,f6471]) ).
fof(f6471,plain,
( spl107_60
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_60])]) ).
fof(f4177,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f1068]) ).
fof(f1068,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6469,plain,
spl107_59,
inference(avatar_split_clause,[],[f4176,f6466]) ).
fof(f6466,plain,
( spl107_59
<=> class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_59])]) ).
fof(f4176,plain,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1128]) ).
fof(f1128,axiom,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6464,plain,
spl107_58,
inference(avatar_split_clause,[],[f4175,f6461]) ).
fof(f6461,plain,
( spl107_58
<=> class_Rings_Oring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_58])]) ).
fof(f4175,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1168]) ).
fof(f1168,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6459,plain,
spl107_57,
inference(avatar_split_clause,[],[f4174,f6456]) ).
fof(f6456,plain,
( spl107_57
<=> class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_57])]) ).
fof(f4174,plain,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1129]) ).
fof(f1129,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6454,plain,
spl107_56,
inference(avatar_split_clause,[],[f4173,f6451]) ).
fof(f6451,plain,
( spl107_56
<=> class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_56])]) ).
fof(f4173,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1123]) ).
fof(f1123,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6449,plain,
spl107_55,
inference(avatar_split_clause,[],[f4172,f6446]) ).
fof(f6446,plain,
( spl107_55
<=> class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_55])]) ).
fof(f4172,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1110]) ).
fof(f1110,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6444,plain,
spl107_54,
inference(avatar_split_clause,[],[f4171,f6441]) ).
fof(f6441,plain,
( spl107_54
<=> class_Rings_Oring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_54])]) ).
fof(f4171,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f1057]) ).
fof(f1057,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6439,plain,
spl107_53,
inference(avatar_split_clause,[],[f4170,f6436]) ).
fof(f6436,plain,
( spl107_53
<=> class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_53])]) ).
fof(f4170,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f1017]) ).
fof(f1017,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6434,plain,
spl107_52,
inference(avatar_split_clause,[],[f4169,f6431]) ).
fof(f6431,plain,
( spl107_52
<=> class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_52])]) ).
fof(f4169,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f1020]) ).
fof(f1020,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6429,plain,
spl107_51,
inference(avatar_split_clause,[],[f4168,f6426]) ).
fof(f6426,plain,
( spl107_51
<=> class_Rings_Oordered__comm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_51])]) ).
fof(f4168,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1021]) ).
fof(f1021,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6424,plain,
spl107_50,
inference(avatar_split_clause,[],[f4167,f6421]) ).
fof(f6421,plain,
( spl107_50
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_50])]) ).
fof(f4167,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/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6419,plain,
spl107_49,
inference(avatar_split_clause,[],[f4166,f6416]) ).
fof(f6416,plain,
( spl107_49
<=> class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_49])]) ).
fof(f4166,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1186]) ).
fof(f1186,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6414,plain,
spl107_48,
inference(avatar_split_clause,[],[f4165,f6411]) ).
fof(f6411,plain,
( spl107_48
<=> class_Rings_Oring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_48])]) ).
fof(f4165,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1210]) ).
fof(f1210,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6409,plain,
spl107_47,
inference(avatar_split_clause,[],[f4164,f6406]) ).
fof(f6406,plain,
( spl107_47
<=> class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_47])]) ).
fof(f4164,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1183]) ).
fof(f1183,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6404,plain,
spl107_46,
inference(avatar_split_clause,[],[f4163,f6401]) ).
fof(f6401,plain,
( spl107_46
<=> class_Divides_Osemiring__div(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_46])]) ).
fof(f4163,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(cnf_transformation,[],[f1086]) ).
fof(f1086,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6399,plain,
spl107_45,
inference(avatar_split_clause,[],[f4162,f6396]) ).
fof(f6396,plain,
( spl107_45
<=> class_Divides_Osemiring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_45])]) ).
fof(f4162,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(cnf_transformation,[],[f1038]) ).
fof(f1038,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6394,plain,
spl107_44,
inference(avatar_split_clause,[],[f4161,f6391]) ).
fof(f6391,plain,
( spl107_44
<=> class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_44])]) ).
fof(f4161,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1146]) ).
fof(f1146,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6389,plain,
spl107_43,
inference(avatar_split_clause,[],[f4160,f6386]) ).
fof(f4160,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(cnf_transformation,[],[f1035]) ).
fof(f1035,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6384,plain,
spl107_42,
inference(avatar_split_clause,[],[f4159,f6381]) ).
fof(f6381,plain,
( spl107_42
<=> class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_42])]) ).
fof(f4159,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1118]) ).
fof(f1118,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6379,plain,
spl107_41,
inference(avatar_split_clause,[],[f4158,f6376]) ).
fof(f4158,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(cnf_transformation,[],[f1013]) ).
fof(f1013,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6374,plain,
spl107_40,
inference(avatar_split_clause,[],[f4157,f6371]) ).
fof(f6371,plain,
( spl107_40
<=> class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_40])]) ).
fof(f4157,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1126]) ).
fof(f1126,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6369,plain,
spl107_39,
inference(avatar_split_clause,[],[f4156,f6366]) ).
fof(f6366,plain,
( spl107_39
<=> class_Rings_Olinordered__ring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_39])]) ).
fof(f4156,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f1019]) ).
fof(f1019,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6364,plain,
spl107_38,
inference(avatar_split_clause,[],[f4155,f6361]) ).
fof(f6361,plain,
( spl107_38
<=> class_Rings_Oordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_38])]) ).
fof(f4155,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1154]) ).
fof(f1154,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6359,plain,
spl107_37,
inference(avatar_split_clause,[],[f4154,f6356]) ).
fof(f6356,plain,
( spl107_37
<=> class_Rings_Oordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_37])]) ).
fof(f4154,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f1042]) ).
fof(f1042,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6354,plain,
spl107_36,
inference(avatar_split_clause,[],[f4153,f6351]) ).
fof(f6351,plain,
( spl107_36
<=> class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_36])]) ).
fof(f4153,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1121]) ).
fof(f1121,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6349,plain,
spl107_35,
inference(avatar_split_clause,[],[f4152,f6346]) ).
fof(f6346,plain,
( spl107_35
<=> class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_35])]) ).
fof(f4152,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1015]) ).
fof(f1015,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6344,plain,
spl107_34,
inference(avatar_split_clause,[],[f4151,f6341]) ).
fof(f6341,plain,
( spl107_34
<=> class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_34])]) ).
fof(f4151,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1131]) ).
fof(f1131,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6339,plain,
spl107_33,
inference(avatar_split_clause,[],[f4150,f6336]) ).
fof(f6336,plain,
( spl107_33
<=> class_Rings_Olinordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_33])]) ).
fof(f4150,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1145]) ).
fof(f1145,axiom,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6334,plain,
spl107_32,
inference(avatar_split_clause,[],[f4149,f6331]) ).
fof(f6331,plain,
( spl107_32
<=> class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_32])]) ).
fof(f4149,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1023]) ).
fof(f1023,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6329,plain,
spl107_31,
inference(avatar_split_clause,[],[f4148,f6326]) ).
fof(f6326,plain,
( spl107_31
<=> class_Rings_Olinordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_31])]) ).
fof(f4148,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f1034]) ).
fof(f1034,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6324,plain,
spl107_30,
inference(avatar_split_clause,[],[f4147,f6321]) ).
fof(f6321,plain,
( spl107_30
<=> class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_30])]) ).
fof(f4147,plain,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1112]) ).
fof(f1112,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6319,plain,
spl107_29,
inference(avatar_split_clause,[],[f4146,f6316]) ).
fof(f6316,plain,
( spl107_29
<=> class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_29])]) ).
fof(f4146,plain,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1130]) ).
fof(f1130,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6314,plain,
spl107_28,
inference(avatar_split_clause,[],[f4145,f6311]) ).
fof(f6311,plain,
( spl107_28
<=> class_Rings_Oordered__ring__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_28])]) ).
fof(f4145,plain,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1142]) ).
fof(f1142,axiom,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6309,plain,
spl107_27,
inference(avatar_split_clause,[],[f4144,f6306]) ).
fof(f6306,plain,
( spl107_27
<=> class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_27])]) ).
fof(f4144,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/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6304,plain,
spl107_26,
inference(avatar_split_clause,[],[f4143,f6301]) ).
fof(f6301,plain,
( spl107_26
<=> class_Rings_Olinordered__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_26])]) ).
fof(f4143,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f1022]) ).
fof(f1022,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6299,plain,
spl107_25,
inference(avatar_split_clause,[],[f4142,f6296]) ).
fof(f6296,plain,
( spl107_25
<=> class_Rings_Oordered__ring__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_25])]) ).
fof(f4142,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(cnf_transformation,[],[f1031]) ).
fof(f1031,axiom,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6294,plain,
spl107_24,
inference(avatar_split_clause,[],[f4141,f6291]) ).
fof(f6291,plain,
( spl107_24
<=> class_Fields_Ofield(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_24])]) ).
fof(f4141,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1170]) ).
fof(f1170,axiom,
class_Fields_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6289,plain,
spl107_23,
inference(avatar_split_clause,[],[f4140,f6286]) ).
fof(f6286,plain,
( spl107_23
<=> class_Fields_Ofield(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_23])]) ).
fof(f4140,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1212]) ).
fof(f1212,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6284,plain,
spl107_22,
inference(avatar_split_clause,[],[f4139,f6281]) ).
fof(f6281,plain,
( spl107_22
<=> class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_22])]) ).
fof(f4139,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1119]) ).
fof(f1119,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6279,plain,
spl107_21,
inference(avatar_split_clause,[],[f4138,f6276]) ).
fof(f6276,plain,
( spl107_21
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_21])]) ).
fof(f4138,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1181]) ).
fof(f1181,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6274,plain,
spl107_20,
inference(avatar_split_clause,[],[f4137,f6271]) ).
fof(f4137,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1125]) ).
fof(f1125,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6269,plain,
spl107_19,
inference(avatar_split_clause,[],[f4136,f6266]) ).
fof(f4136,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1184]) ).
fof(f1184,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6264,plain,
spl107_18,
inference(avatar_split_clause,[],[f4135,f6261]) ).
fof(f6261,plain,
( spl107_18
<=> class_Rings_Odivision__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_18])]) ).
fof(f4135,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1150]) ).
fof(f1150,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6259,plain,
spl107_17,
inference(avatar_split_clause,[],[f4134,f6256]) ).
fof(f4134,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1197]) ).
fof(f1197,axiom,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6254,plain,
spl107_16,
inference(avatar_split_clause,[],[f4133,f6251]) ).
fof(f6251,plain,
( spl107_16
<=> class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_16])]) ).
fof(f4133,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1134]) ).
fof(f1134,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6249,plain,
spl107_15,
inference(avatar_split_clause,[],[f4132,f6246]) ).
fof(f6246,plain,
( spl107_15
<=> class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_15])]) ).
fof(f4132,plain,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1188]) ).
fof(f1188,axiom,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6244,plain,
spl107_14,
inference(avatar_split_clause,[],[f4131,f6241]) ).
fof(f6241,plain,
( spl107_14
<=> class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_14])]) ).
fof(f4131,plain,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1127]) ).
fof(f1127,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6239,plain,
spl107_13,
inference(avatar_split_clause,[],[f4130,f6236]) ).
fof(f6236,plain,
( spl107_13
<=> class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_13])]) ).
fof(f4130,plain,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1185]) ).
fof(f1185,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6234,plain,
spl107_12,
inference(avatar_split_clause,[],[f4129,f6231]) ).
fof(f6231,plain,
( spl107_12
<=> class_Divides_Oring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_12])]) ).
fof(f4129,plain,
class_Divides_Oring__div(tc_Int_Oint),
inference(cnf_transformation,[],[f1050]) ).
fof(f1050,axiom,
class_Divides_Oring__div(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6229,plain,
spl107_11,
inference(avatar_split_clause,[],[f4128,f6226]) ).
fof(f4128,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1116]) ).
fof(f1116,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6224,plain,
spl107_10,
inference(avatar_split_clause,[],[f4127,f6221]) ).
fof(f6221,plain,
( spl107_10
<=> class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_10])]) ).
fof(f4127,plain,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1115]) ).
fof(f1115,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6219,plain,
spl107_9,
inference(avatar_split_clause,[],[f4126,f6216]) ).
fof(f6216,plain,
( spl107_9
<=> class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_9])]) ).
fof(f4126,plain,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1113]) ).
fof(f1113,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6214,plain,
spl107_8,
inference(avatar_split_clause,[],[f4125,f6211]) ).
fof(f4125,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1180]) ).
fof(f1180,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6209,plain,
spl107_7,
inference(avatar_split_clause,[],[f4124,f6206]) ).
fof(f6206,plain,
( spl107_7
<=> class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_7])]) ).
fof(f4124,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1178]) ).
fof(f1178,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6204,plain,
spl107_6,
inference(avatar_split_clause,[],[f4123,f6201]) ).
fof(f6201,plain,
( spl107_6
<=> class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_6])]) ).
fof(f4123,plain,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1179]) ).
fof(f1179,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6199,plain,
spl107_5,
inference(avatar_split_clause,[],[f4122,f6196]) ).
fof(f6196,plain,
( spl107_5
<=> class_RealVector_Oreal__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_5])]) ).
fof(f4122,plain,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1149]) ).
fof(f1149,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6194,plain,
spl107_4,
inference(avatar_split_clause,[],[f4121,f6191]) ).
fof(f6191,plain,
( spl107_4
<=> class_RealVector_Oreal__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_4])]) ).
fof(f4121,plain,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1196]) ).
fof(f1196,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6189,plain,
spl107_3,
inference(avatar_split_clause,[],[f4120,f6186]) ).
fof(f6186,plain,
( spl107_3
<=> class_Fields_Olinordered__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_3])]) ).
fof(f4120,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1140]) ).
fof(f1140,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6184,plain,
spl107_2,
inference(avatar_split_clause,[],[f4119,f6181]) ).
fof(f6181,plain,
( spl107_2
<=> class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_2])]) ).
fof(f4119,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1111]) ).
fof(f1111,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6179,plain,
spl107_1,
inference(avatar_split_clause,[],[f4118,f6176]) ).
fof(f6176,plain,
( spl107_1
<=> class_Orderings_Odense__linorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl107_1])]) ).
fof(f4118,plain,
class_Orderings_Odense__linorder(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1136]) ).
fof(f1136,axiom,
class_Orderings_Odense__linorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW215+1 : TPTP v8.2.0. Released v5.2.0.
% 0.06/0.12 % Command : run_vampire %s %d SAT
% 0.11/0.33 % Computer : n017.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 : Wed Jun 19 08:59:39 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.35 This is a FOF_THM_RFO_SEQ problem
% 0.11/0.36 Running first-order model finding
% 0.11/0.36 Running /export/starexec/sandbox/solver/bin/vampire --mode casc_sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.50 % (7192)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.50 % (7195)fmb+10_1:1_sil=256000:fmbes=contour:i=214858:bce=on_0 on theBenchmark for (2999ds/214858Mi)
% 0.20/0.51 % (7192)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.51 % (7199)ott-4_1:1_sil=4000:sp=reverse_arity:lcm=predicate:newcnf=on:i=115:bce=on:fd=off:fs=off:fsr=off_0 on theBenchmark for (2999ds/115Mi)
% 0.20/0.52 % (7192)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.52 % (7196)fmb+10_1:1_sil=256000:fmbss=23:fmbes=contour:newcnf=on:fmbsr=1.14:i=152523:nm=2:gsp=on:rp=on_0 on theBenchmark for (2999ds/152523Mi)
% 0.20/0.52 % (7192)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.52 % (7193)fmb+10_1:1_sil=256000:i=98885:tgt=full:fmbsr=1.3:fmbss=10_0 on theBenchmark for (2999ds/98885Mi)
% 0.20/0.52 % (7192)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.52 % (7198)ott+11_8:59_sil=16000:sp=occurrence:lsd=20:abs=on:i=146:aac=none:nm=16:fdi=10:rawr=on:nicw=on_0 on theBenchmark for (2999ds/146Mi)
% 0.20/0.52 % (7192)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.52 % (7194)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:i=99418_0 on theBenchmark for (2999ds/99418Mi)
% 0.20/0.52 % (7192)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.52 % (7197)ott+21_1:1_sil=4000:i=104:fsd=on:fd=off:newcnf=on_0 on theBenchmark for (2999ds/104Mi)
% 0.67/0.54 % (7199)Instruction limit reached!
% 0.67/0.54 % (7199)------------------------------
% 0.67/0.54 % (7199)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.67/0.54 % (7199)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.67/0.54 % (7199)Termination reason: Time limit
% 0.67/0.54 % (7199)Termination phase: Saturation
% 0.67/0.54
% 0.67/0.54 % (7199)Memory used [KB]: 3829
% 0.67/0.54 % (7199)Time elapsed: 0.034 s
% 0.67/0.54 % (7199)Instructions burned: 117 (million)
% 0.80/0.58 % (7192)Running in auto input_syntax mode. Trying TPTP
% 0.80/0.58 % (7200)dis+11_1:3_bsr=unit_only:sil=2000:rp=on:newcnf=on:i=404:kws=precedence:lsd=100_0 on theBenchmark for (2999ds/404Mi)
% 0.80/0.58 % (7198)Instruction limit reached!
% 0.80/0.58 % (7198)------------------------------
% 0.80/0.58 % (7198)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.80/0.58 % (7198)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.80/0.58 % (7198)Termination reason: Time limit
% 0.80/0.58 % (7198)Termination phase: Saturation
% 0.80/0.58
% 0.80/0.58 % (7198)Memory used [KB]: 4248
% 0.80/0.58 % (7198)Time elapsed: 0.059 s
% 0.80/0.58 % (7198)Instructions burned: 146 (million)
% 0.80/0.58 % (7197)Instruction limit reached!
% 0.80/0.58 % (7197)------------------------------
% 0.80/0.58 % (7197)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.80/0.58 % (7197)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.80/0.58 % (7197)Termination reason: Time limit
% 0.80/0.58 % (7197)Termination phase: Saturation
% 0.80/0.58
% 0.80/0.58 % (7197)Memory used [KB]: 3923
% 0.80/0.58 % (7197)Time elapsed: 0.060 s
% 0.80/0.58 % (7197)Instructions burned: 105 (million)
% 0.80/0.61 % (7192)Running in auto input_syntax mode. Trying TPTP
% 0.80/0.61 % (7201)ott-21_1:1_sil=4000:sp=const_frequency:i=175:fsr=off:fs=off:av=off_0 on theBenchmark for (2998ds/175Mi)
% 0.80/0.62 % (7192)Running in auto input_syntax mode. Trying TPTP
% 0.80/0.62 % (7202)ott+33_1:1_to=lpo:sil=8000:sp=weighted_frequency:rp=on:i=270:nm=3:fsr=off:sac=on_0 on theBenchmark for (2998ds/270Mi)
% 1.25/0.67 % (7201)Instruction limit reached!
% 1.25/0.67 % (7201)------------------------------
% 1.25/0.67 % (7201)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.25/0.67 % (7201)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.25/0.67 % (7201)Termination reason: Time limit
% 1.25/0.67 % (7201)Termination phase: Saturation
% 1.25/0.67
% 1.25/0.67 % (7201)Memory used [KB]: 4806
% 1.25/0.67 % (7201)Time elapsed: 0.054 s
% 1.25/0.67 % (7201)Instructions burned: 177 (million)
% 1.53/0.70 Cannot represent all propositional literals internally
% 1.53/0.70 % (7196)Refutation not found, incomplete strategy% (7196)------------------------------
% 1.53/0.70 % (7196)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.53/0.70 % (7196)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.53/0.70 % (7196)Termination reason: Refutation not found, incomplete strategy
% 1.53/0.70
% 1.53/0.70 % (7196)Memory used [KB]: 13960
% 1.53/0.70 % (7196)Time elapsed: 0.185 s
% 1.53/0.70 % (7196)Instructions burned: 657 (million)
% 1.53/0.70 % (7192)Running in auto input_syntax mode. Trying TPTP
% 1.53/0.70 % (7206)ott+4_1:1_sil=2000:i=900:bd=off:fsr=off_0 on theBenchmark for (2997ds/900Mi)
% 1.53/0.70 % (7196)------------------------------
% 1.53/0.70 % (7196)------------------------------
% 1.53/0.72 TRYING [1]
% 1.53/0.72 % (7200)Instruction limit reached!
% 1.53/0.72 % (7200)------------------------------
% 1.53/0.72 % (7200)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.53/0.72 % (7200)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.53/0.72 % (7200)Termination reason: Time limit
% 1.53/0.72 % (7200)Termination phase: Saturation
% 1.53/0.72
% 1.53/0.72 % (7200)Memory used [KB]: 6451
% 1.53/0.72 % (7200)Time elapsed: 0.146 s
% 1.53/0.72 % (7200)Instructions burned: 405 (million)
% 1.53/0.74 % (7192)Running in auto input_syntax mode. Trying TPTP
% 1.53/0.74 % (7230)fmb+10_1:1_sil=8000:fde=unused:fmbes=contour:i=7859:nm=2:fmbswr=0_0 on theBenchmark for (2997ds/7859Mi)
% 1.53/0.74 % (7202)Instruction limit reached!
% 1.53/0.74 % (7202)------------------------------
% 1.53/0.74 % (7202)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.53/0.74 % (7202)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.53/0.74 % (7202)Termination reason: Time limit
% 1.53/0.74 % (7202)Termination phase: Saturation
% 1.53/0.74
% 1.53/0.74 % (7202)Memory used [KB]: 6466
% 1.53/0.74 % (7202)Time elapsed: 0.129 s
% 1.53/0.74 % (7202)Instructions burned: 270 (million)
% 1.53/0.75 TRYING [2]
% 2.13/0.76 % (7192)Running in auto input_syntax mode. Trying TPTP
% 2.13/0.76 % (7244)ott+11_1:2_anc=none:sil=2000:sp=const_max:spb=units:s2a=on:i=2145:s2at=5.0:awrs=converge:awrsf=170:rawr=on:gs=on:fsr=off_0 on theBenchmark for (2997ds/2145Mi)
% 2.18/0.78 % (7192)Running in auto input_syntax mode. Trying TPTP
% 2.18/0.78 % (7252)ott-30_1:1024_sil=4000:alpa=true:newcnf=on:i=1187:bs=unit_only:ins=1:amm=off_0 on theBenchmark for (2997ds/1187Mi)
% 2.18/0.78 % (7194)First to succeed.
% 2.32/0.82 % (7194)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-7192"
% 2.32/0.82 % (7192)Running in auto input_syntax mode. Trying TPTP
% 2.32/0.82 % (7194)Refutation found. Thanks to Tanya!
% 2.32/0.82 % SZS status Theorem for theBenchmark
% 2.32/0.82 % SZS output start Proof for theBenchmark
% See solution above
% 2.37/0.85 % (7194)------------------------------
% 2.37/0.85 % (7194)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 2.37/0.85 % (7194)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 2.37/0.85 % (7194)Termination reason: Refutation
% 2.37/0.85
% 2.37/0.85 % (7194)Memory used [KB]: 9216
% 2.37/0.85 % (7194)Time elapsed: 0.300 s
% 2.37/0.85 % (7194)Instructions burned: 833 (million)
% 2.37/0.85 % (7194)------------------------------
% 2.37/0.85 % (7194)------------------------------
% 2.37/0.85 % (7192)Success in time 0.385 s
%------------------------------------------------------------------------------