TSTP Solution File: SWW256+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW256+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 17:29:31 EDT 2024
% Result : Theorem 3.53s 0.91s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1635
% Syntax : Number of formulae : 4740 (1617 unt; 0 def)
% Number of atoms : 10761 (2232 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 9387 (3366 ~;3346 |; 622 &)
% (1236 <=>; 817 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 999 ( 997 usr; 902 prp; 0-4 aty)
% Number of functors : 62 ( 62 usr; 18 con; 0-3 aty)
% Number of variables : 6596 (6481 !; 115 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17113,plain,
$false,
inference(avatar_sat_refutation,[],[f6174,f6179,f6184,f6189,f6194,f6199,f6204,f6209,f6214,f6219,f6224,f6229,f6234,f6239,f6244,f6249,f6254,f6259,f6264,f6269,f6274,f6279,f6284,f6289,f6294,f6299,f6304,f6309,f6314,f6319,f6324,f6329,f6334,f6339,f6344,f6349,f6354,f6359,f6364,f6369,f6374,f6379,f6384,f6389,f6394,f6399,f6404,f6409,f6414,f6419,f6424,f6429,f6434,f6439,f6444,f6449,f6454,f6459,f6464,f6469,f6474,f6479,f6484,f6489,f6494,f6499,f6504,f6509,f6514,f6519,f6524,f6529,f6534,f6539,f6544,f6549,f6554,f6559,f6564,f6569,f6574,f6579,f6584,f6589,f6594,f6599,f6604,f6609,f6614,f6619,f6624,f6629,f6634,f6639,f6644,f6649,f6654,f6659,f6664,f6669,f6674,f6679,f6684,f6689,f6694,f6699,f6704,f6709,f6714,f6719,f6724,f6729,f6734,f6739,f6744,f6749,f6754,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,f7289,f7293,f7297,f7301,f7305,f7310,f7315,f7319,f7323,f7327,f7332,f7337,f7341,f7345,f7349,f7353,f7357,f7361,f7365,f7369,f7373,f7377,f7381,f7385,f7389,f7393,f7397,f7401,f7405,f7409,f7413,f7417,f7421,f7425,f7429,f7433,f7437,f7441,f7445,f7449,f7453,f7457,f7461,f7465,f7469,f7473,f7477,f7481,f7485,f7489,f7493,f7497,f7501,f7505,f7509,f7513,f7517,f7521,f7525,f7529,f7533,f7537,f7541,f7545,f7549,f7553,f7557,f7561,f7565,f7569,f7573,f7577,f7581,f7585,f7589,f7593,f7597,f7601,f7606,f7611,f7616,f7621,f7626,f7631,f7636,f7641,f7646,f7650,f7654,f7658,f7662,f7666,f7670,f7674,f7678,f7682,f7686,f7690,f7694,f7698,f7702,f7707,f7712,f7717,f7722,f7728,f7733,f7737,f7741,f7745,f7749,f7753,f7757,f7761,f7765,f7769,f7773,f7777,f7781,f7785,f7789,f7793,f7797,f7801,f7805,f7809,f7813,f7818,f7823,f7841,f7845,f7850,f7854,f7858,f7862,f7866,f7870,f7874,f7878,f7882,f7886,f7890,f7894,f7898,f7902,f7906,f7910,f7914,f7918,f7922,f7926,f7955,f7960,f7966,f7970,f7974,f7978,f7982,f7986,f7990,f7994,f7998,f8002,f8006,f8012,f8016,f8020,f8024,f8028,f8032,f8036,f8040,f8044,f8048,f8052,f8056,f8060,f8064,f8068,f8072,f8076,f8080,f8084,f8088,f8092,f8096,f8100,f8104,f8108,f8112,f8116,f8120,f8124,f8128,f8132,f8136,f8140,f8144,f8148,f8152,f8156,f8161,f8166,f8190,f8271,f8308,f8352,f8368,f8374,f8383,f8388,f8392,f8396,f8400,f8404,f8408,f8412,f8416,f8420,f8424,f8428,f8432,f8436,f8440,f8444,f8448,f8452,f8456,f8460,f8464,f8468,f8472,f8476,f8480,f8484,f8488,f8492,f8496,f8500,f8504,f8508,f8512,f8516,f8521,f8525,f8530,f8560,f8659,f8769,f8773,f8777,f8781,f8785,f8789,f8793,f8797,f8801,f8805,f8809,f8813,f8817,f8821,f8825,f8831,f8835,f8839,f8843,f8847,f8851,f8855,f8859,f8863,f8867,f8872,f8876,f8880,f8884,f8888,f8892,f8896,f8900,f8904,f8908,f8912,f8917,f8921,f8925,f8929,f8933,f8937,f8941,f8945,f8949,f8953,f8957,f8964,f8968,f8972,f8976,f8980,f8984,f8988,f8992,f8996,f9000,f9005,f9009,f9013,f9017,f9021,f9025,f9029,f9033,f9037,f9041,f9045,f9050,f9054,f9058,f9062,f9066,f9070,f9074,f9078,f9082,f9086,f9090,f9094,f9098,f9102,f9106,f9110,f9114,f9118,f9122,f9126,f9130,f9134,f9138,f9142,f9146,f9150,f9154,f9179,f9259,f9459,f9521,f9736,f9921,f9941,f9945,f9949,f9953,f9957,f9961,f9965,f9969,f9974,f9978,f9982,f9986,f9990,f9994,f9998,f10002,f10006,f10010,f10018,f10022,f10026,f10030,f10034,f10038,f10042,f10046,f10050,f10054,f10058,f10062,f10066,f10070,f10074,f10078,f10082,f10086,f10090,f10094,f10098,f10102,f10106,f10110,f10114,f10118,f10122,f10126,f10130,f10134,f10138,f10142,f10146,f10150,f10154,f10158,f10162,f10166,f10170,f10174,f10178,f10182,f10187,f10191,f10195,f10199,f10203,f10207,f10211,f10215,f10219,f10223,f10227,f10231,f10235,f10240,f10244,f10248,f10252,f10256,f10347,f10617,f10838,f10953,f10957,f10961,f10965,f10969,f10973,f10977,f10981,f10985,f10989,f10994,f10998,f11002,f11006,f11010,f11014,f11018,f11022,f11026,f11030,f11034,f11038,f11042,f11046,f11050,f11054,f11058,f11062,f11066,f11070,f11074,f11079,f11083,f11087,f11091,f11095,f11099,f11103,f11107,f11111,f11115,f11119,f11129,f11133,f11137,f11141,f11145,f11149,f11153,f11157,f11162,f11172,f11334,f11498,f11707,f11951,f11990,f11994,f11998,f12002,f12006,f12010,f12014,f12018,f12022,f12026,f12030,f12034,f12038,f12042,f12046,f12050,f12054,f12058,f12062,f12066,f12070,f12074,f12078,f12082,f12086,f12090,f12094,f12098,f12102,f12106,f12110,f12114,f12118,f12122,f12126,f12130,f12134,f12138,f12142,f12146,f12150,f12154,f12158,f12162,f12166,f12170,f12174,f12178,f12182,f12186,f12190,f12194,f12198,f12202,f12206,f12210,f12214,f12218,f12222,f12226,f12230,f12234,f12238,f12242,f12246,f12250,f12254,f12258,f12262,f12266,f12270,f12274,f12278,f12282,f12286,f12290,f12294,f12298,f12302,f12306,f12310,f12319,f12323,f12327,f12331,f12335,f12339,f12343,f12347,f12351,f12355,f12359,f12363,f12367,f12371,f12375,f12379,f12383,f12387,f12391,f12395,f12399,f12403,f12407,f12411,f12415,f12419,f12423,f12427,f12431,f12435,f12439,f12443,f12447,f12451,f12455,f12459,f12463,f12467,f12471,f12475,f12479,f12483,f12488,f12494,f12499,f12636,f13482,f15129,f15292,f15296,f15300,f15305,f15309,f15313,f15317,f15321,f15325,f15329,f15333,f15337,f15341,f15345,f15350,f15354,f15358,f15362,f15366,f15370,f15374,f15378,f15382,f15386,f15390,f15395,f15399,f15403,f15407,f15411,f15415,f15419,f15423,f15427,f15431,f15435,f15447,f15451,f15455,f15459,f15463,f15467,f15471,f15475,f15479,f15483,f15501,f15505,f15509,f15513,f15517,f15521,f15525,f15530,f15534,f15538,f15542,f15546,f15801,f16510,f17112]) ).
fof(f17112,plain,
( ~ spl53_49
| spl53_224
| ~ spl53_877
| ~ spl53_901 ),
inference(avatar_split_clause,[],[f16954,f16507,f15433,f7286,f6411]) ).
fof(f6411,plain,
( spl53_49
<=> class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_49])]) ).
fof(f7286,plain,
( spl53_224
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Oii ),
introduced(avatar_definition,[new_symbols(naming,[spl53_224])]) ).
fof(f15433,plain,
( spl53_877
<=> ! [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,[spl53_877])]) ).
fof(f16507,plain,
( spl53_901
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Oii),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_901])]) ).
fof(f16954,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Oii
| ~ class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex)
| ~ spl53_877
| ~ spl53_901 ),
inference(trivial_inequality_removal,[],[f16947]) ).
fof(f16947,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Oii
| ~ class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex)
| ~ spl53_877
| ~ spl53_901 ),
inference(superposition,[],[f15434,f16509]) ).
fof(f16509,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Oii),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ spl53_901 ),
inference(avatar_component_clause,[],[f16507]) ).
fof(f15434,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) )
| ~ spl53_877 ),
inference(avatar_component_clause,[],[f15433]) ).
fof(f16510,plain,
( ~ spl53_102
| spl53_901
| ~ spl53_585
| ~ spl53_900 ),
inference(avatar_split_clause,[],[f16059,f15798,f9988,f16507,f6676]) ).
fof(f6676,plain,
( spl53_102
<=> class_Groups_Ogroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_102])]) ).
fof(f9988,plain,
( spl53_585
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Ouminus__class_Ouminus(X1,X0)
| ~ class_Groups_Ogroup__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_585])]) ).
fof(f15798,plain,
( spl53_900
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Oii),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_900])]) ).
fof(f16059,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Oii),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Groups_Ogroup__add(tc_Complex_Ocomplex)
| ~ spl53_585
| ~ spl53_900 ),
inference(trivial_inequality_removal,[],[f16018]) ).
fof(f16018,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Oii),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Groups_Ogroup__add(tc_Complex_Ocomplex)
| ~ spl53_585
| ~ spl53_900 ),
inference(superposition,[],[f9989,f15800]) ).
fof(f15800,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Oii),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ spl53_900 ),
inference(avatar_component_clause,[],[f15798]) ).
fof(f9989,plain,
( ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) != c_Groups_Ouminus__class_Ouminus(X1,X0)
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Groups_Ogroup__add(X1) )
| ~ spl53_585 ),
inference(avatar_component_clause,[],[f9988]) ).
fof(f15801,plain,
( spl53_900
| ~ spl53_19
| ~ spl53_571
| ~ spl53_581
| ~ spl53_842 ),
inference(avatar_split_clause,[],[f15557,f15290,f9972,f9734,f6261,f15798]) ).
fof(f6261,plain,
( spl53_19
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_19])]) ).
fof(f9734,plain,
( spl53_571
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_571])]) ).
fof(f9972,plain,
( spl53_581
<=> ! [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,[spl53_581])]) ).
fof(f15290,plain,
( spl53_842
<=> ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),X0)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_842])]) ).
fof(f15557,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Oii),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ spl53_19
| ~ spl53_571
| ~ spl53_581
| ~ spl53_842 ),
inference(forward_demodulation,[],[f15548,f10301]) ).
fof(f10301,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ spl53_19
| ~ spl53_581 ),
inference(resolution,[],[f9973,f6263]) ).
fof(f6263,plain,
( class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
| ~ spl53_19 ),
inference(avatar_component_clause,[],[f6261]) ).
fof(f9973,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)) )
| ~ spl53_581 ),
inference(avatar_component_clause,[],[f9972]) ).
fof(f15548,plain,
( c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Oii),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ spl53_571
| ~ spl53_842 ),
inference(superposition,[],[f15291,f9735]) ).
fof(f9735,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ spl53_571 ),
inference(avatar_component_clause,[],[f9734]) ).
fof(f15291,plain,
( ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),X0)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)
| ~ spl53_842 ),
inference(avatar_component_clause,[],[f15290]) ).
fof(f15546,plain,
spl53_899,
inference(avatar_split_clause,[],[f6124,f15544]) ).
fof(f15544,plain,
( spl53_899
<=> ! [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,[spl53_899])]) ).
fof(f6124,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,[],[f4805,f4804]) ).
fof(f4804,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,[],[f1754]) ).
fof(f1754,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,[],[f344]) ).
fof(f344,axiom,
! [X11,X24,X25] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X24),X11) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__left) ).
fof(f4805,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,[],[f1755]) ).
fof(f1755,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,[],[f40]) ).
fof(f40,axiom,
! [X11,X24,X25] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X24),X11) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X11),X24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__commute) ).
fof(f15542,plain,
spl53_898,
inference(avatar_split_clause,[],[f6121,f15540]) ).
fof(f15540,plain,
( spl53_898
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_898])]) ).
fof(f6121,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) ),
inference(forward_demodulation,[],[f6120,f4201]) ).
fof(f4201,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f1319]) ).
fof(f1319,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f309]) ).
fof(f309,axiom,
! [X10] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(f6120,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) ),
inference(forward_demodulation,[],[f6119,f4346]) ).
fof(f4346,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,[],[f1455]) ).
fof(f1455,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,[],[f485]) ).
fof(f485,axiom,
! [X3,X10] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X10) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(f6119,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(forward_demodulation,[],[f6118,f4201]) ).
fof(f6118,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(forward_demodulation,[],[f5737,f4346]) ).
fof(f5737,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(definition_unfolding,[],[f4793,f4205,f4205]) ).
fof(f4205,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f1323]) ).
fof(f1323,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rectify,[],[f212]) ).
fof(f212,axiom,
! [X3] : c_Nat_OSuc(X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(f4793,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f3685]) ).
fof(f3685,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ) ),
inference(flattening,[],[f3684]) ).
fof(f3684,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ) ),
inference(nnf_transformation,[],[f1749]) ).
fof(f1749,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ) ),
inference(rectify,[],[f459]) ).
fof(f459,axiom,
! [X8,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13),X8))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X8)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).
fof(f15538,plain,
spl53_897,
inference(avatar_split_clause,[],[f6117,f15536]) ).
fof(f15536,plain,
( spl53_897
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_897])]) ).
fof(f6117,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(forward_demodulation,[],[f6116,f4201]) ).
fof(f6116,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
inference(forward_demodulation,[],[f6115,f4346]) ).
fof(f6115,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(forward_demodulation,[],[f6114,f4201]) ).
fof(f6114,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(forward_demodulation,[],[f5736,f4346]) ).
fof(f5736,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(definition_unfolding,[],[f4794,f4205,f4205]) ).
fof(f4794,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f3685]) ).
fof(f15534,plain,
spl53_896,
inference(avatar_split_clause,[],[f6029,f15532]) ).
fof(f15532,plain,
( spl53_896
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_896])]) ).
fof(f6029,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ),
inference(forward_demodulation,[],[f6028,f4201]) ).
fof(f6028,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ),
inference(forward_demodulation,[],[f6027,f4346]) ).
fof(f6027,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(forward_demodulation,[],[f6026,f4201]) ).
fof(f6026,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(forward_demodulation,[],[f5681,f4346]) ).
fof(f5681,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(definition_unfolding,[],[f4637,f4205,f4205]) ).
fof(f4637,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(cnf_transformation,[],[f2661]) ).
fof(f2661,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(ennf_transformation,[],[f1687]) ).
fof(f1687,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ),
inference(rectify,[],[f81]) ).
fof(f81,axiom,
! [X3,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X25),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__one__le__power) ).
fof(f15530,plain,
~ spl53_895,
inference(avatar_split_clause,[],[f5968,f15527]) ).
fof(f15527,plain,
( spl53_895
<=> c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_895])]) ).
fof(f5968,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____))),
inference(forward_demodulation,[],[f4163,f4162]) ).
fof(f4162,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____),
inference(cnf_transformation,[],[f667]) ).
fof(f667,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pqc0) ).
fof(f4163,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))),
inference(cnf_transformation,[],[f765]) ).
fof(f765,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rnc) ).
fof(f15525,plain,
spl53_894,
inference(avatar_split_clause,[],[f5665,f15523]) ).
fof(f15523,plain,
( spl53_894
<=> ! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_894])]) ).
fof(f5665,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f4576,f4205]) ).
fof(f4576,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3581]) ).
fof(f3581,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
| X0 != X1 )
& ( X0 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(nnf_transformation,[],[f2593]) ).
fof(f2593,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
<=> X0 = X1 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1639]) ).
fof(f1639,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
<=> X0 = X1 ) ),
inference(rectify,[],[f209]) ).
fof(f209,axiom,
! [X8,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,X8)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X8,c_Nat_OSuc(X13))
<=> X8 = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
fof(f15521,plain,
spl53_893,
inference(avatar_split_clause,[],[f5658,f15519]) ).
fof(f15519,plain,
( spl53_893
<=> ! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_893])]) ).
fof(f5658,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f4561,f4205]) ).
fof(f4561,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2575]) ).
fof(f2575,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(flattening,[],[f2574]) ).
fof(f2574,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1625]) ).
fof(f1625,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
=> X0 = X1 ) ),
inference(rectify,[],[f328]) ).
fof(f328,axiom,
! [X10,X3] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X10)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Nat_OSuc(X10))
=> X3 = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).
fof(f15517,plain,
spl53_892,
inference(avatar_split_clause,[],[f5493,f15515]) ).
fof(f15515,plain,
( spl53_892
<=> ! [X0,X3,X2,X1] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,X3),X1),X0) = c_Groups_Ouminus__class_Ouminus(X3,hAPP(X1,X0))
| ~ class_Groups_Ouminus(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_892])]) ).
fof(f5493,plain,
! [X2,X3,X0,X1] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,X3),X1),X0) = c_Groups_Ouminus__class_Ouminus(X3,hAPP(X1,X0))
| ~ class_Groups_Ouminus(X3) ),
inference(cnf_transformation,[],[f3328]) ).
fof(f3328,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,X3),X1),X0) = c_Groups_Ouminus__class_Ouminus(X3,hAPP(X1,X0))
| ~ class_Groups_Ouminus(X3) ),
inference(ennf_transformation,[],[f2226]) ).
fof(f2226,plain,
! [X0,X1,X2,X3] :
( class_Groups_Ouminus(X3)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,X3),X1),X0) = c_Groups_Ouminus__class_Ouminus(X3,hAPP(X1,X0)) ),
inference(rectify,[],[f887]) ).
fof(f887,axiom,
! [X15,X38,X39,X5] :
( class_Groups_Ouminus(X5)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X39,X5),X38),X15) = c_Groups_Ouminus__class_Ouminus(X5,hAPP(X38,X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_uminus__apply) ).
fof(f15513,plain,
spl53_891,
inference(avatar_split_clause,[],[f5492,f15511]) ).
fof(f15511,plain,
( spl53_891
<=> ! [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,[spl53_891])]) ).
fof(f5492,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,[],[f3327]) ).
fof(f3327,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,[],[f3326]) ).
fof(f3326,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,[],[f2225]) ).
fof(f2225,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,[],[f981]) ).
fof(f981,axiom,
! [X33,X20,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( c_Rings_Odvd__class_Odvd(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X20),X33)
=> c_Rings_Odvd__class_Odvd(X5,X4,X33) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__left) ).
fof(f15509,plain,
spl53_890,
inference(avatar_split_clause,[],[f5491,f15507]) ).
fof(f15507,plain,
( spl53_890
<=> ! [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,[spl53_890])]) ).
fof(f5491,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,[],[f3325]) ).
fof(f3325,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,[],[f3324]) ).
fof(f3324,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,[],[f2224]) ).
fof(f2224,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,[],[f980]) ).
fof(f980,axiom,
! [X33,X20,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( c_Rings_Odvd__class_Odvd(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X20),X33)
=> c_Rings_Odvd__class_Odvd(X5,X20,X33) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__right) ).
fof(f15505,plain,
spl53_889,
inference(avatar_split_clause,[],[f5490,f15503]) ).
fof(f15503,plain,
( spl53_889
<=> ! [X0,X3,X2,X1] :
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),X0)
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_889])]) ).
fof(f5490,plain,
! [X2,X3,X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),X0)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3323]) ).
fof(f3323,plain,
! [X0,X1,X2,X3] :
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),X0)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(flattening,[],[f3322]) ).
fof(f3322,plain,
! [X0,X1,X2,X3] :
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,X0)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),X0)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2223]) ).
fof(f2223,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),X0)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X1,X0) ) ),
inference(rectify,[],[f971]) ).
fof(f971,axiom,
! [X6,X14,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5),c_Polynomial_Osmult(X5,X4,X14),X6)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5),X14,X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__dvd__cancel) ).
fof(f15501,plain,
spl53_888,
inference(avatar_split_clause,[],[f5489,f15499]) ).
fof(f15499,plain,
( spl53_888
<=> ! [X0,X3,X2,X1] :
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,c_Polynomial_Osmult(X3,X0,X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_888])]) ).
fof(f5489,plain,
! [X2,X3,X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,c_Polynomial_Osmult(X3,X0,X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(cnf_transformation,[],[f3321]) ).
fof(f3321,plain,
! [X0,X1,X2,X3] :
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,c_Polynomial_Osmult(X3,X0,X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(flattening,[],[f3320]) ).
fof(f3320,plain,
! [X0,X1,X2,X3] :
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,c_Polynomial_Osmult(X3,X0,X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,X1)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f2222]) ).
fof(f2222,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,X1)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X3),X2,c_Polynomial_Osmult(X3,X0,X1)) ) ),
inference(rectify,[],[f972]) ).
fof(f972,axiom,
! [X4,X6,X14,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5),X14,X6)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5),X14,c_Polynomial_Osmult(X5,X4,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__smult) ).
fof(f15483,plain,
spl53_887,
inference(avatar_split_clause,[],[f5485,f15481]) ).
fof(f15481,plain,
( spl53_887
<=> ! [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,[spl53_887])]) ).
fof(f5485,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,[],[f3313]) ).
fof(f3313,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,[],[f3312]) ).
fof(f3312,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,[],[f2218]) ).
fof(f2218,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,[],[f984]) ).
fof(f984,axiom,
! [X20,X33,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( c_Rings_Odvd__class_Odvd(X5,X4,X33)
=> c_Rings_Odvd__class_Odvd(X5,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X20),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult) ).
fof(f15479,plain,
spl53_886,
inference(avatar_split_clause,[],[f5484,f15477]) ).
fof(f15477,plain,
( spl53_886
<=> ! [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,[spl53_886])]) ).
fof(f5484,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,[],[f3311]) ).
fof(f3311,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,[],[f3310]) ).
fof(f3310,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,[],[f2217]) ).
fof(f2217,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,[],[f985]) ).
fof(f985,axiom,
! [X33,X20,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( c_Rings_Odvd__class_Odvd(X5,X4,X20)
=> c_Rings_Odvd__class_Odvd(X5,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X20),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult2) ).
fof(f15475,plain,
spl53_885,
inference(avatar_split_clause,[],[f5353,f15473]) ).
fof(f15473,plain,
( spl53_885
<=> ! [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)
| ~ sP17(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_885])]) ).
fof(f5353,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)
| ~ sP17(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3867]) ).
fof(f3867,plain,
! [X0,X1,X2,X3] :
( ( sP17(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) )
| ~ sP17(X0,X1,X2,X3) ) ),
inference(rectify,[],[f3866]) ).
fof(f3866,plain,
! [X1,X0,X3,X2] :
( ( sP17(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) )
| ~ sP17(X1,X0,X3,X2) ) ),
inference(flattening,[],[f3865]) ).
fof(f3865,plain,
! [X1,X0,X3,X2] :
( ( sP17(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) )
| ~ sP17(X1,X0,X3,X2) ) ),
inference(nnf_transformation,[],[f3507]) ).
fof(f3507,plain,
! [X1,X0,X3,X2] :
( sP17(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,[sP17])]) ).
fof(f15471,plain,
spl53_884,
inference(avatar_split_clause,[],[f5344,f15469]) ).
fof(f15469,plain,
( spl53_884
<=> ! [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)
| ~ sP15(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_884])]) ).
fof(f5344,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)
| ~ sP15(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3862]) ).
fof(f3862,plain,
! [X0,X1,X2,X3] :
( ( sP15(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) )
| ~ sP15(X0,X1,X2,X3) ) ),
inference(rectify,[],[f3861]) ).
fof(f3861,plain,
! [X2,X0,X3,X1] :
( ( sP15(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) )
| ~ sP15(X2,X0,X3,X1) ) ),
inference(flattening,[],[f3860]) ).
fof(f3860,plain,
! [X2,X0,X3,X1] :
( ( sP15(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) )
| ~ sP15(X2,X0,X3,X1) ) ),
inference(nnf_transformation,[],[f3504]) ).
fof(f3504,plain,
! [X2,X0,X3,X1] :
( sP15(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,[sP15])]) ).
fof(f15467,plain,
spl53_883,
inference(avatar_split_clause,[],[f5269,f15465]) ).
fof(f15465,plain,
( spl53_883
<=> ! [X2,X0,X1] :
( sP14(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK46(X0,X1,X2)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_883])]) ).
fof(f5269,plain,
! [X2,X0,X1] :
( sP14(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK46(X0,X1,X2)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(cnf_transformation,[],[f3828]) ).
fof(f3828,plain,
! [X0,X1,X2] :
( ( sP14(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK46(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK46(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) ) )
| ~ sP14(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK46])],[f3826,f3827]) ).
fof(f3827,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(X0,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) = X1 )
=> ( ~ hBOOL(hAPP(X0,sK46(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK46(X0,X1,X2)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f3826,plain,
! [X0,X1,X2] :
( ( sP14(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) ) )
| ~ sP14(X0,X1,X2) ) ),
inference(rectify,[],[f3825]) ).
fof(f3825,plain,
! [X2,X1,X0] :
( ( sP14(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) ) )
| ~ sP14(X2,X1,X0) ) ),
inference(flattening,[],[f3824]) ).
fof(f3824,plain,
! [X2,X1,X0] :
( ( sP14(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) ) )
| ~ sP14(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f3502]) ).
fof(f3502,plain,
! [X2,X1,X0] :
( sP14(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,[sP14])]) ).
fof(f15463,plain,
spl53_882,
inference(avatar_split_clause,[],[f5261,f15461]) ).
fof(f15461,plain,
( spl53_882
<=> ! [X2,X0,X1] :
( sP13(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK45(X0,X1,X2)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_882])]) ).
fof(f5261,plain,
! [X2,X0,X1] :
( sP13(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK45(X0,X1,X2)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(cnf_transformation,[],[f3822]) ).
fof(f3822,plain,
! [X0,X1,X2] :
( ( sP13(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK45(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK45(X0,X1,X2)) = X1 )
| ( ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
& ( ( ! [X4] :
( hBOOL(hAPP(X0,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X1 )
& ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
| ~ sP13(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK45])],[f3820,f3821]) ).
fof(f3821,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(X0,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) = X1 )
=> ( ~ hBOOL(hAPP(X0,sK45(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK45(X0,X1,X2)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f3820,plain,
! [X0,X1,X2] :
( ( sP13(X0,X1,X2)
| ? [X3] :
( ~ hBOOL(hAPP(X0,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) = X1 )
| ( ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
& ( ( ! [X4] :
( hBOOL(hAPP(X0,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X1 )
& ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
| ~ sP13(X0,X1,X2) ) ),
inference(rectify,[],[f3819]) ).
fof(f3819,plain,
! [X2,X1,X0] :
( ( sP13(X2,X1,X0)
| ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X1 )
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) )
& ( ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) )
| ~ sP13(X2,X1,X0) ) ),
inference(flattening,[],[f3818]) ).
fof(f3818,plain,
! [X2,X1,X0] :
( ( sP13(X2,X1,X0)
| ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X1 )
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) )
& ( ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) )
| ~ sP13(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f3500]) ).
fof(f3500,plain,
! [X2,X1,X0] :
( sP13(X2,X1,X0)
<=> ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f15459,plain,
spl53_881,
inference(avatar_split_clause,[],[f5253,f15457]) ).
fof(f15457,plain,
( spl53_881
<=> ! [X2,X0,X1] :
( sP12(X2,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_881])]) ).
fof(f5253,plain,
! [X2,X0,X1] :
( sP12(X2,X0,X1)
| 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,[],[f3817]) ).
fof(f3817,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
| ( ~ sP12(X2,X0,X1)
& ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) )
& ( sP12(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(flattening,[],[f3816]) ).
fof(f3816,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
| ( ~ sP12(X2,X0,X1)
& ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) )
& ( sP12(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(nnf_transformation,[],[f3499]) ).
fof(f3499,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
<=> ( sP12(X2,X0,X1)
| ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ) ),
inference(definition_folding,[],[f2062,f3498]) ).
fof(f3498,plain,
! [X2,X0,X1] :
( sP12(X2,X0,X1)
<=> ? [X3] :
( hBOOL(hAPP(X2,X3))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Nat_OSuc(X3)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f2062,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
<=> ( ? [X3] :
( hBOOL(hAPP(X2,X3))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Nat_OSuc(X3)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X1) )
| ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ) ),
inference(rectify,[],[f723]) ).
fof(f723,axiom,
! [X8,X13,X48] :
( hBOOL(hAPP(X48,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X13,X8)))
<=> ( ? [X82] :
( hBOOL(hAPP(X48,X82))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8),c_Nat_OSuc(X82)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8),X82),X13) )
| ( hBOOL(hAPP(X48,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div_H) ).
fof(f15455,plain,
spl53_880,
inference(avatar_split_clause,[],[f5247,f15453]) ).
fof(f15453,plain,
( spl53_880
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
| ~ sP11(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_880])]) ).
fof(f5247,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
| ~ sP11(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f3811]) ).
fof(f3811,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
| ~ sP11(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) )
& ( ( sP11(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,[],[f3810]) ).
fof(f3810,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
| ~ sP11(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) )
& ( ( sP11(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,[],[f3497]) ).
fof(f3497,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
<=> ( sP11(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,[],[f3102,f3496]) ).
fof(f3496,plain,
! [X2,X1,X0] :
( sP11(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,[sP11])]) ).
fof(f3102,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,[],[f3101]) ).
fof(f3101,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,[],[f2061]) ).
fof(f2061,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,[],[f722]) ).
fof(f722,axiom,
! [X12,X8,X48] :
( hBOOL(hAPP(X48,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X8,X12)))
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X12
=> ! [X69,X59] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X59,X12)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X69),X59) = X8
=> hBOOL(hAPP(X48,X69)) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X12
=> hBOOL(hAPP(X48,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div) ).
fof(f15451,plain,
spl53_879,
inference(avatar_split_clause,[],[f5076,f15449]) ).
fof(f15449,plain,
( spl53_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,[spl53_879])]) ).
fof(f5076,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,[],[f2946]) ).
fof(f2946,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,[],[f1955]) ).
fof(f1955,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,[],[f35]) ).
fof(f35,axiom,
! [X20,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X20) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X20),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(f15447,plain,
spl53_878,
inference(avatar_split_clause,[],[f5064,f15445]) ).
fof(f15445,plain,
( spl53_878
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0)
| ~ class_Groups_Ozero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_878])]) ).
fof(f5064,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0)
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f3750]) ).
fof(f3750,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_OpCons(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 )
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0) ) )
| ~ class_Groups_Ozero(X2) ),
inference(flattening,[],[f3749]) ).
fof(f3749,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_OpCons(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 )
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0) ) )
| ~ class_Groups_Ozero(X2) ),
inference(nnf_transformation,[],[f2935]) ).
fof(f2935,plain,
! [X0,X1,X2] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_OpCons(X2,X1,X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 ) )
| ~ class_Groups_Ozero(X2) ),
inference(ennf_transformation,[],[f1945]) ).
fof(f1945,plain,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_OpCons(X2,X1,X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 ) ) ),
inference(rectify,[],[f810]) ).
fof(f810,axiom,
! [X73,X9,X5] :
( class_Groups_Ozero(X5)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_OpCons(X5,X9,X73)
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X73
& c_Groups_Ozero__class_Ozero(X5) = X9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).
fof(f15435,plain,
spl53_877,
inference(avatar_split_clause,[],[f4934,f15433]) ).
fof(f4934,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,[],[f2790]) ).
fof(f2790,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,[],[f2789]) ).
fof(f2789,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,[],[f1848]) ).
fof(f1848,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,[],[f43]) ).
fof(f43,axiom,
! [X3,X4,X5] :
( class_Rings_Oring__1__no__zero__divisors(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X4
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X3) != c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
fof(f15431,plain,
spl53_876,
inference(avatar_split_clause,[],[f4862,f15429]) ).
fof(f15429,plain,
( spl53_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,[spl53_876])]) ).
fof(f4862,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,[],[f2738]) ).
fof(f2738,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,[],[f1809]) ).
fof(f1809,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,[],[f703]) ).
fof(f703,axiom,
! [X20,X4,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X4,X20)) = c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ominus__class_Ominus(X5,X20,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__minus__commute) ).
fof(f15427,plain,
spl53_875,
inference(avatar_split_clause,[],[f4809,f15425]) ).
fof(f15425,plain,
( spl53_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,[spl53_875])]) ).
fof(f4809,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,[],[f1759]) ).
fof(f1759,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,[],[f483]) ).
fof(f483,axiom,
! [X11,X3,X10] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X3),X11) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(f15423,plain,
spl53_874,
inference(avatar_split_clause,[],[f4808,f15421]) ).
fof(f15421,plain,
( spl53_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,[spl53_874])]) ).
fof(f4808,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,[],[f1758]) ).
fof(f1758,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,[],[f484]) ).
fof(f484,axiom,
! [X36,X21,X7] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X36)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X36)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
fof(f15419,plain,
spl53_873,
inference(avatar_split_clause,[],[f4807,f15417]) ).
fof(f15417,plain,
( spl53_873
<=> ! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_873])]) ).
fof(f4807,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0),
inference(cnf_transformation,[],[f1757]) ).
fof(f1757,plain,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0),
inference(rectify,[],[f563]) ).
fof(f563,axiom,
! [X64,X62,X63] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X63,X62),X64) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X63,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X62,X64)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(f15415,plain,
spl53_872,
inference(avatar_split_clause,[],[f4806,f15413]) ).
fof(f15413,plain,
( spl53_872
<=> ! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_872])]) ).
fof(f4806,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0)),
inference(cnf_transformation,[],[f1756]) ).
fof(f1756,plain,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0)),
inference(rectify,[],[f561]) ).
fof(f561,axiom,
! [X36,X21,X7] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,X36)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X36)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
fof(f15411,plain,
spl53_871,
inference(avatar_split_clause,[],[f4804,f15409]) ).
fof(f15409,plain,
( spl53_871
<=> ! [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,[spl53_871])]) ).
fof(f15407,plain,
spl53_870,
inference(avatar_split_clause,[],[f4803,f15405]) ).
fof(f15405,plain,
( spl53_870
<=> ! [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,[spl53_870])]) ).
fof(f4803,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,[],[f1753]) ).
fof(f1753,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,[],[f342]) ).
fof(f342,axiom,
! [X3,X11,X10] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X11),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel2) ).
fof(f15403,plain,
spl53_869,
inference(avatar_split_clause,[],[f4802,f15401]) ).
fof(f15401,plain,
( spl53_869
<=> ! [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,[spl53_869])]) ).
fof(f4802,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,[],[f1752]) ).
fof(f1752,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,[],[f343]) ).
fof(f343,axiom,
! [X3,X10,X11] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X10),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel) ).
fof(f15399,plain,
spl53_868,
inference(avatar_split_clause,[],[f4791,f15397]) ).
fof(f15397,plain,
( spl53_868
<=> ! [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,[spl53_868])]) ).
fof(f4791,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,[],[f3683]) ).
fof(f3683,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,[],[f3682]) ).
fof(f3682,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,[],[f1748]) ).
fof(f1748,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,[],[f434]) ).
fof(f434,axiom,
! [X8,X13] :
( 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),X13),X8))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X8)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
fof(f15395,plain,
( ~ spl53_867
| ~ spl53_371
| ~ spl53_841 ),
inference(avatar_split_clause,[],[f15213,f15126,f7912,f15392]) ).
fof(f15392,plain,
( spl53_867
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_867])]) ).
fof(f7912,plain,
( spl53_371
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_371])]) ).
fof(f15126,plain,
( spl53_841
<=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_841])]) ).
fof(f15213,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21)
| ~ spl53_371
| ~ spl53_841 ),
inference(superposition,[],[f7913,f15128]) ).
fof(f15128,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl53_841 ),
inference(avatar_component_clause,[],[f15126]) ).
fof(f7913,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl53_371 ),
inference(avatar_component_clause,[],[f7912]) ).
fof(f15390,plain,
spl53_866,
inference(avatar_split_clause,[],[f4790,f15388]) ).
fof(f15388,plain,
( spl53_866
<=> ! [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,[spl53_866])]) ).
fof(f4790,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,[],[f3683]) ).
fof(f15386,plain,
spl53_865,
inference(avatar_split_clause,[],[f4786,f15384]) ).
fof(f15384,plain,
( spl53_865
<=> ! [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,[spl53_865])]) ).
fof(f4786,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,[],[f3679]) ).
fof(f3679,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ) ),
inference(flattening,[],[f3678]) ).
fof(f3678,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ) ),
inference(nnf_transformation,[],[f1746]) ).
fof(f1746,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(rectify,[],[f463]) ).
fof(f463,axiom,
! [X8,X15] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X15),X8))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).
fof(f15382,plain,
spl53_864,
inference(avatar_split_clause,[],[f4757,f15380]) ).
fof(f15380,plain,
( spl53_864
<=> ! [X0,X1] :
( X0 = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_864])]) ).
fof(f4757,plain,
! [X0,X1] :
( X0 = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f3662]) ).
fof(f3662,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ( X0 != X1
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) )
& ( X0 = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(flattening,[],[f3661]) ).
fof(f3661,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ( X0 != X1
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) )
& ( X0 = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(nnf_transformation,[],[f1736]) ).
fof(f1736,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> ( X0 = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
inference(rectify,[],[f560]) ).
fof(f560,axiom,
! [X56,X57] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X57,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X56,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> ( X56 = X57
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X57,X56) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
fof(f15378,plain,
spl53_863,
inference(avatar_split_clause,[],[f4714,f15376]) ).
fof(f15376,plain,
( spl53_863
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_863])]) ).
fof(f4714,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f3642]) ).
fof(f3642,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) )
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1 ) )
& ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) )
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f3641]) ).
fof(f3641,plain,
! [X1,X0] :
( ( sP0(X1,X0)
| ( ( ~ 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)) )
& ( ~ 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) )
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
& ( ( 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)) )
| ( 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) )
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| ~ sP0(X1,X0) ) ),
inference(flattening,[],[f3640]) ).
fof(f3640,plain,
! [X1,X0] :
( ( sP0(X1,X0)
| ( ( ~ 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)) )
& ( ~ 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) )
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
& ( ( 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)) )
| ( 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) )
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| ~ sP0(X1,X0) ) ),
inference(nnf_transformation,[],[f3478]) ).
fof(f3478,plain,
! [X1,X0] :
( sP0(X1,X0)
<=> ( ( 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)) )
| ( 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) )
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f15374,plain,
spl53_862,
inference(avatar_split_clause,[],[f4644,f15372]) ).
fof(f15372,plain,
( spl53_862
<=> ! [X0,X1] :
( c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0))
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_862])]) ).
fof(f4644,plain,
! [X0,X1] :
( c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0))
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(cnf_transformation,[],[f2674]) ).
fof(f2674,plain,
! [X0,X1] :
( c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0))
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(flattening,[],[f2673]) ).
fof(f2673,plain,
! [X0,X1] :
( c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0))
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(ennf_transformation,[],[f1694]) ).
fof(f1694,plain,
! [X0,X1] :
( ( class_Rings_Odivision__ring__inverse__zero(X1)
& class_RealVector_Oreal__normed__div__algebra(X1) )
=> c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0)) ),
inference(rectify,[],[f773]) ).
fof(f773,axiom,
! [X4,X5] :
( ( class_Rings_Odivision__ring__inverse__zero(X5)
& class_RealVector_Oreal__normed__div__algebra(X5) )
=> c_RealVector_Onorm__class_Onorm(X5,c_Rings_Oinverse__class_Oinverse(X5,X4)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__inverse) ).
fof(f15370,plain,
spl53_861,
inference(avatar_split_clause,[],[f4595,f15368]) ).
fof(f15368,plain,
( spl53_861
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_861])]) ).
fof(f4595,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(cnf_transformation,[],[f2613]) ).
fof(f2613,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(ennf_transformation,[],[f1655]) ).
fof(f1655,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0)) ),
inference(rectify,[],[f614]) ).
fof(f614,axiom,
! [X3,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X7)
=> 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),X7),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(f15366,plain,
spl53_860,
inference(avatar_split_clause,[],[f4589,f15364]) ).
fof(f15364,plain,
( spl53_860
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK30(X0,X1),X0)
| ~ hBOOL(hAPP(X1,X0))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_860])]) ).
fof(f4589,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK30(X0,X1),X0)
| ~ hBOOL(hAPP(X1,X0))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(cnf_transformation,[],[f3583]) ).
fof(f3583,plain,
! [X0,X1] :
( ( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK30(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,sK30(X0,X1)) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK30(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,[sK30])],[f2607,f3582]) ).
fof(f3582,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,sK30(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,sK30(X0,X1)) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK30(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f2607,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,[],[f2606]) ).
fof(f2606,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,[],[f1651]) ).
fof(f1651,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,[],[f550]) ).
fof(f550,axiom,
! [X8,X48] :
( ~ hBOOL(hAPP(X48,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X48,X8))
=> ? [X52] :
( hBOOL(hAPP(X48,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X52,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [X69] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X69,X52)
=> ~ hBOOL(hAPP(X48,X69)) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X52,X8) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).
fof(f15362,plain,
spl53_859,
inference(avatar_split_clause,[],[f4534,f15360]) ).
fof(f15360,plain,
( spl53_859
<=> ! [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,[spl53_859])]) ).
fof(f4534,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,[],[f2544]) ).
fof(f2544,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,[],[f1598]) ).
fof(f1598,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,[],[f715]) ).
fof(f715,axiom,
! [X6,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__poly__0__left) ).
fof(f15358,plain,
spl53_858,
inference(avatar_split_clause,[],[f4533,f15356]) ).
fof(f15356,plain,
( spl53_858
<=> ! [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,[spl53_858])]) ).
fof(f4533,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,[],[f2543]) ).
fof(f2543,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,[],[f1597]) ).
fof(f1597,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,[],[f716]) ).
fof(f716,axiom,
! [X14,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X14),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__poly__0__right) ).
fof(f15354,plain,
spl53_857,
inference(avatar_split_clause,[],[f4490,f15352]) ).
fof(f15352,plain,
( spl53_857
<=> ! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X0)
| ~ class_Rings_Ocomm__ring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_857])]) ).
fof(f4490,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X0)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(cnf_transformation,[],[f2505]) ).
fof(f2505,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X0)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(ennf_transformation,[],[f1559]) ).
fof(f1559,plain,
! [X0,X1] :
( class_Rings_Ocomm__ring__1(X1)
=> c_Groups_Ouminus__class_Ouminus(X1,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X0) ),
inference(rectify,[],[f878]) ).
fof(f878,axiom,
! [X7,X5] :
( class_Rings_Ocomm__ring__1(X5)
=> c_Groups_Ouminus__class_Ouminus(X5,X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Oone__class_Oone(X5))),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
fof(f15350,plain,
( spl53_856
| ~ spl53_342
| ~ spl53_837 ),
inference(avatar_split_clause,[],[f15133,f12496,f7779,f15347]) ).
fof(f15347,plain,
( spl53_856
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK50,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_856])]) ).
fof(f7779,plain,
( spl53_342
<=> ! [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,[spl53_342])]) ).
fof(f12496,plain,
( spl53_837
<=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK50,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK52))) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_837])]) ).
fof(f15133,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK50,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21))
| ~ spl53_342
| ~ spl53_837 ),
inference(superposition,[],[f7780,f12498]) ).
fof(f12498,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK50,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK52)))
| ~ spl53_837 ),
inference(avatar_component_clause,[],[f12496]) ).
fof(f7780,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ spl53_342 ),
inference(avatar_component_clause,[],[f7779]) ).
fof(f15345,plain,
spl53_855,
inference(avatar_split_clause,[],[f4485,f15343]) ).
fof(f15343,plain,
( spl53_855
<=> ! [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,[spl53_855])]) ).
fof(f4485,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,[],[f3570]) ).
fof(f3570,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,[],[f2502]) ).
fof(f2502,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,[],[f1556]) ).
fof(f1556,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,[],[f183]) ).
fof(f183,axiom,
! [X9,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X9,X9),c_Groups_Ozero__class_Ozero(X5))
<=> c_Orderings_Oord__class_Oless(X5,X9,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
fof(f15341,plain,
spl53_854,
inference(avatar_split_clause,[],[f4484,f15339]) ).
fof(f15339,plain,
( spl53_854
<=> ! [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,[spl53_854])]) ).
fof(f4484,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,[],[f3570]) ).
fof(f15337,plain,
spl53_853,
inference(avatar_split_clause,[],[f4469,f15335]) ).
fof(f15335,plain,
( spl53_853
<=> ! [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,[spl53_853])]) ).
fof(f4469,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,[],[f3564]) ).
fof(f3564,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,[],[f2491]) ).
fof(f2491,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,[],[f1546]) ).
fof(f1546,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,[],[f100]) ).
fof(f100,axiom,
! [X9,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oplus__class_Oplus(X5,X9,X9),c_Groups_Ozero__class_Ozero(X5))
<=> c_Orderings_Oord__class_Oless(X5,X9,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(f15333,plain,
spl53_852,
inference(avatar_split_clause,[],[f4468,f15331]) ).
fof(f15331,plain,
( spl53_852
<=> ! [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,[spl53_852])]) ).
fof(f4468,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,[],[f3564]) ).
fof(f15329,plain,
spl53_851,
inference(avatar_split_clause,[],[f4467,f15327]) ).
fof(f15327,plain,
( spl53_851
<=> ! [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,[spl53_851])]) ).
fof(f4467,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,[],[f3563]) ).
fof(f3563,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,[],[f2490]) ).
fof(f2490,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,[],[f1545]) ).
fof(f1545,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,[],[f97]) ).
fof(f97,axiom,
! [X9,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,X9,X9))
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(f15325,plain,
spl53_850,
inference(avatar_split_clause,[],[f4466,f15323]) ).
fof(f15323,plain,
( spl53_850
<=> ! [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,[spl53_850])]) ).
fof(f4466,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,[],[f3563]) ).
fof(f15321,plain,
spl53_849,
inference(avatar_split_clause,[],[f4465,f15319]) ).
fof(f15319,plain,
( spl53_849
<=> ! [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,[spl53_849])]) ).
fof(f4465,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,[],[f3562]) ).
fof(f3562,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,[],[f2489]) ).
fof(f2489,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,[],[f1544]) ).
fof(f1544,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,[],[f101]) ).
fof(f101,axiom,
! [X9,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oplus__class_Oplus(X5,X9,X9),c_Groups_Ozero__class_Ozero(X5))
<=> c_Orderings_Oord__class_Oless__eq(X5,X9,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(f15317,plain,
spl53_848,
inference(avatar_split_clause,[],[f4464,f15315]) ).
fof(f15315,plain,
( spl53_848
<=> ! [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,[spl53_848])]) ).
fof(f4464,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,[],[f3562]) ).
fof(f15313,plain,
spl53_847,
inference(avatar_split_clause,[],[f4463,f15311]) ).
fof(f15311,plain,
( spl53_847
<=> ! [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,[spl53_847])]) ).
fof(f4463,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,[],[f3561]) ).
fof(f3561,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,[],[f2488]) ).
fof(f2488,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,[],[f1543]) ).
fof(f1543,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,[],[f98]) ).
fof(f98,axiom,
! [X9,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,X9,X9))
<=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(f15309,plain,
spl53_846,
inference(avatar_split_clause,[],[f4462,f15307]) ).
fof(f15307,plain,
( spl53_846
<=> ! [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,[spl53_846])]) ).
fof(f4462,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,[],[f3561]) ).
fof(f15305,plain,
( ~ spl53_845
| ~ spl53_340
| ~ spl53_837 ),
inference(avatar_split_clause,[],[f15131,f12496,f7771,f15302]) ).
fof(f15302,plain,
( spl53_845
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21),sK50) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_845])]) ).
fof(f7771,plain,
( spl53_340
<=> ! [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,[spl53_340])]) ).
fof(f15131,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21),sK50)
| ~ spl53_340
| ~ spl53_837 ),
inference(superposition,[],[f7772,f12498]) ).
fof(f7772,plain,
( ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1)
| ~ spl53_340 ),
inference(avatar_component_clause,[],[f7771]) ).
fof(f15300,plain,
spl53_844,
inference(avatar_split_clause,[],[f4365,f15298]) ).
fof(f15298,plain,
( spl53_844
<=> ! [X0,X1] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_844])]) ).
fof(f4365,plain,
! [X0,X1] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),
inference(cnf_transformation,[],[f1474]) ).
fof(f1474,plain,
! [X0,X1] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),
inference(rectify,[],[f927]) ).
fof(f927,axiom,
! [X61,X36] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X36,X61)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X36),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X61)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).
fof(f15296,plain,
spl53_843,
inference(avatar_split_clause,[],[f4309,f15294]) ).
fof(f15294,plain,
( spl53_843
<=> ! [X0] :
( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X0)),X0)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_843])]) ).
fof(f4309,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X0)),X0)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 ),
inference(cnf_transformation,[],[f2407]) ).
fof(f2407,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X0)),X0)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 ),
inference(ennf_transformation,[],[f1426]) ).
fof(f1426,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0
=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X0)),X0) ),
inference(rectify,[],[f815]) ).
fof(f815,axiom,
! [X7] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X7
=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X7)),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__inverse__left) ).
fof(f15292,plain,
spl53_842,
inference(avatar_split_clause,[],[f4224,f15290]) ).
fof(f4224,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),X0)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),
inference(cnf_transformation,[],[f1342]) ).
fof(f1342,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),X0)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),
inference(rectify,[],[f871]) ).
fof(f871,axiom,
! [X7] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),X7)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__i__mult__minus) ).
fof(f15129,plain,
( spl53_841
| ~ spl53_330
| ~ spl53_394
| ~ spl53_835 ),
inference(avatar_split_clause,[],[f12490,f12485,f8034,f7730,f15126]) ).
fof(f7730,plain,
( spl53_330
<=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_330])]) ).
fof(f8034,plain,
( spl53_394
<=> ! [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,[spl53_394])]) ).
fof(f12485,plain,
( spl53_835
<=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____),v_k____),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_835])]) ).
fof(f12490,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl53_330
| ~ spl53_394
| ~ spl53_835 ),
inference(forward_demodulation,[],[f12489,f7732]) ).
fof(f7732,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21)
| ~ spl53_330 ),
inference(avatar_component_clause,[],[f7730]) ).
fof(f12489,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl53_394
| ~ spl53_835 ),
inference(forward_demodulation,[],[f12487,f8035]) ).
fof(f8035,plain,
( ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
| ~ spl53_394 ),
inference(avatar_component_clause,[],[f8034]) ).
fof(f12487,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____),v_k____),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl53_835 ),
inference(avatar_component_clause,[],[f12485]) ).
fof(f13482,plain,
( ~ spl53_839
| spl53_840
| ~ spl53_237
| ~ spl53_774 ),
inference(avatar_split_clause,[],[f13402,f12236,f7343,f13480,f13476]) ).
fof(f13476,plain,
( spl53_839
<=> class_Groups_Oordered__ab__group__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_839])]) ).
fof(f13480,plain,
( spl53_840
<=> ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_840])]) ).
fof(f7343,plain,
( spl53_237
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_237])]) ).
fof(f12236,plain,
( spl53_774
<=> ! [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,[spl53_774])]) ).
fof(f13402,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat) )
| ~ spl53_237
| ~ spl53_774 ),
inference(resolution,[],[f12237,f7344]) ).
fof(f7344,plain,
( ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl53_237 ),
inference(avatar_component_clause,[],[f7343]) ).
fof(f12237,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) )
| ~ spl53_774 ),
inference(avatar_component_clause,[],[f12236]) ).
fof(f12636,plain,
( ~ spl53_106
| spl53_838
| ~ spl53_359
| ~ spl53_416 ),
inference(avatar_split_clause,[],[f8334,f8122,f7864,f12634,f6696]) ).
fof(f6696,plain,
( spl53_106
<=> class_Rings_Olinordered__semidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_106])]) ).
fof(f12634,plain,
( spl53_838
<=> ! [X0,X1] : sP9(X0,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_838])]) ).
fof(f7864,plain,
( spl53_359
<=> ! [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,[spl53_359])]) ).
fof(f8122,plain,
( spl53_416
<=> ! [X2,X0,X1] :
( sP9(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,[spl53_416])]) ).
fof(f8334,plain,
( ! [X0,X1] :
( sP9(X0,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Rings_Olinordered__semidom(tc_Int_Oint) )
| ~ spl53_359
| ~ spl53_416 ),
inference(resolution,[],[f8123,f7865]) ).
fof(f7865,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) )
| ~ spl53_359 ),
inference(avatar_component_clause,[],[f7864]) ).
fof(f8123,plain,
( ! [X2,X0,X1] :
( sP9(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ~ spl53_416 ),
inference(avatar_component_clause,[],[f8122]) ).
fof(f12499,plain,
spl53_837,
inference(avatar_split_clause,[],[f6169,f12496]) ).
fof(f6169,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK50,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK52))),
inference(forward_demodulation,[],[f6168,f4170]) ).
fof(f4170,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21),
inference(cnf_transformation,[],[f3515]) ).
fof(f3515,plain,
( ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK21),X1)
& c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f2326,f3514]) ).
fof(f3514,plain,
( ? [X0] :
( ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1)
& c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X0) )
=> ( ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK21),X1)
& c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f2326,plain,
? [X0] :
( ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1)
& c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X0) ),
inference(ennf_transformation,[],[f1289]) ).
fof(f1289,plain,
~ ! [X0] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X0)
=> ~ ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1) ),
inference(rectify,[],[f753]) ).
fof(f753,axiom,
~ ! [X82] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X82)
=> ~ ! [X2] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X2)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X82),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bq_O_A_091_124_Apsize_Aq_A_061_Apsize_Ap_059_AALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(f6168,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK50,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK52))),
inference(forward_demodulation,[],[f6167,f5970]) ).
fof(f5970,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),
inference(forward_demodulation,[],[f5969,f4155]) ).
fof(f4155,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____),
inference(cnf_transformation,[],[f597]) ).
fof(f597,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_q_I1_J) ).
fof(f5969,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),
inference(forward_demodulation,[],[f4164,f4162]) ).
fof(f4164,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),
inference(cnf_transformation,[],[f763]) ).
fof(f763,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lgqr) ).
fof(f6167,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK50,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK52))),
inference(forward_demodulation,[],[f6166,f4162]) ).
fof(f6166,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK50,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK52))),
inference(forward_demodulation,[],[f6165,f4346]) ).
fof(f6165,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK50,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK52),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(forward_demodulation,[],[f6164,f4808]) ).
fof(f6164,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK52),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK50,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(forward_demodulation,[],[f5619,f4809]) ).
fof(f5619,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK52),sK50),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f3917]) ).
fof(f3917,plain,
( ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X3),sK50)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,sK51,sK52)),X3)))
& c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK52),sK50),c_Groups_Oone__class_Oone(tc_Nat_Onat))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != sK50
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != sK51 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK50,sK51,sK52])],[f2319,f3916,f3915]) ).
fof(f3915,plain,
( ? [X0,X1] :
( ? [X2] :
( ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X3),X0)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,X2)),X3)))
& c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X2),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != X1 )
=> ( ? [X2] :
( ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X3),sK50)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,sK51,X2)),X3)))
& c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X2),sK50),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != sK50
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != sK51 ) ),
introduced(choice_axiom,[]) ).
fof(f3916,plain,
( ? [X2] :
( ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X3),sK50)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,sK51,X2)),X3)))
& c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X2),sK50),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
=> ( ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X3),sK50)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,sK51,sK52)),X3)))
& c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK52),sK50),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
introduced(choice_axiom,[]) ).
fof(f2319,plain,
? [X0,X1] :
( ? [X2] :
( ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X3) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X3),X0)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,X2)),X3)))
& c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X2),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != X1 ),
inference(rectify,[],[f849]) ).
fof(f849,axiom,
? [X52,X85] :
( ? [X82] :
( ! [X83] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X83) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X83),X52)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X85,X82)),X83)))
& c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X82),X52),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X52
& c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != X85 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096EX_Ak_Aa_Aqa_O_Aa_A_126_061_A0_A_G_Ak_A_126_061_A0_A_G_Apsize_Aqa_A_L_Ak_A_L_A1_A_061_Apsize_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A_G_A_IALL_Az_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Az_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_L_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aqa_J_Az_J_096) ).
fof(f12494,plain,
( spl53_836
| ~ spl53_197
| ~ spl53_413 ),
inference(avatar_split_clause,[],[f8318,f8110,f7151,f12492]) ).
fof(f12492,plain,
( spl53_836
<=> ! [X0] : c_Polynomial_Osmult(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_836])]) ).
fof(f7151,plain,
( spl53_197
<=> class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_197])]) ).
fof(f8110,plain,
( spl53_413
<=> ! [X0,X1] :
( c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X0) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_413])]) ).
fof(f8318,plain,
( ! [X0] : c_Polynomial_Osmult(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) = X0
| ~ spl53_197
| ~ spl53_413 ),
inference(resolution,[],[f8111,f7153]) ).
fof(f7153,plain,
( class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ~ spl53_197 ),
inference(avatar_component_clause,[],[f7151]) ).
fof(f8111,plain,
( ! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X0) = X0 )
| ~ spl53_413 ),
inference(avatar_component_clause,[],[f8110]) ).
fof(f12488,plain,
spl53_835,
inference(avatar_split_clause,[],[f5973,f12485]) ).
fof(f5973,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____),v_k____),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f5972,f5970]) ).
fof(f5972,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____),v_k____),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),
inference(forward_demodulation,[],[f4166,f4162]) ).
fof(f4166,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____),v_k____),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),
inference(cnf_transformation,[],[f760]) ).
fof(f760,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____),v_k____),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_kas_I3_J) ).
fof(f12483,plain,
spl53_834,
inference(avatar_split_clause,[],[f5952,f12481]) ).
fof(f12481,plain,
( spl53_834
<=> ! [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,[spl53_834])]) ).
fof(f5952,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,[],[f5558]) ).
fof(f5558,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,[],[f3894]) ).
fof(f3894,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,[],[f3427]) ).
fof(f3427,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,[],[f3426]) ).
fof(f3426,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,[],[f2280]) ).
fof(f2280,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,[],[f71]) ).
fof(f71,axiom,
! [X34,X35,X32,X9,X5] :
( class_Groups_Oab__group__add(X5)
=> ( c_Groups_Ominus__class_Ominus(X5,X9,X32) = c_Groups_Ominus__class_Ominus(X5,X35,X34)
=> ( X9 = X32
<=> X34 = X35 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).
fof(f12479,plain,
spl53_833,
inference(avatar_split_clause,[],[f5567,f12477]) ).
fof(f12477,plain,
( spl53_833
<=> ! [X4,X0,X3,X2,X1] :
( X0 = X2
| c_Polynomial_OpCons(X4,X3,X2) != c_Polynomial_OpCons(X4,X1,X0)
| ~ class_Groups_Ozero(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_833])]) ).
fof(f5567,plain,
! [X2,X3,X0,X1,X4] :
( X0 = X2
| c_Polynomial_OpCons(X4,X3,X2) != c_Polynomial_OpCons(X4,X1,X0)
| ~ class_Groups_Ozero(X4) ),
inference(cnf_transformation,[],[f3900]) ).
fof(f3900,plain,
! [X0,X1,X2,X3,X4] :
( ( ( c_Polynomial_OpCons(X4,X3,X2) = c_Polynomial_OpCons(X4,X1,X0)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Polynomial_OpCons(X4,X3,X2) != c_Polynomial_OpCons(X4,X1,X0) ) )
| ~ class_Groups_Ozero(X4) ),
inference(flattening,[],[f3899]) ).
fof(f3899,plain,
! [X0,X1,X2,X3,X4] :
( ( ( c_Polynomial_OpCons(X4,X3,X2) = c_Polynomial_OpCons(X4,X1,X0)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Polynomial_OpCons(X4,X3,X2) != c_Polynomial_OpCons(X4,X1,X0) ) )
| ~ class_Groups_Ozero(X4) ),
inference(nnf_transformation,[],[f3431]) ).
fof(f3431,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Polynomial_OpCons(X4,X3,X2) = c_Polynomial_OpCons(X4,X1,X0)
<=> ( X0 = X2
& X1 = X3 ) )
| ~ class_Groups_Ozero(X4) ),
inference(ennf_transformation,[],[f2284]) ).
fof(f2284,plain,
! [X0,X1,X2,X3,X4] :
( class_Groups_Ozero(X4)
=> ( c_Polynomial_OpCons(X4,X3,X2) = c_Polynomial_OpCons(X4,X1,X0)
<=> ( X0 = X2
& X1 = X3 ) ) ),
inference(rectify,[],[f808]) ).
fof(f808,axiom,
! [X81,X32,X73,X9,X5] :
( class_Groups_Ozero(X5)
=> ( c_Polynomial_OpCons(X5,X9,X73) = c_Polynomial_OpCons(X5,X32,X81)
<=> ( X73 = X81
& X9 = X32 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__eq__iff) ).
fof(f12475,plain,
spl53_832,
inference(avatar_split_clause,[],[f5566,f12473]) ).
fof(f12473,plain,
( spl53_832
<=> ! [X2,X4,X0,X3,X1] :
( X1 = X3
| c_Polynomial_OpCons(X4,X3,X2) != c_Polynomial_OpCons(X4,X1,X0)
| ~ class_Groups_Ozero(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_832])]) ).
fof(f5566,plain,
! [X2,X3,X0,X1,X4] :
( X1 = X3
| c_Polynomial_OpCons(X4,X3,X2) != c_Polynomial_OpCons(X4,X1,X0)
| ~ class_Groups_Ozero(X4) ),
inference(cnf_transformation,[],[f3900]) ).
fof(f12471,plain,
spl53_831,
inference(avatar_split_clause,[],[f5514,f12469]) ).
fof(f12469,plain,
( spl53_831
<=> ! [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,[spl53_831])]) ).
fof(f5514,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,[],[f3362]) ).
fof(f3362,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,[],[f3361]) ).
fof(f3361,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,[],[f2244]) ).
fof(f2244,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,[],[f506]) ).
fof(f506,axiom,
! [X36,X7,X21,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X21,X7)
=> ( c_Orderings_Oord__class_Oless(X5,X36,X21)
=> c_Orderings_Oord__class_Oless(X5,X36,X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(f12467,plain,
spl53_830,
inference(avatar_split_clause,[],[f5513,f12465]) ).
fof(f12465,plain,
( spl53_830
<=> ! [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,[spl53_830])]) ).
fof(f5513,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,[],[f3360]) ).
fof(f3360,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,[],[f3359]) ).
fof(f3359,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,[],[f2243]) ).
fof(f2243,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,[],[f531]) ).
fof(f531,axiom,
! [X36,X7,X21,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X21,X7)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X36,X21)
=> c_Orderings_Oord__class_Oless(X5,X36,X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(f12463,plain,
spl53_829,
inference(avatar_split_clause,[],[f5511,f12461]) ).
fof(f12461,plain,
( spl53_829
<=> ! [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,[spl53_829])]) ).
fof(f5511,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,[],[f3356]) ).
fof(f3356,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,[],[f3355]) ).
fof(f3355,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,[],[f2241]) ).
fof(f2241,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,[],[f529]) ).
fof(f529,axiom,
! [X36,X7,X21,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X21,X7)
=> ( c_Orderings_Oord__class_Oless(X5,X36,X21)
=> c_Orderings_Oord__class_Oless(X5,X36,X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(f12459,plain,
spl53_828,
inference(avatar_split_clause,[],[f5510,f12457]) ).
fof(f12457,plain,
( spl53_828
<=> ! [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,[spl53_828])]) ).
fof(f5510,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,[],[f3354]) ).
fof(f3354,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,[],[f3353]) ).
fof(f3353,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,[],[f2240]) ).
fof(f2240,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,[],[f490]) ).
fof(f490,axiom,
! [X36,X7,X21,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X21,X7)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X36,X21)
=> c_Orderings_Oord__class_Oless__eq(X5,X36,X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(f12455,plain,
spl53_827,
inference(avatar_split_clause,[],[f5506,f12453]) ).
fof(f12453,plain,
( spl53_827
<=> ! [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,[spl53_827])]) ).
fof(f5506,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,[],[f3346]) ).
fof(f3346,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,[],[f3345]) ).
fof(f3345,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,[],[f2236]) ).
fof(f2236,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,[],[f507]) ).
fof(f507,axiom,
! [X36,X21,X7,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X7,X21)
=> ( c_Orderings_Oord__class_Oless(X5,X21,X36)
=> c_Orderings_Oord__class_Oless(X5,X7,X36) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(f12451,plain,
spl53_826,
inference(avatar_split_clause,[],[f5505,f12449]) ).
fof(f12449,plain,
( spl53_826
<=> ! [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,[spl53_826])]) ).
fof(f5505,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,[],[f3344]) ).
fof(f3344,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,[],[f3343]) ).
fof(f3343,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,[],[f2235]) ).
fof(f2235,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,[],[f532]) ).
fof(f532,axiom,
! [X36,X21,X7,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X7,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X21,X36)
=> c_Orderings_Oord__class_Oless(X5,X7,X36) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
fof(f12447,plain,
( spl53_825
| ~ spl53_198
| ~ spl53_413 ),
inference(avatar_split_clause,[],[f8316,f8110,f7156,f12445]) ).
fof(f12445,plain,
( spl53_825
<=> ! [X0] : c_Polynomial_Osmult(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_825])]) ).
fof(f7156,plain,
( spl53_198
<=> class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_198])]) ).
fof(f8316,plain,
( ! [X0] : c_Polynomial_Osmult(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) = X0
| ~ spl53_198
| ~ spl53_413 ),
inference(resolution,[],[f8111,f7158]) ).
fof(f7158,plain,
( class_Rings_Ocomm__semiring__1(tc_Int_Oint)
| ~ spl53_198 ),
inference(avatar_component_clause,[],[f7156]) ).
fof(f12443,plain,
spl53_824,
inference(avatar_split_clause,[],[f5504,f12441]) ).
fof(f12441,plain,
( spl53_824
<=> ! [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,[spl53_824])]) ).
fof(f5504,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,[],[f3342]) ).
fof(f3342,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,[],[f3341]) ).
fof(f3341,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,[],[f2234]) ).
fof(f2234,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,[],[f530]) ).
fof(f530,axiom,
! [X36,X21,X7,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X7,X21)
=> ( c_Orderings_Oord__class_Oless(X5,X21,X36)
=> c_Orderings_Oord__class_Oless(X5,X7,X36) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
fof(f12439,plain,
spl53_823,
inference(avatar_split_clause,[],[f5503,f12437]) ).
fof(f12437,plain,
( spl53_823
<=> ! [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,[spl53_823])]) ).
fof(f5503,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,[],[f3340]) ).
fof(f3340,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,[],[f3339]) ).
fof(f3339,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,[],[f2233]) ).
fof(f2233,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,[],[f492]) ).
fof(f492,axiom,
! [X36,X21,X7,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X7,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X21,X36)
=> c_Orderings_Oord__class_Oless__eq(X5,X7,X36) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).
fof(f12435,plain,
spl53_822,
inference(avatar_split_clause,[],[f5501,f12433]) ).
fof(f12433,plain,
( spl53_822
<=> ! [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,[spl53_822])]) ).
fof(f5501,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,[],[f3887]) ).
fof(f3887,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,[],[f3886]) ).
fof(f3886,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,[],[f3338]) ).
fof(f3338,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,[],[f2232]) ).
fof(f2232,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,[],[f556]) ).
fof(f556,axiom,
! [X0,X1,X5,X39] :
( class_Orderings_Oord(X39)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X5,X39),X1,X0)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X39),X0,X1)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X39),X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__fun__def) ).
fof(f12431,plain,
spl53_821,
inference(avatar_split_clause,[],[f5500,f12429]) ).
fof(f12429,plain,
( spl53_821
<=> ! [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,[spl53_821])]) ).
fof(f5500,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,[],[f3887]) ).
fof(f12427,plain,
spl53_820,
inference(avatar_split_clause,[],[f5487,f12425]) ).
fof(f12425,plain,
( spl53_820
<=> ! [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,[spl53_820])]) ).
fof(f5487,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,[],[f3317]) ).
fof(f3317,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,[],[f3316]) ).
fof(f3316,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,[],[f2220]) ).
fof(f2220,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,[],[f989]) ).
fof(f989,axiom,
! [X33,X20,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( c_Rings_Odvd__class_Odvd(X5,X4,X20)
=> ( c_Rings_Odvd__class_Odvd(X5,X20,X33)
=> c_Rings_Odvd__class_Odvd(X5,X4,X33) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__trans) ).
fof(f12423,plain,
spl53_819,
inference(avatar_split_clause,[],[f5442,f12421]) ).
fof(f12421,plain,
( spl53_819
<=> ! [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,[spl53_819])]) ).
fof(f5442,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,[],[f3266]) ).
fof(f3266,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,[],[f3265]) ).
fof(f3265,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,[],[f2177]) ).
fof(f2177,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,[],[f132]) ).
fof(f132,axiom,
! [X33,X20,X4,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,X4,X20) = c_Groups_Oplus__class_Oplus(X5,X4,X33)
=> X20 = X33 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
fof(f12419,plain,
spl53_818,
inference(avatar_split_clause,[],[f5441,f12417]) ).
fof(f12417,plain,
( spl53_818
<=> ! [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,[spl53_818])]) ).
fof(f5441,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,[],[f3264]) ).
fof(f3264,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,[],[f3263]) ).
fof(f3263,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,[],[f2176]) ).
fof(f2176,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,[],[f130]) ).
fof(f130,axiom,
! [X33,X4,X20,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,X33,X4) = c_Groups_Oplus__class_Oplus(X5,X20,X4)
=> X20 = X33 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
fof(f12415,plain,
spl53_817,
inference(avatar_split_clause,[],[f5439,f12413]) ).
fof(f12413,plain,
( spl53_817
<=> ! [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,[spl53_817])]) ).
fof(f5439,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,[],[f3261]) ).
fof(f3261,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,[],[f3260]) ).
fof(f3260,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,[],[f2174]) ).
fof(f2174,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,[],[f131]) ).
fof(f131,axiom,
! [X33,X20,X4,X5] :
( class_Groups_Ocancel__ab__semigroup__add(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,X4,X20) = c_Groups_Oplus__class_Oplus(X5,X4,X33)
=> X20 = X33 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__imp__eq) ).
fof(f12411,plain,
spl53_816,
inference(avatar_split_clause,[],[f5358,f12409]) ).
fof(f12409,plain,
( spl53_816
<=> ! [X0,X3,X2,X1] :
( sP17(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,[spl53_816])]) ).
fof(f5358,plain,
! [X2,X3,X0,X1] :
( sP17(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,[],[f3867]) ).
fof(f12407,plain,
spl53_815,
inference(avatar_split_clause,[],[f5357,f12405]) ).
fof(f12405,plain,
( spl53_815
<=> ! [X0,X3,X2,X1] :
( sP17(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,[spl53_815])]) ).
fof(f5357,plain,
! [X2,X3,X0,X1] :
( sP17(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,[],[f3867]) ).
fof(f12403,plain,
( spl53_814
| ~ spl53_196
| ~ spl53_413 ),
inference(avatar_split_clause,[],[f8315,f8110,f7146,f12401]) ).
fof(f12401,plain,
( spl53_814
<=> ! [X0] : c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_814])]) ).
fof(f7146,plain,
( spl53_196
<=> class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_196])]) ).
fof(f8315,plain,
( ! [X0] : c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0) = X0
| ~ spl53_196
| ~ spl53_413 ),
inference(resolution,[],[f8111,f7148]) ).
fof(f7148,plain,
( class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ~ spl53_196 ),
inference(avatar_component_clause,[],[f7146]) ).
fof(f12399,plain,
spl53_813,
inference(avatar_split_clause,[],[f5355,f12397]) ).
fof(f12397,plain,
( spl53_813
<=> ! [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)
| ~ sP17(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_813])]) ).
fof(f5355,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)
| ~ sP17(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3867]) ).
fof(f12395,plain,
spl53_812,
inference(avatar_split_clause,[],[f5354,f12393]) ).
fof(f12393,plain,
( spl53_812
<=> ! [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)
| ~ sP17(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_812])]) ).
fof(f5354,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)
| ~ sP17(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3867]) ).
fof(f12391,plain,
spl53_811,
inference(avatar_split_clause,[],[f5349,f12389]) ).
fof(f12389,plain,
( spl53_811
<=> ! [X0,X3,X2,X1] :
( sP15(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,[spl53_811])]) ).
fof(f5349,plain,
! [X2,X3,X0,X1] :
( sP15(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,[],[f3862]) ).
fof(f12387,plain,
spl53_810,
inference(avatar_split_clause,[],[f5348,f12385]) ).
fof(f12385,plain,
( spl53_810
<=> ! [X0,X3,X2,X1] :
( sP15(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,[spl53_810])]) ).
fof(f5348,plain,
! [X2,X3,X0,X1] :
( sP15(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,[],[f3862]) ).
fof(f12383,plain,
spl53_809,
inference(avatar_split_clause,[],[f5346,f12381]) ).
fof(f12381,plain,
( spl53_809
<=> ! [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)
| ~ sP15(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_809])]) ).
fof(f5346,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)
| ~ sP15(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3862]) ).
fof(f12379,plain,
spl53_808,
inference(avatar_split_clause,[],[f5345,f12377]) ).
fof(f12377,plain,
( spl53_808
<=> ! [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)
| ~ sP15(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_808])]) ).
fof(f5345,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)
| ~ sP15(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3862]) ).
fof(f12375,plain,
spl53_807,
inference(avatar_split_clause,[],[f5284,f12373]) ).
fof(f12373,plain,
( spl53_807
<=> ! [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,[spl53_807])]) ).
fof(f5284,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,[],[f3835]) ).
fof(f3835,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,[],[f2070]) ).
fof(f2070,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,[],[f180]) ).
fof(f180,axiom,
! [X8,X13,X12] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X13),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X8))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(f12371,plain,
spl53_806,
inference(avatar_split_clause,[],[f5283,f12369]) ).
fof(f12369,plain,
( spl53_806
<=> ! [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,[spl53_806])]) ).
fof(f5283,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,[],[f3835]) ).
fof(f12367,plain,
spl53_805,
inference(avatar_split_clause,[],[f5282,f12365]) ).
fof(f12365,plain,
( spl53_805
<=> ! [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,[spl53_805])]) ).
fof(f5282,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,[],[f3834]) ).
fof(f3834,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,[],[f2069]) ).
fof(f2069,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,[],[f179]) ).
fof(f179,axiom,
! [X8,X13,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X13),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X8))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(f12363,plain,
spl53_804,
inference(avatar_split_clause,[],[f5281,f12361]) ).
fof(f12361,plain,
( spl53_804
<=> ! [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,[spl53_804])]) ).
fof(f5281,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,[],[f3834]) ).
fof(f12359,plain,
( spl53_803
| ~ spl53_199
| ~ spl53_413 ),
inference(avatar_split_clause,[],[f8314,f8110,f7161,f12357]) ).
fof(f12357,plain,
( spl53_803
<=> ! [X0] : c_Polynomial_Osmult(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_803])]) ).
fof(f7161,plain,
( spl53_199
<=> class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_199])]) ).
fof(f8314,plain,
( ! [X0] : c_Polynomial_Osmult(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) = X0
| ~ spl53_199
| ~ spl53_413 ),
inference(resolution,[],[f8111,f7163]) ).
fof(f7163,plain,
( class_Rings_Ocomm__semiring__1(tc_Nat_Onat)
| ~ spl53_199 ),
inference(avatar_component_clause,[],[f7161]) ).
fof(f12355,plain,
spl53_802,
inference(avatar_split_clause,[],[f5276,f12353]) ).
fof(f12353,plain,
( spl53_802
<=> ! [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,[spl53_802])]) ).
fof(f5276,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,[],[f3831]) ).
fof(f3831,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,[],[f2066]) ).
fof(f2066,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,[],[f213]) ).
fof(f213,axiom,
! [X12,X42,X43] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X43,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X42,X12))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X43,X12),X42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__conv) ).
fof(f12351,plain,
spl53_801,
inference(avatar_split_clause,[],[f5275,f12349]) ).
fof(f12349,plain,
( spl53_801
<=> ! [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,[spl53_801])]) ).
fof(f5275,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,[],[f3831]) ).
fof(f12347,plain,
spl53_800,
inference(avatar_split_clause,[],[f5274,f12345]) ).
fof(f12345,plain,
( spl53_800
<=> ! [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,[spl53_800])]) ).
fof(f5274,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,[],[f3830]) ).
fof(f3830,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,[],[f2065]) ).
fof(f2065,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,[],[f216]) ).
fof(f216,axiom,
! [X43,X12,X42] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X42,X12),X43)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X43,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv) ).
fof(f12343,plain,
spl53_799,
inference(avatar_split_clause,[],[f5273,f12341]) ).
fof(f12341,plain,
( spl53_799
<=> ! [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,[spl53_799])]) ).
fof(f5273,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,[],[f3830]) ).
fof(f12339,plain,
spl53_798,
inference(avatar_split_clause,[],[f5203,f12337]) ).
fof(f12337,plain,
( spl53_798
<=> ! [X2,X0,X1] :
( X0 = X1
| c_Int_Onumber__class_Onumber__of(X2,X1) != c_Int_Onumber__class_Onumber__of(X2,X0)
| ~ class_Int_Oring__char__0(X2)
| ~ class_Int_Onumber__ring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_798])]) ).
fof(f5203,plain,
! [X2,X0,X1] :
( X0 = X1
| c_Int_Onumber__class_Onumber__of(X2,X1) != c_Int_Onumber__class_Onumber__of(X2,X0)
| ~ class_Int_Oring__char__0(X2)
| ~ class_Int_Onumber__ring(X2) ),
inference(cnf_transformation,[],[f3778]) ).
fof(f3778,plain,
! [X0,X1,X2] :
( ( ( c_Int_Onumber__class_Onumber__of(X2,X1) = c_Int_Onumber__class_Onumber__of(X2,X0)
| X0 != X1 )
& ( X0 = X1
| c_Int_Onumber__class_Onumber__of(X2,X1) != c_Int_Onumber__class_Onumber__of(X2,X0) ) )
| ~ class_Int_Oring__char__0(X2)
| ~ class_Int_Onumber__ring(X2) ),
inference(nnf_transformation,[],[f3091]) ).
fof(f3091,plain,
! [X0,X1,X2] :
( ( c_Int_Onumber__class_Onumber__of(X2,X1) = c_Int_Onumber__class_Onumber__of(X2,X0)
<=> X0 = X1 )
| ~ class_Int_Oring__char__0(X2)
| ~ class_Int_Onumber__ring(X2) ),
inference(flattening,[],[f3090]) ).
fof(f3090,plain,
! [X0,X1,X2] :
( ( c_Int_Onumber__class_Onumber__of(X2,X1) = c_Int_Onumber__class_Onumber__of(X2,X0)
<=> X0 = X1 )
| ~ class_Int_Oring__char__0(X2)
| ~ class_Int_Onumber__ring(X2) ),
inference(ennf_transformation,[],[f2054]) ).
fof(f2054,plain,
! [X0,X1,X2] :
( ( class_Int_Oring__char__0(X2)
& class_Int_Onumber__ring(X2) )
=> ( c_Int_Onumber__class_Onumber__of(X2,X1) = c_Int_Onumber__class_Onumber__of(X2,X0)
<=> X0 = X1 ) ),
inference(rectify,[],[f582]) ).
fof(f582,axiom,
! [X40,X15,X5] :
( ( class_Int_Oring__char__0(X5)
& class_Int_Onumber__ring(X5) )
=> ( c_Int_Onumber__class_Onumber__of(X5,X15) = c_Int_Onumber__class_Onumber__of(X5,X40)
<=> X15 = X40 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of) ).
fof(f12335,plain,
spl53_797,
inference(avatar_split_clause,[],[f5197,f12333]) ).
fof(f12333,plain,
( spl53_797
<=> ! [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,[spl53_797])]) ).
fof(f5197,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,[],[f3775]) ).
fof(f3775,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,[],[f3085]) ).
fof(f3085,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,[],[f3084]) ).
fof(f3084,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,[],[f2051]) ).
fof(f2051,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,[],[f719]) ).
fof(f719,axiom,
! [X81,X73,X5] :
( ( class_Rings_Oidom(X5)
& class_Int_Oring__char__0(X5) )
=> ( c_Polynomial_Opoly(X5,X73) = c_Polynomial_Opoly(X5,X81)
<=> X73 = X81 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__eq__iff) ).
fof(f12331,plain,
spl53_796,
inference(avatar_split_clause,[],[f5160,f12329]) ).
fof(f12329,plain,
( spl53_796
<=> ! [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,[spl53_796])]) ).
fof(f5160,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,[],[f3042]) ).
fof(f3042,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,[],[f2023]) ).
fof(f2023,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,[],[f167]) ).
fof(f167,axiom,
! [X11,X24,X25] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X24)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X11),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).
fof(f12327,plain,
spl53_795,
inference(avatar_split_clause,[],[f5153,f12325]) ).
fof(f12325,plain,
( spl53_795
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_795])]) ).
fof(f5153,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
inference(cnf_transformation,[],[f3034]) ).
fof(f3034,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
inference(ennf_transformation,[],[f2016]) ).
fof(f2016,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) ),
inference(rectify,[],[f565]) ).
fof(f565,axiom,
! [X11,X24,X25] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X25,X24)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,X11),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X24,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
fof(f12323,plain,
spl53_794,
inference(avatar_split_clause,[],[f5131,f12321]) ).
fof(f12321,plain,
( spl53_794
<=> ! [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,[spl53_794])]) ).
fof(f5131,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,[],[f3012]) ).
fof(f3012,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,[],[f1999]) ).
fof(f1999,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,[],[f166]) ).
fof(f166,axiom,
! [X11,X24,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X24)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X11),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1) ).
fof(f12319,plain,
spl53_793,
inference(avatar_split_clause,[],[f5130,f12317]) ).
fof(f12317,plain,
( spl53_793
<=> ! [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,[spl53_793])]) ).
fof(f5130,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,[],[f3011]) ).
fof(f3011,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,[],[f1998]) ).
fof(f1998,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,[],[f361]) ).
fof(f361,axiom,
! [X49,X3,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X3)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X49,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X49,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
fof(f12310,plain,
spl53_792,
inference(avatar_split_clause,[],[f5129,f12308]) ).
fof(f12308,plain,
( spl53_792
<=> ! [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,[spl53_792])]) ).
fof(f5129,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,[],[f3010]) ).
fof(f3010,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,[],[f1997]) ).
fof(f1997,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,[],[f360]) ).
fof(f360,axiom,
! [X49,X3,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X3)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,X49),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X49)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono) ).
fof(f12306,plain,
spl53_791,
inference(avatar_split_clause,[],[f5128,f12304]) ).
fof(f12304,plain,
( spl53_791
<=> ! [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,[spl53_791])]) ).
fof(f5128,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,[],[f3009]) ).
fof(f3009,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,[],[f1996]) ).
fof(f1996,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,[],[f673]) ).
fof(f673,axiom,
! [X11,X3,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X3)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X10,X11),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__mono) ).
fof(f12302,plain,
spl53_790,
inference(avatar_split_clause,[],[f5127,f12300]) ).
fof(f12300,plain,
( spl53_790
<=> ! [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,[spl53_790])]) ).
fof(f5127,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,[],[f3008]) ).
fof(f3008,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,[],[f1995]) ).
fof(f1995,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,[],[f217]) ).
fof(f217,axiom,
! [X10,X3,X11] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X3)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X10),X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff) ).
fof(f12298,plain,
spl53_789,
inference(avatar_split_clause,[],[f5119,f12296]) ).
fof(f12296,plain,
( spl53_789
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_789])]) ).
fof(f5119,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(cnf_transformation,[],[f2997]) ).
fof(f2997,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(ennf_transformation,[],[f1987]) ).
fof(f1987,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) ),
inference(rectify,[],[f566]) ).
fof(f566,axiom,
! [X11,X24,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X25,X24)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,X25),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__mono) ).
fof(f12294,plain,
spl53_788,
inference(avatar_split_clause,[],[f5117,f12292]) ).
fof(f12292,plain,
( spl53_788
<=> ! [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,[spl53_788])]) ).
fof(f5117,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,[],[f2994]) ).
fof(f2994,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,[],[f1985]) ).
fof(f1985,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,[],[f694]) ).
fof(f694,axiom,
! [X36,X21,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7,X21)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X36,X7),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X36,X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__left__mono) ).
fof(f12290,plain,
spl53_787,
inference(avatar_split_clause,[],[f5090,f12288]) ).
fof(f12288,plain,
( spl53_787
<=> ! [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,[spl53_787])]) ).
fof(f5090,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,[],[f3752]) ).
fof(f3752,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,[],[f3751]) ).
fof(f3751,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,[],[f2964]) ).
fof(f2964,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,[],[f1967]) ).
fof(f1967,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,[],[f545]) ).
fof(f545,axiom,
! [X40,X15,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X15,X40)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(X5,X40,X15)
& c_Orderings_Oord__class_Oless__eq(X5,X15,X40) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(f12286,plain,
spl53_786,
inference(avatar_split_clause,[],[f5063,f12284]) ).
fof(f12284,plain,
( spl53_786
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0)
| ~ class_Groups_Ozero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_786])]) ).
fof(f5063,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0)
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f3750]) ).
fof(f12282,plain,
spl53_785,
inference(avatar_split_clause,[],[f5039,f12280]) ).
fof(f12280,plain,
( spl53_785
<=> ! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| ~ class_Groups_Ogroup__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_785])]) ).
fof(f5039,plain,
! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| ~ class_Groups_Ogroup__add(X2) ),
inference(cnf_transformation,[],[f3743]) ).
fof(f3743,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0) )
& ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0)
| c_Groups_Ouminus__class_Ouminus(X2,X0) != X1 ) )
| ~ class_Groups_Ogroup__add(X2) ),
inference(nnf_transformation,[],[f2903]) ).
fof(f2903,plain,
! [X0,X1,X2] :
( ( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
<=> c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0) )
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f1926]) ).
fof(f1926,plain,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> ( c_Groups_Ouminus__class_Ouminus(X2,X0) = X1
<=> c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0) ) ),
inference(rectify,[],[f917]) ).
fof(f917,axiom,
! [X32,X9,X5] :
( class_Groups_Ogroup__add(X5)
=> ( c_Groups_Ouminus__class_Ouminus(X5,X32) = X9
<=> c_Groups_Ozero__class_Ozero(X5) = c_Groups_Oplus__class_Oplus(X5,X9,X32) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).
fof(f12278,plain,
spl53_784,
inference(avatar_split_clause,[],[f5033,f12276]) ).
fof(f12276,plain,
( spl53_784
<=> ! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,X1) = X0
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| ~ class_Groups_Ogroup__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_784])]) ).
fof(f5033,plain,
! [X2,X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X2,X1) = X0
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| ~ class_Groups_Ogroup__add(X2) ),
inference(cnf_transformation,[],[f2900]) ).
fof(f2900,plain,
! [X0,X1,X2] :
( c_Groups_Ouminus__class_Ouminus(X2,X1) = X0
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| ~ class_Groups_Ogroup__add(X2) ),
inference(flattening,[],[f2899]) ).
fof(f2899,plain,
! [X0,X1,X2] :
( c_Groups_Ouminus__class_Ouminus(X2,X1) = X0
| c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oplus__class_Oplus(X2,X1,X0)
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f1923]) ).
fof(f1923,plain,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X0)
=> c_Groups_Ouminus__class_Ouminus(X2,X1) = X0 ) ),
inference(rectify,[],[f914]) ).
fof(f914,axiom,
! [X20,X4,X5] :
( class_Groups_Ogroup__add(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) = c_Groups_Oplus__class_Oplus(X5,X4,X20)
=> c_Groups_Ouminus__class_Ouminus(X5,X4) = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__unique) ).
fof(f12274,plain,
spl53_783,
inference(avatar_split_clause,[],[f4921,f12272]) ).
fof(f12272,plain,
( spl53_783
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ class_Groups_Oordered__ab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_783])]) ).
fof(f4921,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(cnf_transformation,[],[f3716]) ).
fof(f3716,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1) )
& ( c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(nnf_transformation,[],[f2770]) ).
fof(f2770,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless(X2,X0,X1) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(ennf_transformation,[],[f1837]) ).
fof(f1837,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless(X2,X0,X1) ) ),
inference(rectify,[],[f901]) ).
fof(f901,axiom,
! [X9,X32,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ouminus__class_Ouminus(X5,X32),c_Groups_Ouminus__class_Ouminus(X5,X9))
<=> c_Orderings_Oord__class_Oless(X5,X9,X32) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).
fof(f12270,plain,
( spl53_782
| ~ spl53_133
| ~ spl53_410 ),
inference(avatar_split_clause,[],[f8298,f8098,f6831,f12268]) ).
fof(f12268,plain,
( spl53_782
<=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_782])]) ).
fof(f6831,plain,
( spl53_133
<=> class_Groups_Omonoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_133])]) ).
fof(f8098,plain,
( spl53_410
<=> ! [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,[spl53_410])]) ).
fof(f8298,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) = X0
| ~ spl53_133
| ~ spl53_410 ),
inference(resolution,[],[f8099,f6833]) ).
fof(f6833,plain,
( class_Groups_Omonoid__add(tc_RealDef_Oreal)
| ~ spl53_133 ),
inference(avatar_component_clause,[],[f6831]) ).
fof(f8099,plain,
( ! [X0,X1] :
( ~ class_Groups_Omonoid__add(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 )
| ~ spl53_410 ),
inference(avatar_component_clause,[],[f8098]) ).
fof(f12266,plain,
spl53_781,
inference(avatar_split_clause,[],[f4920,f12264]) ).
fof(f12264,plain,
( spl53_781
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Oordered__ab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_781])]) ).
fof(f4920,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(cnf_transformation,[],[f3716]) ).
fof(f12262,plain,
spl53_780,
inference(avatar_split_clause,[],[f4918,f12260]) ).
fof(f12260,plain,
( spl53_780
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Oordered__ab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_780])]) ).
fof(f4918,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(cnf_transformation,[],[f3715]) ).
fof(f3715,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1) )
& ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(nnf_transformation,[],[f2769]) ).
fof(f2769,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(X2,X0,X1) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(ennf_transformation,[],[f1836]) ).
fof(f1836,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(X2,X0,X1) ) ),
inference(rectify,[],[f884]) ).
fof(f884,axiom,
! [X9,X32,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X32),c_Groups_Ouminus__class_Ouminus(X5,X9))
<=> c_Orderings_Oord__class_Oless__eq(X5,X9,X32) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).
fof(f12258,plain,
spl53_779,
inference(avatar_split_clause,[],[f4917,f12256]) ).
fof(f12256,plain,
( spl53_779
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1)
| ~ class_Groups_Oordered__ab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_779])]) ).
fof(f4917,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1)
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(cnf_transformation,[],[f3714]) ).
fof(f3714,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) )
& ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) ) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(nnf_transformation,[],[f2768]) ).
fof(f2768,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
<=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(ennf_transformation,[],[f1835]) ).
fof(f1835,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
<=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) ) ),
inference(rectify,[],[f900]) ).
fof(f900,axiom,
! [X32,X9,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ouminus__class_Ouminus(X5,X9),X32)
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ouminus__class_Ouminus(X5,X32),X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__less__iff) ).
fof(f12254,plain,
spl53_778,
inference(avatar_split_clause,[],[f4915,f12252]) ).
fof(f12252,plain,
( spl53_778
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ class_Groups_Oordered__ab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_778])]) ).
fof(f4915,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(cnf_transformation,[],[f3713]) ).
fof(f3713,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) )
& ( c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(nnf_transformation,[],[f2767]) ).
fof(f2767,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(ennf_transformation,[],[f1834]) ).
fof(f1834,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) ) ),
inference(rectify,[],[f899]) ).
fof(f899,axiom,
! [X32,X9,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X9,c_Groups_Ouminus__class_Ouminus(X5,X32))
<=> c_Orderings_Oord__class_Oless(X5,X32,c_Groups_Ouminus__class_Ouminus(X5,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__iff) ).
fof(f12250,plain,
spl53_777,
inference(avatar_split_clause,[],[f4913,f12248]) ).
fof(f12248,plain,
( spl53_777
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1)
| ~ class_Groups_Oordered__ab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_777])]) ).
fof(f4913,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1)
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(cnf_transformation,[],[f3712]) ).
fof(f3712,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) )
& ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0) ) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(nnf_transformation,[],[f2766]) ).
fof(f2766,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
<=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(ennf_transformation,[],[f1833]) ).
fof(f1833,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
<=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),X1) ) ),
inference(rectify,[],[f883]) ).
fof(f883,axiom,
! [X32,X9,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X9),X32)
<=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X32),X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__le__iff) ).
fof(f12246,plain,
spl53_776,
inference(avatar_split_clause,[],[f4911,f12244]) ).
fof(f12244,plain,
( spl53_776
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ class_Groups_Oordered__ab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_776])]) ).
fof(f4911,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(cnf_transformation,[],[f3711]) ).
fof(f3711,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) )
& ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(nnf_transformation,[],[f2765]) ).
fof(f2765,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) )
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(ennf_transformation,[],[f1832]) ).
fof(f1832,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ouminus__class_Ouminus(X2,X1)) ) ),
inference(rectify,[],[f882]) ).
fof(f882,axiom,
! [X32,X9,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X9,c_Groups_Ouminus__class_Ouminus(X5,X32))
<=> c_Orderings_Oord__class_Oless__eq(X5,X32,c_Groups_Ouminus__class_Ouminus(X5,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__minus__iff) ).
fof(f12242,plain,
spl53_775,
inference(avatar_split_clause,[],[f4909,f12240]) ).
fof(f12240,plain,
( spl53_775
<=> ! [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,[spl53_775])]) ).
fof(f4909,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,[],[f3710]) ).
fof(f3710,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,[],[f2764]) ).
fof(f2764,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,[],[f1831]) ).
fof(f1831,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,[],[f400]) ).
fof(f400,axiom,
! [X32,X9,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X9,X32)
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ominus__class_Ominus(X5,X9,X32),c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).
fof(f12238,plain,
spl53_774,
inference(avatar_split_clause,[],[f4908,f12236]) ).
fof(f4908,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,[],[f3710]) ).
fof(f12234,plain,
spl53_773,
inference(avatar_split_clause,[],[f4907,f12232]) ).
fof(f12232,plain,
( spl53_773
<=> ! [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,[spl53_773])]) ).
fof(f4907,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,[],[f3709]) ).
fof(f3709,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,[],[f2763]) ).
fof(f2763,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,[],[f1830]) ).
fof(f1830,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,[],[f419]) ).
fof(f419,axiom,
! [X32,X9,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X9,X32)
<=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ominus__class_Ominus(X5,X9,X32),c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).
fof(f12230,plain,
spl53_772,
inference(avatar_split_clause,[],[f4906,f12228]) ).
fof(f12228,plain,
( spl53_772
<=> ! [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,[spl53_772])]) ).
fof(f4906,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,[],[f3709]) ).
fof(f12226,plain,
( spl53_771
| ~ spl53_132
| ~ spl53_410 ),
inference(avatar_split_clause,[],[f8295,f8098,f6826,f12224]) ).
fof(f12224,plain,
( spl53_771
<=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_771])]) ).
fof(f6826,plain,
( spl53_132
<=> class_Groups_Omonoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_132])]) ).
fof(f8295,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0) = X0
| ~ spl53_132
| ~ spl53_410 ),
inference(resolution,[],[f8099,f6828]) ).
fof(f6828,plain,
( class_Groups_Omonoid__add(tc_Complex_Ocomplex)
| ~ spl53_132 ),
inference(avatar_component_clause,[],[f6826]) ).
fof(f12222,plain,
spl53_770,
inference(avatar_split_clause,[],[f4905,f12220]) ).
fof(f12220,plain,
( spl53_770
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Groups_Oordered__ab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_770])]) ).
fof(f4905,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(cnf_transformation,[],[f2762]) ).
fof(f2762,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(flattening,[],[f2761]) ).
fof(f2761,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Groups_Oordered__ab__group__add(X2) ),
inference(ennf_transformation,[],[f1829]) ).
fof(f1829,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1)) ) ),
inference(rectify,[],[f885]) ).
fof(f885,axiom,
! [X20,X4,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X20)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X20),c_Groups_Ouminus__class_Ouminus(X5,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).
fof(f12218,plain,
spl53_769,
inference(avatar_split_clause,[],[f4894,f12216]) ).
fof(f12216,plain,
( spl53_769
<=> ! [X2,X0,X1] :
( sP5(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,[spl53_769])]) ).
fof(f4894,plain,
! [X2,X0,X1] :
( sP5(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,[],[f3702]) ).
fof(f3702,plain,
! [X0,X1,X2] :
( ( sP5(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) )
| ~ sP5(X0,X1,X2) ) ),
inference(rectify,[],[f3701]) ).
fof(f3701,plain,
! [X0,X2,X1] :
( ( sP5(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) )
| ~ sP5(X0,X2,X1) ) ),
inference(flattening,[],[f3700]) ).
fof(f3700,plain,
! [X0,X2,X1] :
( ( sP5(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) )
| ~ sP5(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f3487]) ).
fof(f3487,plain,
! [X0,X2,X1] :
( sP5(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,[sP5])]) ).
fof(f12214,plain,
spl53_768,
inference(avatar_split_clause,[],[f4893,f12212]) ).
fof(f12212,plain,
( spl53_768
<=> ! [X2,X0,X1] :
( sP5(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,[spl53_768])]) ).
fof(f4893,plain,
! [X2,X0,X1] :
( sP5(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,[],[f3702]) ).
fof(f12210,plain,
spl53_767,
inference(avatar_split_clause,[],[f4892,f12208]) ).
fof(f12208,plain,
( spl53_767
<=> ! [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))
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_767])]) ).
fof(f4892,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))
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f3702]) ).
fof(f12206,plain,
spl53_766,
inference(avatar_split_clause,[],[f4891,f12204]) ).
fof(f12204,plain,
( spl53_766
<=> ! [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)
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_766])]) ).
fof(f4891,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)
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f3702]) ).
fof(f12202,plain,
spl53_765,
inference(avatar_split_clause,[],[f4890,f12200]) ).
fof(f12200,plain,
( spl53_765
<=> ! [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))
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_765])]) ).
fof(f4890,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))
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f3702]) ).
fof(f12198,plain,
spl53_764,
inference(avatar_split_clause,[],[f4889,f12196]) ).
fof(f12196,plain,
( spl53_764
<=> ! [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)
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_764])]) ).
fof(f4889,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)
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f3702]) ).
fof(f12194,plain,
spl53_763,
inference(avatar_split_clause,[],[f4885,f12192]) ).
fof(f12192,plain,
( spl53_763
<=> ! [X2,X0,X1] :
( sP3(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,[spl53_763])]) ).
fof(f4885,plain,
! [X2,X0,X1] :
( sP3(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,[],[f3697]) ).
fof(f3697,plain,
! [X0,X1,X2] :
( ( sP3(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) )
| ~ sP3(X0,X1,X2) ) ),
inference(rectify,[],[f3696]) ).
fof(f3696,plain,
! [X2,X0,X1] :
( ( sP3(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) )
| ~ sP3(X2,X0,X1) ) ),
inference(flattening,[],[f3695]) ).
fof(f3695,plain,
! [X2,X0,X1] :
( ( sP3(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) )
| ~ sP3(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f3484]) ).
fof(f3484,plain,
! [X2,X0,X1] :
( sP3(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,[sP3])]) ).
fof(f12190,plain,
spl53_762,
inference(avatar_split_clause,[],[f4884,f12188]) ).
fof(f12188,plain,
( spl53_762
<=> ! [X2,X0,X1] :
( sP3(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,[spl53_762])]) ).
fof(f4884,plain,
! [X2,X0,X1] :
( sP3(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,[],[f3697]) ).
fof(f12186,plain,
spl53_761,
inference(avatar_split_clause,[],[f4883,f12184]) ).
fof(f12184,plain,
( spl53_761
<=> ! [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)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_761])]) ).
fof(f4883,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)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f3697]) ).
fof(f12182,plain,
( spl53_760
| ~ spl53_133
| ~ spl53_408 ),
inference(avatar_split_clause,[],[f8293,f8090,f6831,f12180]) ).
fof(f12180,plain,
( spl53_760
<=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_760])]) ).
fof(f8090,plain,
( spl53_408
<=> ! [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,[spl53_408])]) ).
fof(f8293,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = X0
| ~ spl53_133
| ~ spl53_408 ),
inference(resolution,[],[f8091,f6833]) ).
fof(f8091,plain,
( ! [X0,X1] :
( ~ class_Groups_Omonoid__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 )
| ~ spl53_408 ),
inference(avatar_component_clause,[],[f8090]) ).
fof(f12178,plain,
spl53_759,
inference(avatar_split_clause,[],[f4882,f12176]) ).
fof(f12176,plain,
( spl53_759
<=> ! [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)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_759])]) ).
fof(f4882,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)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f3697]) ).
fof(f12174,plain,
spl53_758,
inference(avatar_split_clause,[],[f4881,f12172]) ).
fof(f12172,plain,
( spl53_758
<=> ! [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)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_758])]) ).
fof(f4881,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)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f3697]) ).
fof(f12170,plain,
spl53_757,
inference(avatar_split_clause,[],[f4880,f12168]) ).
fof(f12168,plain,
( spl53_757
<=> ! [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)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_757])]) ).
fof(f4880,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)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f3697]) ).
fof(f12166,plain,
spl53_756,
inference(avatar_split_clause,[],[f4846,f12164]) ).
fof(f12164,plain,
( spl53_756
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Lattices_Oboolean__algebra(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_756])]) ).
fof(f4846,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(cnf_transformation,[],[f3691]) ).
fof(f3691,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X0,X1) )
& ( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0)) ) )
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(nnf_transformation,[],[f2715]) ).
fof(f2715,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(X2,X0,X1) )
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(ennf_transformation,[],[f1795]) ).
fof(f1795,plain,
! [X0,X1,X2] :
( class_Lattices_Oboolean__algebra(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Orderings_Oord__class_Oless__eq(X2,X0,X1) ) ),
inference(rectify,[],[f881]) ).
fof(f881,axiom,
! [X40,X15,X5] :
( class_Lattices_Oboolean__algebra(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X15),c_Groups_Ouminus__class_Ouminus(X5,X40))
<=> c_Orderings_Oord__class_Oless__eq(X5,X40,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__le__compl__iff) ).
fof(f12162,plain,
spl53_755,
inference(avatar_split_clause,[],[f4842,f12160]) ).
fof(f12160,plain,
( spl53_755
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Lattices_Oboolean__algebra(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_755])]) ).
fof(f4842,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(cnf_transformation,[],[f2711]) ).
fof(f2711,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(flattening,[],[f2710]) ).
fof(f2710,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(ennf_transformation,[],[f1792]) ).
fof(f1792,plain,
! [X0,X1,X2] :
( class_Lattices_Oboolean__algebra(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ouminus__class_Ouminus(X2,X0),c_Groups_Ouminus__class_Ouminus(X2,X1)) ) ),
inference(rectify,[],[f880]) ).
fof(f880,axiom,
! [X21,X7,X5] :
( class_Lattices_Oboolean__algebra(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X7,X21)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X21),c_Groups_Ouminus__class_Ouminus(X5,X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__mono) ).
fof(f12158,plain,
spl53_754,
inference(avatar_split_clause,[],[f4754,f12156]) ).
fof(f12156,plain,
( spl53_754
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_754])]) ).
fof(f4754,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ),
inference(cnf_transformation,[],[f3659]) ).
fof(f3659,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(nnf_transformation,[],[f1734]) ).
fof(f1734,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ),
inference(rectify,[],[f952]) ).
fof(f952,axiom,
! [X40,X15] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X15,X40),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X40,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__less__0__iff) ).
fof(f12154,plain,
spl53_753,
inference(avatar_split_clause,[],[f4753,f12152]) ).
fof(f12152,plain,
( spl53_753
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_753])]) ).
fof(f4753,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(cnf_transformation,[],[f3659]) ).
fof(f12150,plain,
spl53_752,
inference(avatar_split_clause,[],[f4752,f12148]) ).
fof(f12148,plain,
( spl53_752
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_752])]) ).
fof(f4752,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0) ),
inference(cnf_transformation,[],[f3658]) ).
fof(f3658,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),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,X1,X0)) ) ),
inference(nnf_transformation,[],[f1733]) ).
fof(f1733,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0) ),
inference(rectify,[],[f953]) ).
fof(f953,axiom,
! [X40,X15] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X15,X40))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X15),X40) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__0__less__add__iff) ).
fof(f12146,plain,
spl53_751,
inference(avatar_split_clause,[],[f4751,f12144]) ).
fof(f12144,plain,
( spl53_751
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),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,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_751])]) ).
fof(f4751,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),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,X1,X0)) ),
inference(cnf_transformation,[],[f3658]) ).
fof(f12142,plain,
spl53_750,
inference(avatar_split_clause,[],[f4744,f12140]) ).
fof(f12140,plain,
( spl53_750
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_750])]) ).
fof(f4744,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ),
inference(cnf_transformation,[],[f3654]) ).
fof(f3654,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(nnf_transformation,[],[f1729]) ).
fof(f1729,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ),
inference(rectify,[],[f950]) ).
fof(f950,axiom,
! [X40,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X15,X40),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X40,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__le__0__iff) ).
fof(f12138,plain,
( spl53_749
| ~ spl53_132
| ~ spl53_408 ),
inference(avatar_split_clause,[],[f8290,f8090,f6826,f12136]) ).
fof(f12136,plain,
( spl53_749
<=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_749])]) ).
fof(f8290,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X0
| ~ spl53_132
| ~ spl53_408 ),
inference(resolution,[],[f8091,f6828]) ).
fof(f12134,plain,
spl53_748,
inference(avatar_split_clause,[],[f4743,f12132]) ).
fof(f12132,plain,
( spl53_748
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_748])]) ).
fof(f4743,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(cnf_transformation,[],[f3654]) ).
fof(f12130,plain,
spl53_747,
inference(avatar_split_clause,[],[f4742,f12128]) ).
fof(f12128,plain,
( spl53_747
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_747])]) ).
fof(f4742,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0) ),
inference(cnf_transformation,[],[f3653]) ).
fof(f3653,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)) ) ),
inference(nnf_transformation,[],[f1728]) ).
fof(f1728,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0) ),
inference(rectify,[],[f951]) ).
fof(f951,axiom,
! [X40,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X15,X40))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X15),X40) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__0__le__add__iff) ).
fof(f12126,plain,
spl53_746,
inference(avatar_split_clause,[],[f4741,f12124]) ).
fof(f12124,plain,
( spl53_746
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_746])]) ).
fof(f4741,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)) ),
inference(cnf_transformation,[],[f3653]) ).
fof(f12122,plain,
spl53_745,
inference(avatar_split_clause,[],[f4654,f12120]) ).
fof(f12120,plain,
( spl53_745
<=> ! [X0,X1] :
( X0 = X1
| hAPP(X1,sK31(X0,X1)) != hAPP(X0,sK31(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_745])]) ).
fof(f4654,plain,
! [X0,X1] :
( X0 = X1
| hAPP(X1,sK31(X0,X1)) != hAPP(X0,sK31(X0,X1)) ),
inference(cnf_transformation,[],[f3595]) ).
fof(f3595,plain,
! [X0,X1] :
( X0 = X1
| hAPP(X1,sK31(X0,X1)) != hAPP(X0,sK31(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f2684,f3594]) ).
fof(f3594,plain,
! [X0,X1] :
( ? [X2] : hAPP(X1,X2) != hAPP(X0,X2)
=> hAPP(X1,sK31(X0,X1)) != hAPP(X0,sK31(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f2684,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',fact_ext) ).
fof(f12118,plain,
spl53_744,
inference(avatar_split_clause,[],[f4495,f12116]) ).
fof(f12116,plain,
( spl53_744
<=> ! [X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0)
| ~ class_Groups_Oab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_744])]) ).
fof(f4495,plain,
! [X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0)
| ~ class_Groups_Oab__group__add(X1) ),
inference(cnf_transformation,[],[f2510]) ).
fof(f2510,plain,
! [X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0)
| ~ class_Groups_Oab__group__add(X1) ),
inference(ennf_transformation,[],[f1564]) ).
fof(f1564,plain,
! [X0,X1] :
( class_Groups_Oab__group__add(X1)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X0) ),
inference(rectify,[],[f870]) ).
fof(f870,axiom,
! [X6,X5] :
( class_Groups_Oab__group__add(X5)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X6) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__poly__code_I1_J) ).
fof(f12114,plain,
spl53_743,
inference(avatar_split_clause,[],[f4477,f12112]) ).
fof(f12112,plain,
( spl53_743
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_743])]) ).
fof(f4477,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3568]) ).
fof(f3568,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
& ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1)) ) )
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f2495]) ).
fof(f2495,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f1550]) ).
fof(f1550,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
inference(rectify,[],[f920]) ).
fof(f920,axiom,
! [X9,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ouminus__class_Ouminus(X5,X9),c_Groups_Ozero__class_Ozero(X5))
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).
fof(f12110,plain,
spl53_742,
inference(avatar_split_clause,[],[f4476,f12108]) ).
fof(f12108,plain,
( spl53_742
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_742])]) ).
fof(f4476,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3568]) ).
fof(f12106,plain,
spl53_741,
inference(avatar_split_clause,[],[f4475,f12104]) ).
fof(f12104,plain,
( spl53_741
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_741])]) ).
fof(f4475,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3567]) ).
fof(f3567,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
& ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0)) ) )
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f2494]) ).
fof(f2494,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
<=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f1549]) ).
fof(f1549,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
<=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
inference(rectify,[],[f922]) ).
fof(f922,axiom,
! [X9,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Ouminus__class_Ouminus(X5,X9))
<=> c_Orderings_Oord__class_Oless(X5,X9,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).
fof(f12102,plain,
spl53_740,
inference(avatar_split_clause,[],[f4474,f12100]) ).
fof(f12100,plain,
( spl53_740
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_Groups_Oordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_740])]) ).
fof(f4474,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3567]) ).
fof(f12098,plain,
spl53_739,
inference(avatar_split_clause,[],[f4473,f12096]) ).
fof(f12096,plain,
( spl53_739
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_739])]) ).
fof(f4473,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3566]) ).
fof(f3566,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
& ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1)) ) )
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f2493]) ).
fof(f2493,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f1548]) ).
fof(f1548,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
inference(rectify,[],[f924]) ).
fof(f924,axiom,
! [X9,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X9),c_Groups_Ozero__class_Ozero(X5))
<=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).
fof(f12094,plain,
( spl53_738
| ~ spl53_103
| ~ spl53_407 ),
inference(avatar_split_clause,[],[f8288,f8086,f6681,f12092]) ).
fof(f12092,plain,
( spl53_738
<=> ! [X0] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_738])]) ).
fof(f6681,plain,
( spl53_103
<=> class_Groups_Ogroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_103])]) ).
fof(f8086,plain,
( spl53_407
<=> ! [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,[spl53_407])]) ).
fof(f8288,plain,
( ! [X0] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = X0
| ~ spl53_103
| ~ spl53_407 ),
inference(resolution,[],[f8087,f6683]) ).
fof(f6683,plain,
( class_Groups_Ogroup__add(tc_RealDef_Oreal)
| ~ spl53_103 ),
inference(avatar_component_clause,[],[f6681]) ).
fof(f8087,plain,
( ! [X0,X1] :
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 )
| ~ spl53_407 ),
inference(avatar_component_clause,[],[f8086]) ).
fof(f12090,plain,
spl53_737,
inference(avatar_split_clause,[],[f4472,f12088]) ).
fof(f12088,plain,
( spl53_737
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_737])]) ).
fof(f4472,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3566]) ).
fof(f12086,plain,
spl53_736,
inference(avatar_split_clause,[],[f4471,f12084]) ).
fof(f12084,plain,
( spl53_736
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_736])]) ).
fof(f4471,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3565]) ).
fof(f3565,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
& ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0)) ) )
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f2492]) ).
fof(f2492,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
<=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f1547]) ).
fof(f1547,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
<=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
inference(rectify,[],[f926]) ).
fof(f926,axiom,
! [X9,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Ouminus__class_Ouminus(X5,X9))
<=> c_Orderings_Oord__class_Oless__eq(X5,X9,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).
fof(f12082,plain,
spl53_735,
inference(avatar_split_clause,[],[f4470,f12080]) ).
fof(f12080,plain,
( spl53_735
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_Groups_Oordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_735])]) ).
fof(f4470,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3565]) ).
fof(f12078,plain,
spl53_734,
inference(avatar_split_clause,[],[f4408,f12076]) ).
fof(f12076,plain,
( spl53_734
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Fields_Olinordered__field(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_734])]) ).
fof(f4408,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Fields_Olinordered__field(X1) ),
inference(cnf_transformation,[],[f2436]) ).
fof(f2436,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Fields_Olinordered__field(X1) ),
inference(flattening,[],[f2435]) ).
fof(f2435,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Fields_Olinordered__field(X1) ),
inference(ennf_transformation,[],[f1503]) ).
fof(f1503,plain,
! [X0,X1] :
( class_Fields_Olinordered__field(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_Rings_Oinverse__class_Oinverse(X1,X0)) ) ),
inference(rectify,[],[f834]) ).
fof(f834,axiom,
! [X4,X5] :
( class_Fields_Olinordered__field(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Rings_Oinverse__class_Oinverse(X5,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_positive__imp__inverse__positive) ).
fof(f12074,plain,
spl53_733,
inference(avatar_split_clause,[],[f4407,f12072]) ).
fof(f12072,plain,
( spl53_733
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_733])]) ).
fof(f4407,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(cnf_transformation,[],[f2434]) ).
fof(f2434,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(flattening,[],[f2433]) ).
fof(f2433,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(ennf_transformation,[],[f1502]) ).
fof(f1502,plain,
! [X0,X1] :
( class_Fields_Olinordered__field(X1)
=> ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
=> c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1)) ) ),
inference(rectify,[],[f832]) ).
fof(f832,axiom,
! [X4,X5] :
( class_Fields_Olinordered__field(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X4,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,c_Rings_Oinverse__class_Oinverse(X5,X4),c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__imp__inverse__negative) ).
fof(f12070,plain,
spl53_732,
inference(avatar_split_clause,[],[f4406,f12068]) ).
fof(f12068,plain,
( spl53_732
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_732])]) ).
fof(f4406,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(cnf_transformation,[],[f3544]) ).
fof(f3544,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
& ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(nnf_transformation,[],[f2432]) ).
fof(f2432,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(ennf_transformation,[],[f1501]) ).
fof(f1501,plain,
! [X0,X1] :
( class_Fields_Olinordered__field__inverse__zero(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
inference(rectify,[],[f835]) ).
fof(f835,axiom,
! [X9,X5] :
( class_Fields_Olinordered__field__inverse__zero(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Rings_Oinverse__class_Oinverse(X5,X9),c_Groups_Ozero__class_Ozero(X5))
<=> c_Orderings_Oord__class_Oless(X5,X9,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__negative__iff__negative) ).
fof(f12066,plain,
spl53_731,
inference(avatar_split_clause,[],[f4405,f12064]) ).
fof(f12064,plain,
( spl53_731
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_731])]) ).
fof(f4405,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(cnf_transformation,[],[f3544]) ).
fof(f12062,plain,
spl53_730,
inference(avatar_split_clause,[],[f4404,f12060]) ).
fof(f12060,plain,
( spl53_730
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_730])]) ).
fof(f4404,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(cnf_transformation,[],[f3543]) ).
fof(f3543,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
| ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X0)
& ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) )
& ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X0)
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(flattening,[],[f3542]) ).
fof(f3542,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
| ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X0)
& ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) )
& ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X0)
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(nnf_transformation,[],[f2431]) ).
fof(f2431,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
<=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X0)
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(ennf_transformation,[],[f1500]) ).
fof(f1500,plain,
! [X0,X1] :
( class_Fields_Olinordered__field__inverse__zero(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
<=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X0)
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ) ),
inference(rectify,[],[f847]) ).
fof(f847,axiom,
! [X15,X5] :
( class_Fields_Olinordered__field__inverse__zero(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Rings_Oinverse__class_Oinverse(X5,X15),c_Groups_Oone__class_Oone(X5))
<=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X15)
| c_Orderings_Oord__class_Oless__eq(X5,X15,c_Groups_Ozero__class_Ozero(X5)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__less__1__iff) ).
fof(f12058,plain,
spl53_729,
inference(avatar_split_clause,[],[f4403,f12056]) ).
fof(f12056,plain,
( spl53_729
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_729])]) ).
fof(f4403,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(cnf_transformation,[],[f3543]) ).
fof(f12054,plain,
spl53_728,
inference(avatar_split_clause,[],[f4401,f12052]) ).
fof(f12052,plain,
( spl53_728
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_728])]) ).
fof(f4401,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(cnf_transformation,[],[f3541]) ).
fof(f3541,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(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),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(nnf_transformation,[],[f2430]) ).
fof(f2430,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(ennf_transformation,[],[f1499]) ).
fof(f1499,plain,
! [X0,X1] :
( class_Fields_Olinordered__field__inverse__zero(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
inference(rectify,[],[f836]) ).
fof(f836,axiom,
! [X9,X5] :
( class_Fields_Olinordered__field__inverse__zero(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Rings_Oinverse__class_Oinverse(X5,X9))
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__positive__iff__positive) ).
fof(f12050,plain,
( spl53_727
| ~ spl53_104
| ~ spl53_407 ),
inference(avatar_split_clause,[],[f8286,f8086,f6686,f12048]) ).
fof(f12048,plain,
( spl53_727
<=> ! [X0] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_727])]) ).
fof(f6686,plain,
( spl53_104
<=> class_Groups_Ogroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_104])]) ).
fof(f8286,plain,
( ! [X0] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0
| ~ spl53_104
| ~ spl53_407 ),
inference(resolution,[],[f8087,f6688]) ).
fof(f6688,plain,
( class_Groups_Ogroup__add(tc_Int_Oint)
| ~ spl53_104 ),
inference(avatar_component_clause,[],[f6686]) ).
fof(f12046,plain,
spl53_726,
inference(avatar_split_clause,[],[f4400,f12044]) ).
fof(f12044,plain,
( spl53_726
<=> ! [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_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_726])]) ).
fof(f4400,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_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(cnf_transformation,[],[f3541]) ).
fof(f12042,plain,
spl53_725,
inference(avatar_split_clause,[],[f4398,f12040]) ).
fof(f12040,plain,
( spl53_725
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_725])]) ).
fof(f4398,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(cnf_transformation,[],[f3540]) ).
fof(f3540,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
& ( ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oone__class_Oone(X1))
& c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(flattening,[],[f3539]) ).
fof(f3539,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
& ( ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oone__class_Oone(X1))
& c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(nnf_transformation,[],[f2429]) ).
fof(f2429,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
<=> ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oone__class_Oone(X1))
& c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(ennf_transformation,[],[f1498]) ).
fof(f1498,plain,
! [X0,X1] :
( class_Fields_Olinordered__field__inverse__zero(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
<=> ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Oone__class_Oone(X1))
& c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ) ),
inference(rectify,[],[f843]) ).
fof(f843,axiom,
! [X15,X5] :
( class_Fields_Olinordered__field__inverse__zero(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),c_Rings_Oinverse__class_Oinverse(X5,X15))
<=> ( c_Orderings_Oord__class_Oless(X5,X15,c_Groups_Oone__class_Oone(X5))
& c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X15) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__inverse__iff) ).
fof(f12038,plain,
spl53_724,
inference(avatar_split_clause,[],[f4397,f12036]) ).
fof(f12036,plain,
( spl53_724
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_724])]) ).
fof(f4397,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(cnf_transformation,[],[f3540]) ).
fof(f12034,plain,
spl53_723,
inference(avatar_split_clause,[],[f4396,f12032]) ).
fof(f12032,plain,
( spl53_723
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_723])]) ).
fof(f4396,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(cnf_transformation,[],[f3538]) ).
fof(f3538,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
& ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(nnf_transformation,[],[f2428]) ).
fof(f2428,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(ennf_transformation,[],[f1497]) ).
fof(f1497,plain,
! [X0,X1] :
( class_Fields_Olinordered__field__inverse__zero(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
inference(rectify,[],[f826]) ).
fof(f826,axiom,
! [X9,X5] :
( class_Fields_Olinordered__field__inverse__zero(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Rings_Oinverse__class_Oinverse(X5,X9),c_Groups_Ozero__class_Ozero(X5))
<=> c_Orderings_Oord__class_Oless__eq(X5,X9,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__nonpositive__iff__nonpositive) ).
fof(f12030,plain,
spl53_722,
inference(avatar_split_clause,[],[f4395,f12028]) ).
fof(f12028,plain,
( spl53_722
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_722])]) ).
fof(f4395,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_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(cnf_transformation,[],[f3538]) ).
fof(f12026,plain,
spl53_721,
inference(avatar_split_clause,[],[f4394,f12024]) ).
fof(f12024,plain,
( spl53_721
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_721])]) ).
fof(f4394,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(cnf_transformation,[],[f3537]) ).
fof(f3537,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
| ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X0)
& ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) )
& ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X0)
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(flattening,[],[f3536]) ).
fof(f3536,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
| ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X0)
& ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) )
& ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X0)
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(nnf_transformation,[],[f2427]) ).
fof(f2427,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
<=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X0)
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(ennf_transformation,[],[f1496]) ).
fof(f1496,plain,
! [X0,X1] :
( class_Fields_Olinordered__field__inverse__zero(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
<=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X0)
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ) ),
inference(rectify,[],[f841]) ).
fof(f841,axiom,
! [X15,X5] :
( class_Fields_Olinordered__field__inverse__zero(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Rings_Oinverse__class_Oinverse(X5,X15),c_Groups_Oone__class_Oone(X5))
<=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5),X15)
| c_Orderings_Oord__class_Oless__eq(X5,X15,c_Groups_Ozero__class_Ozero(X5)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__le__1__iff) ).
fof(f12022,plain,
spl53_720,
inference(avatar_split_clause,[],[f4393,f12020]) ).
fof(f12020,plain,
( spl53_720
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_720])]) ).
fof(f4393,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X0),c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(cnf_transformation,[],[f3537]) ).
fof(f12018,plain,
spl53_719,
inference(avatar_split_clause,[],[f4391,f12016]) ).
fof(f12016,plain,
( spl53_719
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_719])]) ).
fof(f4391,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(cnf_transformation,[],[f3535]) ).
fof(f3535,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(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),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(nnf_transformation,[],[f2426]) ).
fof(f2426,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(ennf_transformation,[],[f1495]) ).
fof(f1495,plain,
! [X0,X1] :
( class_Fields_Olinordered__field__inverse__zero(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
inference(rectify,[],[f825]) ).
fof(f825,axiom,
! [X9,X5] :
( class_Fields_Olinordered__field__inverse__zero(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),c_Rings_Oinverse__class_Oinverse(X5,X9))
<=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__nonnegative__iff__nonnegative) ).
fof(f12014,plain,
spl53_718,
inference(avatar_split_clause,[],[f4390,f12012]) ).
fof(f12012,plain,
( spl53_718
<=> ! [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_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_718])]) ).
fof(f4390,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_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(cnf_transformation,[],[f3535]) ).
fof(f12010,plain,
spl53_717,
inference(avatar_split_clause,[],[f4388,f12008]) ).
fof(f12008,plain,
( spl53_717
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_717])]) ).
fof(f4388,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(cnf_transformation,[],[f3534]) ).
fof(f3534,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
& ( ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
& c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(flattening,[],[f3533]) ).
fof(f3533,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
& ( ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
& c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(nnf_transformation,[],[f2425]) ).
fof(f2425,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
<=> ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
& c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(ennf_transformation,[],[f1494]) ).
fof(f1494,plain,
! [X0,X1] :
( class_Fields_Olinordered__field__inverse__zero(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
<=> ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oone__class_Oone(X1))
& c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ) ),
inference(rectify,[],[f821]) ).
fof(f821,axiom,
! [X15,X5] :
( class_Fields_Olinordered__field__inverse__zero(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5),c_Rings_Oinverse__class_Oinverse(X5,X15))
<=> ( c_Orderings_Oord__class_Oless__eq(X5,X15,c_Groups_Oone__class_Oone(X5))
& c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X15) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__inverse__iff) ).
fof(f12006,plain,
( spl53_716
| ~ spl53_102
| ~ spl53_407 ),
inference(avatar_split_clause,[],[f8285,f8086,f6676,f12004]) ).
fof(f12004,plain,
( spl53_716
<=> ! [X0] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_716])]) ).
fof(f8285,plain,
( ! [X0] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X0
| ~ spl53_102
| ~ spl53_407 ),
inference(resolution,[],[f8087,f6678]) ).
fof(f6678,plain,
( class_Groups_Ogroup__add(tc_Complex_Ocomplex)
| ~ spl53_102 ),
inference(avatar_component_clause,[],[f6676]) ).
fof(f12002,plain,
spl53_715,
inference(avatar_split_clause,[],[f4387,f12000]) ).
fof(f12000,plain,
( spl53_715
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_715])]) ).
fof(f4387,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(cnf_transformation,[],[f3534]) ).
fof(f11998,plain,
spl53_714,
inference(avatar_split_clause,[],[f4330,f11996]) ).
fof(f11996,plain,
( spl53_714
<=> ! [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,[spl53_714])]) ).
fof(f4330,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,[],[f3530]) ).
fof(f3530,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,[],[f1442]) ).
fof(f1442,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,[],[f750]) ).
fof(f750,axiom,
! [X15] :
( ~ 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),X15),X15))
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).
fof(f11994,plain,
spl53_713,
inference(avatar_split_clause,[],[f4223,f11992]) ).
fof(f11992,plain,
( spl53_713
<=> ! [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,[spl53_713])]) ).
fof(f4223,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,[],[f1341]) ).
fof(f1341,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,[],[f352]) ).
fof(f352,axiom,
! [X10] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10),X10))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__cube) ).
fof(f11990,plain,
spl53_712,
inference(avatar_split_clause,[],[f4171,f11988]) ).
fof(f11988,plain,
( spl53_712
<=> ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK21),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_712])]) ).
fof(f4171,plain,
! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK21),X1),
inference(cnf_transformation,[],[f3515]) ).
fof(f11951,plain,
( spl53_711
| ~ spl53_103
| ~ spl53_406 ),
inference(avatar_split_clause,[],[f8284,f8082,f6681,f11949]) ).
fof(f11949,plain,
( spl53_711
<=> ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_711])]) ).
fof(f8082,plain,
( spl53_406
<=> ! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0
| ~ class_Groups_Ogroup__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_406])]) ).
fof(f8284,plain,
( ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)) = X0
| ~ spl53_103
| ~ spl53_406 ),
inference(resolution,[],[f8083,f6683]) ).
fof(f8083,plain,
( ! [X0,X1] :
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0 )
| ~ spl53_406 ),
inference(avatar_component_clause,[],[f8082]) ).
fof(f11707,plain,
( spl53_710
| ~ spl53_102
| ~ spl53_406 ),
inference(avatar_split_clause,[],[f8281,f8082,f6676,f11705]) ).
fof(f11705,plain,
( spl53_710
<=> ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_710])]) ).
fof(f8281,plain,
( ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) = X0
| ~ spl53_102
| ~ spl53_406 ),
inference(resolution,[],[f8083,f6678]) ).
fof(f11498,plain,
( spl53_709
| ~ spl53_103
| ~ spl53_405 ),
inference(avatar_split_clause,[],[f8280,f8078,f6681,f11496]) ).
fof(f11496,plain,
( spl53_709
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_709])]) ).
fof(f8078,plain,
( spl53_405
<=> ! [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,[spl53_405])]) ).
fof(f8280,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X0)
| ~ spl53_103
| ~ spl53_405 ),
inference(resolution,[],[f8079,f6683]) ).
fof(f8079,plain,
( ! [X0,X1] :
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ominus__class_Ominus(X1,X0,X0) )
| ~ spl53_405 ),
inference(avatar_component_clause,[],[f8078]) ).
fof(f11334,plain,
( spl53_708
| ~ spl53_104
| ~ spl53_405 ),
inference(avatar_split_clause,[],[f8278,f8078,f6686,f11332]) ).
fof(f11332,plain,
( spl53_708
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_708])]) ).
fof(f8278,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X0)
| ~ spl53_104
| ~ spl53_405 ),
inference(resolution,[],[f8079,f6688]) ).
fof(f11172,plain,
( spl53_707
| ~ spl53_102
| ~ spl53_405 ),
inference(avatar_split_clause,[],[f8277,f8078,f6676,f11170]) ).
fof(f11170,plain,
( spl53_707
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_707])]) ).
fof(f8277,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X0)
| ~ spl53_102
| ~ spl53_405 ),
inference(resolution,[],[f8079,f6678]) ).
fof(f11162,plain,
spl53_706,
inference(avatar_split_clause,[],[f5919,f11160]) ).
fof(f11160,plain,
( spl53_706
<=> ! [X2,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_706])]) ).
fof(f5919,plain,
! [X2,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(equality_resolution,[],[f5255]) ).
fof(f5255,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
| ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f3817]) ).
fof(f11157,plain,
spl53_705,
inference(avatar_split_clause,[],[f5918,f11155]) ).
fof(f11155,plain,
( spl53_705
<=> ! [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,[spl53_705])]) ).
fof(f5918,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,[],[f5245]) ).
fof(f5245,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,[],[f3811]) ).
fof(f11153,plain,
spl53_704,
inference(avatar_split_clause,[],[f5788,f11151]) ).
fof(f11151,plain,
( spl53_704
<=> ! [X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_704])]) ).
fof(f5788,plain,
! [X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(equality_resolution,[],[f4488]) ).
fof(f4488,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = c_Groups_Oone__class_Oone(X1)
| c_Groups_Oone__class_Oone(X1) != X0
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(cnf_transformation,[],[f3572]) ).
fof(f3572,plain,
! [X0,X1] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = c_Groups_Oone__class_Oone(X1)
| ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) != X0
& c_Groups_Oone__class_Oone(X1) != X0 ) )
& ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) = X0
| c_Groups_Oone__class_Oone(X1) = X0
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) != c_Groups_Oone__class_Oone(X1) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(flattening,[],[f3571]) ).
fof(f3571,plain,
! [X0,X1] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = c_Groups_Oone__class_Oone(X1)
| ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) != X0
& c_Groups_Oone__class_Oone(X1) != X0 ) )
& ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) = X0
| c_Groups_Oone__class_Oone(X1) = X0
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) != c_Groups_Oone__class_Oone(X1) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(nnf_transformation,[],[f2504]) ).
fof(f2504,plain,
! [X0,X1] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = c_Groups_Oone__class_Oone(X1)
<=> ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) = X0
| c_Groups_Oone__class_Oone(X1) = X0 ) )
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(ennf_transformation,[],[f1558]) ).
fof(f1558,plain,
! [X0,X1] :
( class_Rings_Oring__1__no__zero__divisors(X1)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = c_Groups_Oone__class_Oone(X1)
<=> ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)) = X0
| c_Groups_Oone__class_Oone(X1) = X0 ) ) ),
inference(rectify,[],[f877]) ).
fof(f877,axiom,
! [X15,X5] :
( class_Rings_Oring__1__no__zero__divisors(X5)
=> ( c_Groups_Oone__class_Oone(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X15),X15)
<=> ( c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Oone__class_Oone(X5)) = X15
| c_Groups_Oone__class_Oone(X5) = X15 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).
fof(f11149,plain,
spl53_703,
inference(avatar_split_clause,[],[f5644,f11147]) ).
fof(f11147,plain,
( spl53_703
<=> ! [X0] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK26(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_703])]) ).
fof(f5644,plain,
! [X0] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK26(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(definition_unfolding,[],[f4326,f4205]) ).
fof(f4326,plain,
! [X0] :
( c_Nat_OSuc(sK26(X0)) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(cnf_transformation,[],[f3528]) ).
fof(f3528,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ! [X1] : c_Nat_OSuc(X1) != X0 )
& ( c_Nat_OSuc(sK26(X0)) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f3526,f3527]) ).
fof(f3527,plain,
! [X0] :
( ? [X2] : c_Nat_OSuc(X2) = X0
=> c_Nat_OSuc(sK26(X0)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f3526,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ! [X1] : c_Nat_OSuc(X1) != X0 )
& ( ? [X2] : c_Nat_OSuc(X2) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
inference(rectify,[],[f3525]) ).
fof(f3525,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ! [X1] : c_Nat_OSuc(X1) != X0 )
& ( ? [X1] : c_Nat_OSuc(X1) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
inference(nnf_transformation,[],[f1440]) ).
fof(f1440,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
<=> ? [X1] : c_Nat_OSuc(X1) = X0 ),
inference(rectify,[],[f430]) ).
fof(f430,axiom,
! [X8] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X8)
<=> ? [X60] : c_Nat_OSuc(X60) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
fof(f11145,plain,
spl53_702,
inference(avatar_split_clause,[],[f5356,f11143]) ).
fof(f11143,plain,
( spl53_702
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ sP17(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_702])]) ).
fof(f5356,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ sP17(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3867]) ).
fof(f11141,plain,
spl53_701,
inference(avatar_split_clause,[],[f5347,f11139]) ).
fof(f11139,plain,
( spl53_701
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ sP15(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_701])]) ).
fof(f5347,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ sP15(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3862]) ).
fof(f11137,plain,
spl53_700,
inference(avatar_split_clause,[],[f5265,f11135]) ).
fof(f11135,plain,
( spl53_700
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ sP14(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_700])]) ).
fof(f5265,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)
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f3828]) ).
fof(f11133,plain,
spl53_699,
inference(avatar_split_clause,[],[f5257,f11131]) ).
fof(f11131,plain,
( spl53_699
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ sP13(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_699])]) ).
fof(f5257,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ sP13(X0,X1,X2) ),
inference(cnf_transformation,[],[f3822]) ).
fof(f11129,plain,
spl53_698,
inference(avatar_split_clause,[],[f5220,f11127]) ).
fof(f11127,plain,
( spl53_698
<=> ! [X2,X0,X1] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0)
| hAPP(X0,sK36(X0)) != hAPP(X0,sK37(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_698])]) ).
fof(f5220,plain,
! [X2,X0,X1] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0)
| hAPP(X0,sK36(X0)) != hAPP(X0,sK37(X0)) ),
inference(cnf_transformation,[],[f3789]) ).
fof(f3789,plain,
! [X0,X1,X2] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0)
| hAPP(X0,sK36(X0)) != hAPP(X0,sK37(X0)) )
& ( ! [X5,X6] : hAPP(X0,X5) = hAPP(X0,X6)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK36,sK37])],[f3787,f3788]) ).
fof(f3788,plain,
! [X0] :
( ? [X3,X4] : hAPP(X0,X3) != hAPP(X0,X4)
=> hAPP(X0,sK36(X0)) != hAPP(X0,sK37(X0)) ),
introduced(choice_axiom,[]) ).
fof(f3787,plain,
! [X0,X1,X2] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0)
| ? [X3,X4] : hAPP(X0,X3) != hAPP(X0,X4) )
& ( ! [X5,X6] : hAPP(X0,X5) = hAPP(X0,X6)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0) ) ),
inference(rectify,[],[f3786]) ).
fof(f3786,plain,
! [X0,X1,X2] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0)
| ? [X3,X4] : hAPP(X0,X3) != hAPP(X0,X4) )
& ( ! [X3,X4] : hAPP(X0,X3) = hAPP(X0,X4)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f2059]) ).
fof(f2059,plain,
! [X0,X1,X2] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0)
<=> ! [X3,X4] : hAPP(X0,X3) = hAPP(X0,X4) ),
inference(rectify,[],[f700]) ).
fof(f700,axiom,
! [X1,X39,X5] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X5,X39,X1)
<=> ! [X2,X80] : hAPP(X1,X2) = hAPP(X1,X80) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_constant__def) ).
fof(f11119,plain,
spl53_697,
inference(avatar_split_clause,[],[f5096,f11117]) ).
fof(f11117,plain,
( spl53_697
<=> ! [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,[spl53_697])]) ).
fof(f5096,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,[],[f2976]) ).
fof(f2976,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,[],[f2975]) ).
fof(f2975,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,[],[f1973]) ).
fof(f1973,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,[],[f493]) ).
fof(f493,axiom,
! [X21,X7,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X7,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X21,X7)
=> X7 = X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).
fof(f11115,plain,
spl53_696,
inference(avatar_split_clause,[],[f5091,f11113]) ).
fof(f11113,plain,
( spl53_696
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| X0 = X1
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_696])]) ).
fof(f5091,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| X0 = X1
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f2966]) ).
fof(f2966,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| X0 = X1
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f2965]) ).
fof(f2965,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| X0 = X1
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f1968]) ).
fof(f1968,plain,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( X0 != X1
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
=> c_Orderings_Oord__class_Oless(X2,X1,X0) ) ) ),
inference(rectify,[],[f540]) ).
fof(f540,axiom,
! [X20,X4,X5] :
( class_Orderings_Oorder(X5)
=> ( X4 != X20
=> ( c_Orderings_Oord__class_Oless__eq(X5,X4,X20)
=> c_Orderings_Oord__class_Oless(X5,X4,X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
fof(f11111,plain,
spl53_695,
inference(avatar_split_clause,[],[f5031,f11109]) ).
fof(f11109,plain,
( spl53_695
<=> ! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = X0
| ~ class_Groups_Ogroup__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_695])]) ).
fof(f5031,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = X0
| ~ class_Groups_Ogroup__add(X2) ),
inference(cnf_transformation,[],[f2897]) ).
fof(f2897,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = X0
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f1921]) ).
fof(f1921,plain,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),c_Groups_Oplus__class_Oplus(X2,X1,X0)) = X0 ),
inference(rectify,[],[f931]) ).
fof(f931,axiom,
! [X20,X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),c_Groups_Oplus__class_Oplus(X5,X4,X20)) = X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add__cancel) ).
fof(f11107,plain,
spl53_694,
inference(avatar_split_clause,[],[f5030,f11105]) ).
fof(f11105,plain,
( spl53_694
<=> ! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)) = X0
| ~ class_Groups_Ogroup__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_694])]) ).
fof(f5030,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)) = X0
| ~ class_Groups_Ogroup__add(X2) ),
inference(cnf_transformation,[],[f2896]) ).
fof(f2896,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)) = X0
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f1920]) ).
fof(f1920,plain,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oplus__class_Oplus(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)) = X0 ),
inference(rectify,[],[f930]) ).
fof(f930,axiom,
! [X20,X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Oplus__class_Oplus(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),X20)) = X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__minus__cancel) ).
fof(f11103,plain,
spl53_693,
inference(avatar_split_clause,[],[f5029,f11101]) ).
fof(f11101,plain,
( spl53_693
<=> ! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ominus__class_Ominus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Ogroup__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_693])]) ).
fof(f5029,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ominus__class_Ominus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Ogroup__add(X2) ),
inference(cnf_transformation,[],[f2895]) ).
fof(f2895,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ominus__class_Ominus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f1919]) ).
fof(f1919,plain,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Ominus__class_Ominus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(rectify,[],[f863]) ).
fof(f863,axiom,
! [X20,X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,X4,X20) = c_Groups_Ominus__class_Ominus(X5,X4,c_Groups_Ouminus__class_Ouminus(X5,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).
fof(f11099,plain,
spl53_692,
inference(avatar_split_clause,[],[f5028,f11097]) ).
fof(f11097,plain,
( spl53_692
<=> ! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Ogroup__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_692])]) ).
fof(f5028,plain,
! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Ogroup__add(X2) ),
inference(cnf_transformation,[],[f2894]) ).
fof(f2894,plain,
! [X0,X1,X2] :
( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f1918]) ).
fof(f1918,plain,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(rectify,[],[f865]) ).
fof(f865,axiom,
! [X20,X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ominus__class_Ominus(X5,X4,X20) = c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Ouminus__class_Ouminus(X5,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__def) ).
fof(f11095,plain,
spl53_691,
inference(avatar_split_clause,[],[f5009,f11093]) ).
fof(f11093,plain,
( spl53_691
<=> ! [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,[spl53_691])]) ).
fof(f5009,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,[],[f3732]) ).
fof(f3732,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,[],[f2882]) ).
fof(f2882,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,[],[f2881]) ).
fof(f2881,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,[],[f1908]) ).
fof(f1908,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,[],[f541]) ).
fof(f541,axiom,
! [X40,X15,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X15,X40)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X15,X40)
<=> X15 = X40 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(f11091,plain,
spl53_690,
inference(avatar_split_clause,[],[f5001,f11089]) ).
fof(f11089,plain,
( spl53_690
<=> ! [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,[spl53_690])]) ).
fof(f5001,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,[],[f2868]) ).
fof(f2868,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,[],[f2867]) ).
fof(f2867,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,[],[f1901]) ).
fof(f1901,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,[],[f521]) ).
fof(f521,axiom,
! [X21,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X21,X7)
| X7 = X21
| c_Orderings_Oord__class_Oless(X5,X7,X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
fof(f11087,plain,
spl53_689,
inference(avatar_split_clause,[],[f4995,f11085]) ).
fof(f11085,plain,
( spl53_689
<=> ! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Oab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_689])]) ).
fof(f4995,plain,
! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Oab__group__add(X2) ),
inference(cnf_transformation,[],[f2859]) ).
fof(f2859,plain,
! [X0,X1,X2] :
( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Groups_Oab__group__add(X2) ),
inference(ennf_transformation,[],[f1895]) ).
fof(f1895,plain,
! [X0,X1,X2] :
( class_Groups_Oab__group__add(X2)
=> c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(rectify,[],[f864]) ).
fof(f864,axiom,
! [X20,X4,X5] :
( class_Groups_Oab__group__add(X5)
=> c_Groups_Ominus__class_Ominus(X5,X4,X20) = c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Ouminus__class_Ouminus(X5,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__diff__minus) ).
fof(f11083,plain,
spl53_688,
inference(avatar_split_clause,[],[f4994,f11081]) ).
fof(f11081,plain,
( spl53_688
<=> ! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(X2,X0,X1) = c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0))
| ~ class_Groups_Oab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_688])]) ).
fof(f4994,plain,
! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(X2,X0,X1) = c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0))
| ~ class_Groups_Oab__group__add(X2) ),
inference(cnf_transformation,[],[f2858]) ).
fof(f2858,plain,
! [X0,X1,X2] :
( c_Groups_Ominus__class_Ominus(X2,X0,X1) = c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0))
| ~ class_Groups_Oab__group__add(X2) ),
inference(ennf_transformation,[],[f1894]) ).
fof(f1894,plain,
! [X0,X1,X2] :
( class_Groups_Oab__group__add(X2)
=> c_Groups_Ominus__class_Ominus(X2,X0,X1) = c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0)) ),
inference(rectify,[],[f867]) ).
fof(f867,axiom,
! [X20,X4,X5] :
( class_Groups_Oab__group__add(X5)
=> c_Groups_Ominus__class_Ominus(X5,X20,X4) = c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Ominus__class_Ominus(X5,X4,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__diff__eq) ).
fof(f11079,plain,
( spl53_687
| ~ spl53_365
| ~ spl53_634 ),
inference(avatar_split_clause,[],[f10487,f10184,f7888,f11076]) ).
fof(f11076,plain,
( spl53_687
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_k____,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_687])]) ).
fof(f7888,plain,
( spl53_365
<=> ! [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,[spl53_365])]) ).
fof(f10184,plain,
( spl53_634
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_k____,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_634])]) ).
fof(f10487,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_k____,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21))
| ~ spl53_365
| ~ spl53_634 ),
inference(resolution,[],[f10186,f7889]) ).
fof(f7889,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| ~ spl53_365 ),
inference(avatar_component_clause,[],[f7888]) ).
fof(f10186,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_k____,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21))
| ~ spl53_634 ),
inference(avatar_component_clause,[],[f10184]) ).
fof(f11074,plain,
spl53_686,
inference(avatar_split_clause,[],[f4948,f11072]) ).
fof(f11072,plain,
( spl53_686
<=> ! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Rings_Ocomm__ring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_686])]) ).
fof(f4948,plain,
! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(cnf_transformation,[],[f2808]) ).
fof(f2808,plain,
! [X0,X1,X2] :
( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(ennf_transformation,[],[f1861]) ).
fof(f1861,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__ring__1(X2)
=> c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0)) ),
inference(rectify,[],[f866]) ).
fof(f866,axiom,
! [X21,X7,X5] :
( class_Rings_Ocomm__ring__1(X5)
=> c_Groups_Ominus__class_Ominus(X5,X7,X21) = c_Groups_Oplus__class_Oplus(X5,X7,c_Groups_Ouminus__class_Ouminus(X5,X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).
fof(f11070,plain,
spl53_685,
inference(avatar_split_clause,[],[f4927,f11068]) ).
fof(f11068,plain,
( spl53_685
<=> ! [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,[spl53_685])]) ).
fof(f4927,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,[],[f2782]) ).
fof(f2782,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,[],[f2781]) ).
fof(f2781,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,[],[f1843]) ).
fof(f1843,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,[],[f141]) ).
fof(f141,axiom,
! [X21,X7,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( X7 != X21
=> ( ~ c_Orderings_Oord__class_Oless(X5,X7,X21)
=> c_Orderings_Oord__class_Oless(X5,X21,X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(f11066,plain,
spl53_684,
inference(avatar_split_clause,[],[f4773,f11064]) ).
fof(f11064,plain,
( spl53_684
<=> ! [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,[spl53_684])]) ).
fof(f4773,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,[],[f3671]) ).
fof(f3671,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,[],[f3670]) ).
fof(f3670,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,[],[f1742]) ).
fof(f1742,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,[],[f365]) ).
fof(f365,axiom,
! [X8,X13] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13),X8) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X8
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
fof(f11062,plain,
spl53_683,
inference(avatar_split_clause,[],[f4772,f11060]) ).
fof(f11060,plain,
( spl53_683
<=> ! [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,[spl53_683])]) ).
fof(f4772,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,[],[f3671]) ).
fof(f11058,plain,
spl53_682,
inference(avatar_split_clause,[],[f4571,f11056]) ).
fof(f11056,plain,
( spl53_682
<=> ! [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,[spl53_682])]) ).
fof(f4571,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,[],[f2586]) ).
fof(f2586,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,[],[f1634]) ).
fof(f1634,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,[],[f218]) ).
fof(f218,axiom,
! [X10,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X10)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,X3)) = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).
fof(f11054,plain,
spl53_681,
inference(avatar_split_clause,[],[f4570,f11052]) ).
fof(f11052,plain,
( spl53_681
<=> ! [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,[spl53_681])]) ).
fof(f4570,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,[],[f2585]) ).
fof(f2585,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,[],[f1633]) ).
fof(f1633,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,[],[f359]) ).
fof(f359,axiom,
! [X3,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X3)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X25)) = X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
fof(f11050,plain,
spl53_680,
inference(avatar_split_clause,[],[f4560,f11048]) ).
fof(f11048,plain,
( spl53_680
<=> ! [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,[spl53_680])]) ).
fof(f4560,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,[],[f2573]) ).
fof(f2573,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,[],[f1624]) ).
fof(f1624,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,[],[f214]) ).
fof(f214,axiom,
! [X3,X10] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X3)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,X3)) = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
fof(f11046,plain,
spl53_679,
inference(avatar_split_clause,[],[f4517,f11044]) ).
fof(f11044,plain,
( spl53_679
<=> ! [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,[spl53_679])]) ).
fof(f4517,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,[],[f3577]) ).
fof(f3577,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,[],[f2528]) ).
fof(f2528,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,[],[f1582]) ).
fof(f1582,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,[],[f593]) ).
fof(f593,axiom,
! [X73,X5] :
( class_Groups_Ozero(X5)
=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X5,X73)
<=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X73 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psize__eq__0__iff) ).
fof(f11042,plain,
spl53_678,
inference(avatar_split_clause,[],[f4491,f11040]) ).
fof(f11040,plain,
( spl53_678
<=> ! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,c_Int_Onumber__class_Onumber__of(X1,X0)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Int_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_678])]) ).
fof(f4491,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,c_Int_Onumber__class_Onumber__of(X1,X0)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Int_Onumber__ring(X1) ),
inference(cnf_transformation,[],[f2506]) ).
fof(f2506,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,c_Int_Onumber__class_Onumber__of(X1,X0)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f1560]) ).
fof(f1560,plain,
! [X0,X1] :
( class_Int_Onumber__ring(X1)
=> c_Groups_Ouminus__class_Ouminus(X1,c_Int_Onumber__class_Onumber__of(X1,X0)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
inference(rectify,[],[f940]) ).
fof(f940,axiom,
! [X61,X5] :
( class_Int_Onumber__ring(X5)
=> c_Groups_Ouminus__class_Ouminus(X5,c_Int_Onumber__class_Onumber__of(X5,X61)) = c_Int_Onumber__class_Onumber__of(X5,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X61)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__minus) ).
fof(f11038,plain,
spl53_677,
inference(avatar_split_clause,[],[f4483,f11036]) ).
fof(f11036,plain,
( spl53_677
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_677])]) ).
fof(f4483,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(cnf_transformation,[],[f3569]) ).
fof(f3569,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
& ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0)) ) )
| ~ class_Rings_Olinordered__idom(X1) ),
inference(nnf_transformation,[],[f2501]) ).
fof(f2501,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
<=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
| ~ class_Rings_Olinordered__idom(X1) ),
inference(ennf_transformation,[],[f1555]) ).
fof(f1555,plain,
! [X0,X1] :
( class_Rings_Olinordered__idom(X1)
=> ( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
<=> c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
inference(rectify,[],[f921]) ).
fof(f921,axiom,
! [X9,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X9,c_Groups_Ouminus__class_Ouminus(X5,X9))
<=> c_Orderings_Oord__class_Oless(X5,X9,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).
fof(f11034,plain,
spl53_676,
inference(avatar_split_clause,[],[f4482,f11032]) ).
fof(f11032,plain,
( spl53_676
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_Rings_Olinordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_676])]) ).
fof(f4482,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(cnf_transformation,[],[f3569]) ).
fof(f11030,plain,
spl53_675,
inference(avatar_split_clause,[],[f4481,f11028]) ).
fof(f11028,plain,
( spl53_675
<=> ! [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,[spl53_675])]) ).
fof(f4481,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,[],[f2500]) ).
fof(f2500,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,[],[f2499]) ).
fof(f2499,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,[],[f1554]) ).
fof(f1554,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,[],[f643]) ).
fof(f643,axiom,
! [X4,X5] :
( class_Divides_Osemiring__div(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X4
=> c_Groups_Oone__class_Oone(X5) = c_Divides_Odiv__class_Odiv(X5,X4,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__self) ).
fof(f11026,plain,
spl53_674,
inference(avatar_split_clause,[],[f4458,f11024]) ).
fof(f11024,plain,
( spl53_674
<=> ! [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,[spl53_674])]) ).
fof(f4458,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,[],[f3559]) ).
fof(f3559,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,[],[f2486]) ).
fof(f2486,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,[],[f1541]) ).
fof(f1541,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,[],[f228]) ).
fof(f228,axiom,
! [X9,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) = c_Groups_Oplus__class_Oplus(X5,X9,X9)
<=> c_Groups_Ozero__class_Ozero(X5) = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
fof(f11022,plain,
spl53_673,
inference(avatar_split_clause,[],[f4457,f11020]) ).
fof(f11020,plain,
( spl53_673
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_673])]) ).
fof(f4457,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3558]) ).
fof(f3558,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
& ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0) ) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f2485]) ).
fof(f2485,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f1540]) ).
fof(f1540,plain,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
inference(rectify,[],[f919]) ).
fof(f919,axiom,
! [X9,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ouminus__class_Ouminus(X5,X9),X9)
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).
fof(f11018,plain,
spl53_672,
inference(avatar_split_clause,[],[f4456,f11016]) ).
fof(f11016,plain,
( spl53_672
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_672])]) ).
fof(f4456,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3558]) ).
fof(f11014,plain,
spl53_671,
inference(avatar_split_clause,[],[f4455,f11012]) ).
fof(f11012,plain,
( spl53_671
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_671])]) ).
fof(f4455,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3557]) ).
fof(f3557,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
& ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0) ) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f2484]) ).
fof(f2484,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f1539]) ).
fof(f1539,plain,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
inference(rectify,[],[f923]) ).
fof(f923,axiom,
! [X9,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ouminus__class_Ouminus(X5,X9),X9)
<=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).
fof(f11010,plain,
spl53_670,
inference(avatar_split_clause,[],[f4454,f11008]) ).
fof(f11008,plain,
( spl53_670
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_670])]) ).
fof(f4454,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3557]) ).
fof(f11006,plain,
spl53_669,
inference(avatar_split_clause,[],[f4453,f11004]) ).
fof(f11004,plain,
( spl53_669
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_669])]) ).
fof(f4453,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3556]) ).
fof(f3556,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
& ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0)) ) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f2483]) ).
fof(f2483,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
<=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f1538]) ).
fof(f1538,plain,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
<=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ) ),
inference(rectify,[],[f925]) ).
fof(f925,axiom,
! [X9,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X9,c_Groups_Ouminus__class_Ouminus(X5,X9))
<=> c_Orderings_Oord__class_Oless__eq(X5,X9,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).
fof(f11002,plain,
spl53_668,
inference(avatar_split_clause,[],[f4452,f11000]) ).
fof(f11000,plain,
( spl53_668
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_668])]) ).
fof(f4452,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3556]) ).
fof(f10998,plain,
spl53_667,
inference(avatar_split_clause,[],[f4437,f10996]) ).
fof(f10996,plain,
( spl53_667
<=> ! [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,[spl53_667])]) ).
fof(f4437,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,[],[f3549]) ).
fof(f3549,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,[],[f2472]) ).
fof(f2472,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,[],[f1527]) ).
fof(f1527,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,[],[f677]) ).
fof(f677,axiom,
! [X15,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X15))
<=> c_Groups_Ozero__class_Ozero(X5) != X15 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).
fof(f10994,plain,
( ~ spl53_666
| spl53_655
| ~ spl53_356
| ~ spl53_627 ),
inference(avatar_split_clause,[],[f10676,f10156,f7852,f10836,f10991]) ).
fof(f10991,plain,
( spl53_666
<=> class_Groups_Ogroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_666])]) ).
fof(f10836,plain,
( spl53_655
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_655])]) ).
fof(f7852,plain,
( spl53_356
<=> ! [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,[spl53_356])]) ).
fof(f10156,plain,
( spl53_627
<=> ! [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,[spl53_627])]) ).
fof(f10676,plain,
( ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ class_Groups_Ogroup__add(tc_Nat_Onat) )
| ~ spl53_356
| ~ spl53_627 ),
inference(trivial_inequality_removal,[],[f10673]) ).
fof(f10673,plain,
( ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ class_Groups_Ogroup__add(tc_Nat_Onat) )
| ~ spl53_356
| ~ spl53_627 ),
inference(superposition,[],[f10157,f7853]) ).
fof(f7853,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)
| ~ spl53_356 ),
inference(avatar_component_clause,[],[f7852]) ).
fof(f10157,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) )
| ~ spl53_627 ),
inference(avatar_component_clause,[],[f10156]) ).
fof(f10989,plain,
spl53_665,
inference(avatar_split_clause,[],[f4434,f10987]) ).
fof(f10987,plain,
( spl53_665
<=> ! [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,[spl53_665])]) ).
fof(f4434,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,[],[f3548]) ).
fof(f3548,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,[],[f2471]) ).
fof(f2471,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,[],[f1526]) ).
fof(f1526,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,[],[f679]) ).
fof(f679,axiom,
! [X15,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X15),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Groups_Ozero__class_Ozero(X5) = X15 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__le__zero__iff) ).
fof(f10985,plain,
spl53_664,
inference(avatar_split_clause,[],[f4424,f10983]) ).
fof(f10983,plain,
( spl53_664
<=> ! [X0,X1] :
( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = X0
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Rings_Odivision__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_664])]) ).
fof(f4424,plain,
! [X0,X1] :
( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = X0
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Rings_Odivision__ring(X1) ),
inference(cnf_transformation,[],[f2458]) ).
fof(f2458,plain,
! [X0,X1] :
( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = X0
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Rings_Odivision__ring(X1) ),
inference(flattening,[],[f2457]) ).
fof(f2457,plain,
! [X0,X1] :
( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = X0
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Rings_Odivision__ring(X1) ),
inference(ennf_transformation,[],[f1517]) ).
fof(f1517,plain,
! [X0,X1] :
( class_Rings_Odivision__ring(X1)
=> ( c_Groups_Ozero__class_Ozero(X1) != X0
=> c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = X0 ) ),
inference(rectify,[],[f780]) ).
fof(f780,axiom,
! [X4,X5] :
( class_Rings_Odivision__ring(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X4
=> c_Rings_Oinverse__class_Oinverse(X5,c_Rings_Oinverse__class_Oinverse(X5,X4)) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__inverse__inverse__eq) ).
fof(f10981,plain,
spl53_663,
inference(avatar_split_clause,[],[f4419,f10979]) ).
fof(f10979,plain,
( spl53_663
<=> ! [X0,X1] :
( c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_663])]) ).
fof(f4419,plain,
! [X0,X1] :
( c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(cnf_transformation,[],[f2451]) ).
fof(f2451,plain,
! [X0,X1] :
( c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Oinverse(X1,X0))
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(ennf_transformation,[],[f1513]) ).
fof(f1513,plain,
! [X0,X1] :
( class_Rings_Odivision__ring__inverse__zero(X1)
=> c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) ),
inference(rectify,[],[f945]) ).
fof(f945,axiom,
! [X4,X5] :
( class_Rings_Odivision__ring__inverse__zero(X5)
=> c_Rings_Oinverse__class_Oinverse(X5,c_Groups_Ouminus__class_Ouminus(X5,X4)) = c_Groups_Ouminus__class_Ouminus(X5,c_Rings_Oinverse__class_Oinverse(X5,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__minus__eq) ).
fof(f10977,plain,
spl53_662,
inference(avatar_split_clause,[],[f4363,f10975]) ).
fof(f10975,plain,
( spl53_662
<=> ! [X0,X1] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_662])]) ).
fof(f4363,plain,
! [X0,X1] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0),
inference(cnf_transformation,[],[f1472]) ).
fof(f1472,plain,
! [X0,X1] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X0),
inference(rectify,[],[f874]) ).
fof(f874,axiom,
! [X20,X4] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X20)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4),X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zminus2) ).
fof(f10973,plain,
spl53_661,
inference(avatar_split_clause,[],[f4362,f10971]) ).
fof(f10971,plain,
( spl53_661
<=> ! [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,[spl53_661])]) ).
fof(f4362,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,[],[f1471]) ).
fof(f1471,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,[],[f67]) ).
fof(f67,axiom,
! [X3,X10] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
fof(f10969,plain,
spl53_660,
inference(avatar_split_clause,[],[f4361,f10967]) ).
fof(f10967,plain,
( spl53_660
<=> ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_660])]) ).
fof(f4361,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1),
inference(cnf_transformation,[],[f1470]) ).
fof(f1470,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1),
inference(rectify,[],[f473]) ).
fof(f473,axiom,
! [X61,X36] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),X61) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__commute) ).
fof(f10965,plain,
spl53_659,
inference(avatar_split_clause,[],[f4360,f10963]) ).
fof(f10963,plain,
( spl53_659
<=> ! [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,[spl53_659])]) ).
fof(f4360,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,[],[f1469]) ).
fof(f1469,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,[],[f741]) ).
fof(f741,axiom,
! [X61,X36] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X36),X61) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X61),X36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__commute) ).
fof(f10961,plain,
spl53_658,
inference(avatar_split_clause,[],[f4359,f10959]) ).
fof(f10959,plain,
( spl53_658
<=> ! [X0,X1] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_658])]) ).
fof(f4359,plain,
! [X0,X1] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),
inference(cnf_transformation,[],[f1468]) ).
fof(f1468,plain,
! [X0,X1] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),
inference(rectify,[],[f875]) ).
fof(f875,axiom,
! [X20,X4] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X20) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zminus__zminus) ).
fof(f10957,plain,
spl53_657,
inference(avatar_split_clause,[],[f4308,f10955]) ).
fof(f10955,plain,
( spl53_657
<=> ! [X0] :
( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_657])]) ).
fof(f4308,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2406]) ).
fof(f2406,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1425]) ).
fof(f1425,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
inference(rectify,[],[f817]) ).
fof(f817,axiom,
! [X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X5)) = c_Polynomial_OpCons(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__poly__def) ).
fof(f10953,plain,
spl53_656,
inference(avatar_split_clause,[],[f4290,f10951]) ).
fof(f10951,plain,
( spl53_656
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Groups_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_656])]) ).
fof(f4290,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f2388]) ).
fof(f2388,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Groups_Ozero(X0) ),
inference(ennf_transformation,[],[f1407]) ).
fof(f1407,plain,
! [X0] :
( class_Groups_Ozero(X0)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
inference(rectify,[],[f811]) ).
fof(f811,axiom,
! [X5] :
( class_Groups_Ozero(X5)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_OpCons(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__0__0) ).
fof(f10838,plain,
( ~ spl53_654
| spl53_655
| ~ spl53_356
| ~ spl53_626 ),
inference(avatar_split_clause,[],[f10668,f10152,f7852,f10836,f10832]) ).
fof(f10832,plain,
( spl53_654
<=> class_Groups_Oab__group__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_654])]) ).
fof(f10152,plain,
( spl53_626
<=> ! [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,[spl53_626])]) ).
fof(f10668,plain,
( ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ class_Groups_Oab__group__add(tc_Nat_Onat) )
| ~ spl53_356
| ~ spl53_626 ),
inference(trivial_inequality_removal,[],[f10665]) ).
fof(f10665,plain,
( ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ class_Groups_Oab__group__add(tc_Nat_Onat) )
| ~ spl53_356
| ~ spl53_626 ),
inference(superposition,[],[f10153,f7853]) ).
fof(f10153,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) )
| ~ spl53_626 ),
inference(avatar_component_clause,[],[f10152]) ).
fof(f10617,plain,
( spl53_653
| ~ spl53_104
| ~ spl53_227
| ~ spl53_405
| ~ spl53_576 ),
inference(avatar_split_clause,[],[f10289,f9951,f8078,f7299,f6686,f10615]) ).
fof(f10615,plain,
( spl53_653
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat__Transfer_Otsub(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_653])]) ).
fof(f7299,plain,
( spl53_227
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_227])]) ).
fof(f9951,plain,
( spl53_576
<=> ! [X0,X1] :
( c_Nat__Transfer_Otsub(X0,X1) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_576])]) ).
fof(f10289,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat__Transfer_Otsub(X0,X0)
| ~ spl53_104
| ~ spl53_227
| ~ spl53_405
| ~ spl53_576 ),
inference(forward_demodulation,[],[f10277,f8278]) ).
fof(f10277,plain,
( ! [X0] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X0) = c_Nat__Transfer_Otsub(X0,X0)
| ~ spl53_227
| ~ spl53_576 ),
inference(resolution,[],[f9952,f7300]) ).
fof(f7300,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0)
| ~ spl53_227 ),
inference(avatar_component_clause,[],[f7299]) ).
fof(f9952,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| c_Nat__Transfer_Otsub(X0,X1) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1) )
| ~ spl53_576 ),
inference(avatar_component_clause,[],[f9951]) ).
fof(f10347,plain,
( ~ spl53_126
| spl53_652
| ~ spl53_380
| ~ spl53_554 ),
inference(avatar_split_clause,[],[f9844,f9104,f7976,f10345,f6796]) ).
fof(f6796,plain,
( spl53_126
<=> class_Rings_Odvd(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_126])]) ).
fof(f10345,plain,
( spl53_652
<=> ! [X0] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_652])]) ).
fof(f7976,plain,
( spl53_380
<=> ! [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,[spl53_380])]) ).
fof(f9104,plain,
( spl53_554
<=> ! [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,[spl53_554])]) ).
fof(f9844,plain,
( ! [X0] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X0,X0)
| ~ class_Rings_Odvd(tc_Nat_Onat) )
| ~ spl53_380
| ~ spl53_554 ),
inference(superposition,[],[f9105,f7977]) ).
fof(f7977,plain,
( ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| ~ spl53_380 ),
inference(avatar_component_clause,[],[f7976]) ).
fof(f9105,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) )
| ~ spl53_554 ),
inference(avatar_component_clause,[],[f9104]) ).
fof(f10256,plain,
spl53_651,
inference(avatar_split_clause,[],[f5864,f10254]) ).
fof(f10254,plain,
( spl53_651
<=> ! [X2,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)))
| ~ class_Rings_Oidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_651])]) ).
fof(f5864,plain,
! [X2,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)))
| ~ class_Rings_Oidom(X2) ),
inference(equality_resolution,[],[f4974]) ).
fof(f4974,plain,
! [X2,X0,X1] :
( c_Polynomial_Osmult(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f3726]) ).
fof(f3726,plain,
! [X0,X1,X2] :
( ( ( c_Polynomial_Osmult(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
& c_Groups_Ozero__class_Ozero(X2) != X1 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1
| c_Polynomial_Osmult(X2,X1,X0) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) )
| ~ class_Rings_Oidom(X2) ),
inference(flattening,[],[f3725]) ).
fof(f3725,plain,
! [X0,X1,X2] :
( ( ( c_Polynomial_Osmult(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
& c_Groups_Ozero__class_Ozero(X2) != X1 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1
| c_Polynomial_Osmult(X2,X1,X0) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) )
| ~ class_Rings_Oidom(X2) ),
inference(nnf_transformation,[],[f2836]) ).
fof(f2836,plain,
! [X0,X1,X2] :
( ( c_Polynomial_Osmult(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1 ) )
| ~ class_Rings_Oidom(X2) ),
inference(ennf_transformation,[],[f1878]) ).
fof(f1878,plain,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( c_Polynomial_Osmult(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1 ) ) ),
inference(rectify,[],[f785]) ).
fof(f785,axiom,
! [X73,X9,X5] :
( class_Rings_Oidom(X5)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_Osmult(X5,X9,X73)
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X73
| c_Groups_Ozero__class_Ozero(X5) = X9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__eq__0__iff) ).
fof(f10252,plain,
spl53_650,
inference(avatar_split_clause,[],[f5863,f10250]) ).
fof(f10250,plain,
( spl53_650
<=> ! [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,[spl53_650])]) ).
fof(f5863,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,[],[f4970]) ).
fof(f4970,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,[],[f3724]) ).
fof(f3724,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,[],[f3723]) ).
fof(f3723,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,[],[f2835]) ).
fof(f2835,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,[],[f1877]) ).
fof(f1877,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,[],[f751]) ).
fof(f751,axiom,
! [X9,X73,X5] :
( class_Rings_Oidom(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Polynomial_Opoly(X5,X73),X9)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X5,X9,X73)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = X73 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__root) ).
fof(f10248,plain,
spl53_649,
inference(avatar_split_clause,[],[f5860,f10246]) ).
fof(f10246,plain,
( spl53_649
<=> ! [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,[spl53_649])]) ).
fof(f5860,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,[],[f4931]) ).
fof(f4931,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,[],[f3718]) ).
fof(f3718,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,[],[f3717]) ).
fof(f3717,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,[],[f2787]) ).
fof(f2787,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,[],[f1846]) ).
fof(f1846,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,[],[f65]) ).
fof(f65,axiom,
! [X32,X9,X5] :
( class_Rings_Oring__no__zero__divisors(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X32)
<=> ( c_Groups_Ozero__class_Ozero(X5) = X32
| c_Groups_Ozero__class_Ozero(X5) = X9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
fof(f10244,plain,
spl53_648,
inference(avatar_split_clause,[],[f5859,f10242]) ).
fof(f10242,plain,
( spl53_648
<=> ! [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,[spl53_648])]) ).
fof(f5859,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,[],[f4932]) ).
fof(f4932,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,[],[f3718]) ).
fof(f10240,plain,
~ spl53_647,
inference(avatar_split_clause,[],[f5774,f10237]) ).
fof(f10237,plain,
( spl53_647
<=> 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,[spl53_647])]) ).
fof(f5774,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,[],[f4331]) ).
fof(f4331,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,[],[f3530]) ).
fof(f10235,plain,
spl53_646,
inference(avatar_split_clause,[],[f5703,f10233]) ).
fof(f10233,plain,
( spl53_646
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_646])]) ).
fof(f5703,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(definition_unfolding,[],[f4696,f4205]) ).
fof(f4696,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
inference(cnf_transformation,[],[f3629]) ).
fof(f3629,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
inference(nnf_transformation,[],[f1717]) ).
fof(f1717,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f205]) ).
fof(f205,axiom,
! [X8,X13] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,c_Nat_OSuc(X8))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
fof(f10231,plain,
( ~ spl53_120
| spl53_645
| ~ spl53_379
| ~ spl53_554 ),
inference(avatar_split_clause,[],[f9843,f9104,f7972,f10229,f6766]) ).
fof(f6766,plain,
( spl53_120
<=> class_Rings_Odvd(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_120])]) ).
fof(f10229,plain,
( spl53_645
<=> ! [X0] : c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_645])]) ).
fof(f7972,plain,
( spl53_379
<=> ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_379])]) ).
fof(f9843,plain,
( ! [X0] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X0,X0)
| ~ class_Rings_Odvd(tc_Int_Oint) )
| ~ spl53_379
| ~ spl53_554 ),
inference(superposition,[],[f9105,f7973]) ).
fof(f7973,plain,
( ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0
| ~ spl53_379 ),
inference(avatar_component_clause,[],[f7972]) ).
fof(f10227,plain,
spl53_644,
inference(avatar_split_clause,[],[f5690,f10225]) ).
fof(f10225,plain,
( spl53_644
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_644])]) ).
fof(f5690,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f4660,f4205]) ).
fof(f4660,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3599]) ).
fof(f3599,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f1702]) ).
fof(f1702,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ),
inference(rectify,[],[f332]) ).
fof(f332,axiom,
! [X8,X13] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,X8)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X8,c_Nat_OSuc(X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).
fof(f10223,plain,
spl53_643,
inference(avatar_split_clause,[],[f5689,f10221]) ).
fof(f10221,plain,
( spl53_643
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_643])]) ).
fof(f5689,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(definition_unfolding,[],[f4661,f4205]) ).
fof(f4661,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ),
inference(cnf_transformation,[],[f3599]) ).
fof(f10219,plain,
spl53_642,
inference(avatar_split_clause,[],[f5688,f10217]) ).
fof(f10217,plain,
( spl53_642
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_642])]) ).
fof(f5688,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f4658,f4205]) ).
fof(f4658,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3598]) ).
fof(f3598,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f1701]) ).
fof(f1701,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1) ),
inference(rectify,[],[f338]) ).
fof(f338,axiom,
! [X8,X13] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,X8)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X8),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
fof(f10215,plain,
spl53_641,
inference(avatar_split_clause,[],[f5687,f10213]) ).
fof(f10213,plain,
( spl53_641
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_641])]) ).
fof(f5687,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(definition_unfolding,[],[f4659,f4205]) ).
fof(f4659,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X1) ),
inference(cnf_transformation,[],[f3598]) ).
fof(f10211,plain,
spl53_640,
inference(avatar_split_clause,[],[f5673,f10209]) ).
fof(f10209,plain,
( spl53_640
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_640])]) ).
fof(f5673,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
inference(definition_unfolding,[],[f4623,f4205]) ).
fof(f4623,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ),
inference(cnf_transformation,[],[f2642]) ).
fof(f2642,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ),
inference(ennf_transformation,[],[f1674]) ).
fof(f1674,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f210]) ).
fof(f210,axiom,
! [X3,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X10),X3)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
fof(f10207,plain,
spl53_639,
inference(avatar_split_clause,[],[f5666,f10205]) ).
fof(f10205,plain,
( spl53_639
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_639])]) ).
fof(f5666,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f4584,f4205]) ).
fof(f4584,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2600]) ).
fof(f2600,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1646]) ).
fof(f1646,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ),
inference(rectify,[],[f208]) ).
fof(f208,axiom,
! [X3,X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X3)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X10),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leI) ).
fof(f10203,plain,
spl53_638,
inference(avatar_split_clause,[],[f5662,f10201]) ).
fof(f10201,plain,
( spl53_638
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_638])]) ).
fof(f5662,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f4568,f4205]) ).
fof(f4568,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2583]) ).
fof(f2583,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1631]) ).
fof(f1631,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
inference(rectify,[],[f207]) ).
fof(f207,axiom,
! [X3,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X3)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,c_Nat_OSuc(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
fof(f10199,plain,
spl53_637,
inference(avatar_split_clause,[],[f5279,f10197]) ).
fof(f10197,plain,
( spl53_637
<=> ! [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,[spl53_637])]) ).
fof(f5279,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,[],[f3833]) ).
fof(f3833,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,[],[f2068]) ).
fof(f2068,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,[],[f482]) ).
fof(f482,axiom,
! [X8,X13,X12] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X13) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X8)
<=> X8 = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
fof(f10195,plain,
spl53_636,
inference(avatar_split_clause,[],[f5277,f10193]) ).
fof(f10193,plain,
( spl53_636
<=> ! [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,[spl53_636])]) ).
fof(f5277,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,[],[f3832]) ).
fof(f3832,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,[],[f2067]) ).
fof(f2067,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,[],[f481]) ).
fof(f481,axiom,
! [X8,X12,X13] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,X12) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X12)
<=> X8 = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
fof(f10191,plain,
spl53_635,
inference(avatar_split_clause,[],[f5234,f10189]) ).
fof(f10189,plain,
( spl53_635
<=> ! [X2,X0,X1] :
( sP8(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK41(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_635])]) ).
fof(f5234,plain,
! [X2,X0,X1] :
( sP8(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK41(X0,X1,X2)) ),
inference(cnf_transformation,[],[f3803]) ).
fof(f3803,plain,
! [X0,X1,X2] :
( ( sP8(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK40(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK40(X0,X1,X2)),sK41(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,sK41(X0,X1,X2),X2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK41(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)
| ~ sP8(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40,sK41])],[f3800,f3802,f3801]) ).
fof(f3801,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,sK40(X0,X1,X2)))
& ? [X4] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK40(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(f3802,plain,
! [X0,X1,X2] :
( ? [X4] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK40(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),sK40(X0,X1,X2)),sK41(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,sK41(X0,X1,X2),X2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK41(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3800,plain,
! [X0,X1,X2] :
( ( sP8(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)
| ~ sP8(X0,X1,X2) ) ),
inference(rectify,[],[f3799]) ).
fof(f3799,plain,
! [X2,X1,X0] :
( ( sP8(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)
| ~ sP8(X2,X1,X0) ) ),
inference(flattening,[],[f3798]) ).
fof(f3798,plain,
! [X2,X1,X0] :
( ( sP8(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)
| ~ sP8(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f3492]) ).
fof(f3492,plain,
! [X2,X1,X0] :
( sP8(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,[sP8])]) ).
fof(f10187,plain,
( spl53_634
| ~ spl53_469
| ~ spl53_528 ),
inference(avatar_split_clause,[],[f9637,f8998,f8527,f10184]) ).
fof(f8527,plain,
( spl53_469
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_469])]) ).
fof(f8998,plain,
( spl53_528
<=> ! [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,[spl53_528])]) ).
fof(f9637,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_k____,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21))
| ~ spl53_469
| ~ spl53_528 ),
inference(resolution,[],[f8999,f8529]) ).
fof(f8529,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21))
| ~ spl53_469 ),
inference(avatar_component_clause,[],[f8527]) ).
fof(f8999,plain,
( ! [X2,X0,X1] :
( ~ 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) )
| ~ spl53_528 ),
inference(avatar_component_clause,[],[f8998]) ).
fof(f10182,plain,
spl53_633,
inference(avatar_split_clause,[],[f5229,f10180]) ).
fof(f10180,plain,
( spl53_633
<=> ! [X2,X0,X1] :
( sP9(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK39(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_633])]) ).
fof(f5229,plain,
! [X2,X0,X1] :
( sP9(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK39(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3797]) ).
fof(f3797,plain,
! [X0,X1,X2] :
( ( sP9(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK38(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK38(X0,X1,X2)),sK39(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK39(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,sK39(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))
| ~ sP9(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39])],[f3794,f3796,f3795]) ).
fof(f3795,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,sK38(X0,X1,X2)))
& ? [X4] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK38(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(f3796,plain,
! [X0,X1,X2] :
( ? [X4] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK38(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),sK38(X0,X1,X2)),sK39(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK39(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,sK39(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3794,plain,
! [X0,X1,X2] :
( ( sP9(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))
| ~ sP9(X0,X1,X2) ) ),
inference(rectify,[],[f3793]) ).
fof(f3793,plain,
! [X2,X1,X0] :
( ( sP9(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))
| ~ sP9(X2,X1,X0) ) ),
inference(flattening,[],[f3792]) ).
fof(f3792,plain,
! [X2,X1,X0] :
( ( sP9(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))
| ~ sP9(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f3493]) ).
fof(f3493,plain,
! [X2,X1,X0] :
( sP9(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,[sP9])]) ).
fof(f10178,plain,
spl53_632,
inference(avatar_split_clause,[],[f5141,f10176]) ).
fof(f10176,plain,
( spl53_632
<=> ! [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,[spl53_632])]) ).
fof(f5141,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,[],[f3023]) ).
fof(f3023,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,[],[f3022]) ).
fof(f3022,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,[],[f2009]) ).
fof(f2009,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,[],[f164]) ).
fof(f164,axiom,
! [X11,X24,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X24)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X11)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
fof(f10174,plain,
spl53_631,
inference(avatar_split_clause,[],[f5120,f10172]) ).
fof(f10172,plain,
( spl53_631
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_631])]) ).
fof(f5120,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(cnf_transformation,[],[f2999]) ).
fof(f2999,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(flattening,[],[f2998]) ).
fof(f2998,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(ennf_transformation,[],[f1988]) ).
fof(f1988,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X0) ) ),
inference(rectify,[],[f606]) ).
fof(f606,axiom,
! [X11,X24,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X25,X24)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X24,X11)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X25,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__trans) ).
fof(f10170,plain,
spl53_630,
inference(avatar_split_clause,[],[f5118,f10168]) ).
fof(f10168,plain,
( spl53_630
<=> ! [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,[spl53_630])]) ).
fof(f5118,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,[],[f2996]) ).
fof(f2996,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,[],[f2995]) ).
fof(f2995,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,[],[f1986]) ).
fof(f1986,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,[],[f695]) ).
fof(f695,axiom,
! [X11,X24,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25,X24)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,X11)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__trans) ).
fof(f10166,plain,
spl53_629,
inference(avatar_split_clause,[],[f5059,f10164]) ).
fof(f10164,plain,
( spl53_629
<=> ! [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,[spl53_629])]) ).
fof(f5059,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,[],[f3747]) ).
fof(f3747,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,[],[f2933]) ).
fof(f2933,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,[],[f1943]) ).
fof(f1943,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,[],[f276]) ).
fof(f276,axiom,
! [X9,X32,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( c_Groups_Oplus__class_Oplus(X5,X32,X9) = X32
<=> c_Groups_Ozero__class_Ozero(X5) = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(f10162,plain,
spl53_628,
inference(avatar_split_clause,[],[f5044,f10160]) ).
fof(f10160,plain,
( spl53_628
<=> ! [X2,X0,X1] :
( X0 = X1
| c_Groups_Ouminus__class_Ouminus(X2,X0) != c_Groups_Ouminus__class_Ouminus(X2,X1)
| ~ class_Groups_Ogroup__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_628])]) ).
fof(f5044,plain,
! [X2,X0,X1] :
( X0 = X1
| c_Groups_Ouminus__class_Ouminus(X2,X0) != c_Groups_Ouminus__class_Ouminus(X2,X1)
| ~ class_Groups_Ogroup__add(X2) ),
inference(cnf_transformation,[],[f3746]) ).
fof(f3746,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ouminus__class_Ouminus(X2,X0) = c_Groups_Ouminus__class_Ouminus(X2,X1)
| X0 != X1 )
& ( X0 = X1
| c_Groups_Ouminus__class_Ouminus(X2,X0) != c_Groups_Ouminus__class_Ouminus(X2,X1) ) )
| ~ class_Groups_Ogroup__add(X2) ),
inference(nnf_transformation,[],[f2906]) ).
fof(f2906,plain,
! [X0,X1,X2] :
( ( c_Groups_Ouminus__class_Ouminus(X2,X0) = c_Groups_Ouminus__class_Ouminus(X2,X1)
<=> X0 = X1 )
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f1929]) ).
fof(f1929,plain,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> ( c_Groups_Ouminus__class_Ouminus(X2,X0) = c_Groups_Ouminus__class_Ouminus(X2,X1)
<=> X0 = X1 ) ),
inference(rectify,[],[f892]) ).
fof(f892,axiom,
! [X32,X9,X5] :
( class_Groups_Ogroup__add(X5)
=> ( c_Groups_Ouminus__class_Ouminus(X5,X32) = c_Groups_Ouminus__class_Ouminus(X5,X9)
<=> X9 = X32 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).
fof(f10158,plain,
spl53_627,
inference(avatar_split_clause,[],[f5040,f10156]) ).
fof(f5040,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,[],[f3744]) ).
fof(f3744,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,[],[f2904]) ).
fof(f2904,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,[],[f1927]) ).
fof(f1927,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,[],[f59]) ).
fof(f59,axiom,
! [X32,X9,X5] :
( class_Groups_Ogroup__add(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) = c_Groups_Ominus__class_Ominus(X5,X9,X32)
<=> X9 = X32 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__minus__eq) ).
fof(f10154,plain,
spl53_626,
inference(avatar_split_clause,[],[f5018,f10152]) ).
fof(f5018,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,[],[f3736]) ).
fof(f3736,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,[],[f2888]) ).
fof(f2888,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,[],[f1912]) ).
fof(f1912,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,[],[f60]) ).
fof(f60,axiom,
! [X32,X9,X5] :
( class_Groups_Oab__group__add(X5)
=> ( X9 = X32
<=> c_Groups_Ozero__class_Ozero(X5) = c_Groups_Ominus__class_Ominus(X5,X9,X32) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).
fof(f10150,plain,
spl53_625,
inference(avatar_split_clause,[],[f4954,f10148]) ).
fof(f10148,plain,
( spl53_625
<=> ! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
| ~ c_Rings_Odvd__class_Odvd(X2,X1,X0)
| ~ class_Rings_Ocomm__ring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_625])]) ).
fof(f4954,plain,
! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
| ~ c_Rings_Odvd__class_Odvd(X2,X1,X0)
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(cnf_transformation,[],[f3720]) ).
fof(f3720,plain,
! [X0,X1,X2] :
( ( ( c_Rings_Odvd__class_Odvd(X2,c_Groups_Ouminus__class_Ouminus(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_Ouminus__class_Ouminus(X2,X1),X0) ) )
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(nnf_transformation,[],[f2812]) ).
fof(f2812,plain,
! [X0,X1,X2] :
( ( c_Rings_Odvd__class_Odvd(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
<=> c_Rings_Odvd__class_Odvd(X2,X1,X0) )
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(ennf_transformation,[],[f1865]) ).
fof(f1865,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__ring__1(X2)
=> ( c_Rings_Odvd__class_Odvd(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
<=> c_Rings_Odvd__class_Odvd(X2,X1,X0) ) ),
inference(rectify,[],[f965]) ).
fof(f965,axiom,
! [X40,X15,X5] :
( class_Rings_Ocomm__ring__1(X5)
=> ( c_Rings_Odvd__class_Odvd(X5,c_Groups_Ouminus__class_Ouminus(X5,X15),X40)
<=> c_Rings_Odvd__class_Odvd(X5,X15,X40) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__dvd__iff) ).
fof(f10146,plain,
spl53_624,
inference(avatar_split_clause,[],[f4953,f10144]) ).
fof(f10144,plain,
( spl53_624
<=> ! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(X2,X1,X0)
| ~ c_Rings_Odvd__class_Odvd(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
| ~ class_Rings_Ocomm__ring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_624])]) ).
fof(f4953,plain,
! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(X2,X1,X0)
| ~ c_Rings_Odvd__class_Odvd(X2,c_Groups_Ouminus__class_Ouminus(X2,X1),X0)
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(cnf_transformation,[],[f3720]) ).
fof(f10142,plain,
spl53_623,
inference(avatar_split_clause,[],[f4952,f10140]) ).
fof(f10140,plain,
( spl53_623
<=> ! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ c_Rings_Odvd__class_Odvd(X2,X1,X0)
| ~ class_Rings_Ocomm__ring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_623])]) ).
fof(f4952,plain,
! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ c_Rings_Odvd__class_Odvd(X2,X1,X0)
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(cnf_transformation,[],[f3719]) ).
fof(f3719,plain,
! [X0,X1,X2] :
( ( ( c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Ouminus__class_Ouminus(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_Ouminus__class_Ouminus(X2,X0)) ) )
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(nnf_transformation,[],[f2811]) ).
fof(f2811,plain,
! [X0,X1,X2] :
( ( c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Rings_Odvd__class_Odvd(X2,X1,X0) )
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(ennf_transformation,[],[f1864]) ).
fof(f1864,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__ring__1(X2)
=> ( c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
<=> c_Rings_Odvd__class_Odvd(X2,X1,X0) ) ),
inference(rectify,[],[f964]) ).
fof(f964,axiom,
! [X40,X15,X5] :
( class_Rings_Ocomm__ring__1(X5)
=> ( c_Rings_Odvd__class_Odvd(X5,X15,c_Groups_Ouminus__class_Ouminus(X5,X40))
<=> c_Rings_Odvd__class_Odvd(X5,X15,X40) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__minus__iff) ).
fof(f10138,plain,
spl53_622,
inference(avatar_split_clause,[],[f4951,f10136]) ).
fof(f10136,plain,
( spl53_622
<=> ! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(X2,X1,X0)
| ~ c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Rings_Ocomm__ring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_622])]) ).
fof(f4951,plain,
! [X2,X0,X1] :
( c_Rings_Odvd__class_Odvd(X2,X1,X0)
| ~ c_Rings_Odvd__class_Odvd(X2,X1,c_Groups_Ouminus__class_Ouminus(X2,X0))
| ~ class_Rings_Ocomm__ring__1(X2) ),
inference(cnf_transformation,[],[f3719]) ).
fof(f10134,plain,
spl53_621,
inference(avatar_split_clause,[],[f4849,f10132]) ).
fof(f10132,plain,
( spl53_621
<=> ! [X2,X0,X1] :
( X0 = X1
| c_Rings_Oinverse__class_Oinverse(X2,X0) != c_Rings_Oinverse__class_Oinverse(X2,X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_621])]) ).
fof(f4849,plain,
! [X2,X0,X1] :
( X0 = X1
| c_Rings_Oinverse__class_Oinverse(X2,X0) != c_Rings_Oinverse__class_Oinverse(X2,X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X2) ),
inference(cnf_transformation,[],[f2718]) ).
fof(f2718,plain,
! [X0,X1,X2] :
( X0 = X1
| c_Rings_Oinverse__class_Oinverse(X2,X0) != c_Rings_Oinverse__class_Oinverse(X2,X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X2) ),
inference(flattening,[],[f2717]) ).
fof(f2717,plain,
! [X0,X1,X2] :
( X0 = X1
| c_Rings_Oinverse__class_Oinverse(X2,X0) != c_Rings_Oinverse__class_Oinverse(X2,X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X2) ),
inference(ennf_transformation,[],[f1797]) ).
fof(f1797,plain,
! [X0,X1,X2] :
( class_Rings_Odivision__ring__inverse__zero(X2)
=> ( c_Rings_Oinverse__class_Oinverse(X2,X0) = c_Rings_Oinverse__class_Oinverse(X2,X1)
=> X0 = X1 ) ),
inference(rectify,[],[f788]) ).
fof(f788,axiom,
! [X20,X4,X5] :
( class_Rings_Odivision__ring__inverse__zero(X5)
=> ( c_Rings_Oinverse__class_Oinverse(X5,X4) = c_Rings_Oinverse__class_Oinverse(X5,X20)
=> X4 = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__eq__imp__eq) ).
fof(f10130,plain,
spl53_620,
inference(avatar_split_clause,[],[f4844,f10128]) ).
fof(f10128,plain,
( spl53_620
<=> ! [X2,X0,X1] :
( X0 = X1
| c_Groups_Ouminus__class_Ouminus(X2,X0) != c_Groups_Ouminus__class_Ouminus(X2,X1)
| ~ class_Lattices_Oboolean__algebra(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_620])]) ).
fof(f4844,plain,
! [X2,X0,X1] :
( X0 = X1
| c_Groups_Ouminus__class_Ouminus(X2,X0) != c_Groups_Ouminus__class_Ouminus(X2,X1)
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(cnf_transformation,[],[f3690]) ).
fof(f3690,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ouminus__class_Ouminus(X2,X0) = c_Groups_Ouminus__class_Ouminus(X2,X1)
| X0 != X1 )
& ( X0 = X1
| c_Groups_Ouminus__class_Ouminus(X2,X0) != c_Groups_Ouminus__class_Ouminus(X2,X1) ) )
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(nnf_transformation,[],[f2714]) ).
fof(f2714,plain,
! [X0,X1,X2] :
( ( c_Groups_Ouminus__class_Ouminus(X2,X0) = c_Groups_Ouminus__class_Ouminus(X2,X1)
<=> X0 = X1 )
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(ennf_transformation,[],[f1794]) ).
fof(f1794,plain,
! [X0,X1,X2] :
( class_Lattices_Oboolean__algebra(X2)
=> ( c_Groups_Ouminus__class_Ouminus(X2,X0) = c_Groups_Ouminus__class_Ouminus(X2,X1)
<=> X0 = X1 ) ),
inference(rectify,[],[f888]) ).
fof(f888,axiom,
! [X40,X15,X5] :
( class_Lattices_Oboolean__algebra(X5)
=> ( c_Groups_Ouminus__class_Ouminus(X5,X15) = c_Groups_Ouminus__class_Ouminus(X5,X40)
<=> X15 = X40 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).
fof(f10126,plain,
spl53_619,
inference(avatar_split_clause,[],[f4767,f10124]) ).
fof(f10124,plain,
( spl53_619
<=> ! [X0,X1] :
( X0 = X1
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_619])]) ).
fof(f4767,plain,
! [X0,X1] :
( X0 = X1
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)) ),
inference(cnf_transformation,[],[f3667]) ).
fof(f3667,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0))
| X0 != X1 )
& ( X0 = X1
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)) ) ),
inference(nnf_transformation,[],[f1740]) ).
fof(f1740,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0))
<=> X0 = X1 ),
inference(rectify,[],[f935]) ).
fof(f935,axiom,
! [X9,X15] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X15,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X9))
<=> X9 = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).
fof(f10122,plain,
spl53_618,
inference(avatar_split_clause,[],[f4763,f10120]) ).
fof(f10120,plain,
( spl53_618
<=> ! [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,[spl53_618])]) ).
fof(f4763,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,[],[f3664]) ).
fof(f3664,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,[],[f1738]) ).
fof(f1738,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,[],[f440]) ).
fof(f440,axiom,
! [X13,X8] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X8,X13))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__diff) ).
fof(f10118,plain,
spl53_617,
inference(avatar_split_clause,[],[f4762,f10116]) ).
fof(f10116,plain,
( spl53_617
<=> ! [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,[spl53_617])]) ).
fof(f4762,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,[],[f3664]) ).
fof(f10114,plain,
spl53_616,
inference(avatar_split_clause,[],[f4758,f10112]) ).
fof(f10112,plain,
( spl53_616
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_616])]) ).
fof(f4758,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3662]) ).
fof(f10110,plain,
spl53_615,
inference(avatar_split_clause,[],[f4756,f10108]) ).
fof(f10108,plain,
( spl53_615
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_615])]) ).
fof(f4756,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3660]) ).
fof(f3660,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(nnf_transformation,[],[f1735]) ).
fof(f1735,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(rectify,[],[f559]) ).
fof(f559,axiom,
! [X56,X57] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X57,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X56,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X57,X56) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).
fof(f10106,plain,
spl53_614,
inference(avatar_split_clause,[],[f4755,f10104]) ).
fof(f10104,plain,
( spl53_614
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_614])]) ).
fof(f4755,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f3660]) ).
fof(f10102,plain,
( spl53_613
| ~ spl53_457
| ~ spl53_571 ),
inference(avatar_split_clause,[],[f9833,f9734,f8478,f10100]) ).
fof(f10100,plain,
( spl53_613
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1))
| ~ sP7(X1,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_613])]) ).
fof(f8478,plain,
( spl53_457
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_457])]) ).
fof(f9833,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1))
| ~ sP7(X1,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0)) )
| ~ spl53_457
| ~ spl53_571 ),
inference(superposition,[],[f8479,f9735]) ).
fof(f8479,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP7(X0,X1,X2) )
| ~ spl53_457 ),
inference(avatar_component_clause,[],[f8478]) ).
fof(f10098,plain,
spl53_612,
inference(avatar_split_clause,[],[f4749,f10096]) ).
fof(f10096,plain,
( spl53_612
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_612])]) ).
fof(f4749,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) ),
inference(cnf_transformation,[],[f3657]) ).
fof(f3657,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) ) ),
inference(nnf_transformation,[],[f1732]) ).
fof(f1732,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(rectify,[],[f562]) ).
fof(f562,axiom,
! [X56,X57] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X57,c_Groups_Oone__class_Oone(tc_Int_Oint)),X56)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X57,X56) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add1__zle__eq) ).
fof(f10094,plain,
spl53_611,
inference(avatar_split_clause,[],[f4746,f10092]) ).
fof(f10092,plain,
( spl53_611
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_611])]) ).
fof(f4746,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3655]) ).
fof(f3655,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(nnf_transformation,[],[f1730]) ).
fof(f1730,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(rectify,[],[f554]) ).
fof(f554,axiom,
! [X56,X57] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X57,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X56,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X57,X56) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).
fof(f10090,plain,
spl53_610,
inference(avatar_split_clause,[],[f4745,f10088]) ).
fof(f10088,plain,
( spl53_610
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_610])]) ).
fof(f4745,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f3655]) ).
fof(f10086,plain,
spl53_609,
inference(avatar_split_clause,[],[f4717,f10084]) ).
fof(f10084,plain,
( spl53_609
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_609])]) ).
fof(f4717,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3642]) ).
fof(f10082,plain,
spl53_608,
inference(avatar_split_clause,[],[f4716,f10080]) ).
fof(f10080,plain,
( spl53_608
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_608])]) ).
fof(f4716,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(cnf_transformation,[],[f3642]) ).
fof(f10078,plain,
spl53_607,
inference(avatar_split_clause,[],[f4709,f10076]) ).
fof(f10076,plain,
( spl53_607
<=> ! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) = X0
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_607])]) ).
fof(f4709,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) = X0
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f3639]) ).
fof(f3639,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)
| c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) != X0 )
& ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) = X0
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0) ) ),
inference(nnf_transformation,[],[f1722]) ).
fof(f1722,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)
<=> c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) = X0 ),
inference(rectify,[],[f934]) ).
fof(f934,axiom,
! [X40,X15] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X15,X40)
<=> c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X15) = X40 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__eq__0__iff) ).
fof(f10074,plain,
spl53_606,
inference(avatar_split_clause,[],[f4678,f10072]) ).
fof(f10072,plain,
( spl53_606
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_606])]) ).
fof(f4678,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3615]) ).
fof(f3615,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
inference(nnf_transformation,[],[f1709]) ).
fof(f1709,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(rectify,[],[f553]) ).
fof(f553,axiom,
! [X67,X12] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X12,X67)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X12,X67),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__bin__lemma) ).
fof(f10070,plain,
spl53_605,
inference(avatar_split_clause,[],[f4677,f10068]) ).
fof(f10068,plain,
( spl53_605
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_605])]) ).
fof(f4677,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3615]) ).
fof(f10066,plain,
spl53_604,
inference(avatar_split_clause,[],[f4672,f10064]) ).
fof(f10064,plain,
( spl53_604
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK33(X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_604])]) ).
fof(f4672,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK33(X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3612]) ).
fof(f3612,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,sK33(X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f3610,f3611]) ).
fof(f3611,plain,
! [X0,X1] :
( ? [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) = X0
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK33(X0,X1)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f3610,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,[],[f3609]) ).
fof(f3609,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,[],[f1707]) ).
fof(f1707,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,[],[f190]) ).
fof(f190,axiom,
! [X8,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,X8)
<=> ? [X52] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,X52) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
fof(f10062,plain,
spl53_603,
inference(avatar_split_clause,[],[f4670,f10060]) ).
fof(f10060,plain,
( spl53_603
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK32(X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_603])]) ).
fof(f4670,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK32(X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3608]) ).
fof(f3608,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,sK32(X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f3606,f3607]) ).
fof(f3607,plain,
! [X0,X1] :
( ? [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) = X0
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK32(X0,X1)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f3606,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,[],[f3605]) ).
fof(f3605,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,[],[f1706]) ).
fof(f1706,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,[],[f548]) ).
fof(f548,axiom,
! [X67,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X67)
<=> ? [X68] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X68) = X67 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).
fof(f10058,plain,
spl53_602,
inference(avatar_split_clause,[],[f4663,f10056]) ).
fof(f10056,plain,
( spl53_602
<=> ! [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,[spl53_602])]) ).
fof(f4663,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,[],[f3600]) ).
fof(f3600,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,[],[f1703]) ).
fof(f1703,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,[],[f678]) ).
fof(f678,axiom,
! [X40,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X40)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X15,X40),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__eq__diff) ).
fof(f10054,plain,
spl53_601,
inference(avatar_split_clause,[],[f4662,f10052]) ).
fof(f10052,plain,
( spl53_601
<=> ! [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,[spl53_601])]) ).
fof(f4662,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,[],[f3600]) ).
fof(f10050,plain,
spl53_600,
inference(avatar_split_clause,[],[f4578,f10048]) ).
fof(f10048,plain,
( spl53_600
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_600])]) ).
fof(f4578,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f2594]) ).
fof(f2594,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(ennf_transformation,[],[f1640]) ).
fof(f1640,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) ),
inference(rectify,[],[f564]) ).
fof(f564,axiom,
! [X36,X61] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X61,X36)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X61,c_Groups_Oone__class_Oone(tc_Int_Oint)),X36) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).
fof(f10046,plain,
spl53_599,
inference(avatar_split_clause,[],[f4547,f10044]) ).
fof(f10044,plain,
( spl53_599
<=> ! [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,[spl53_599])]) ).
fof(f4547,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,[],[f2557]) ).
fof(f2557,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,[],[f1611]) ).
fof(f1611,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,[],[f42]) ).
fof(f42,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ozero__class_Ozero(X5)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(f10042,plain,
spl53_598,
inference(avatar_split_clause,[],[f4546,f10040]) ).
fof(f10040,plain,
( spl53_598
<=> ! [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,[spl53_598])]) ).
fof(f4546,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,[],[f2556]) ).
fof(f2556,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,[],[f1610]) ).
fof(f1610,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,[],[f41]) ).
fof(f41,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(f10038,plain,
spl53_597,
inference(avatar_split_clause,[],[f4545,f10036]) ).
fof(f10036,plain,
( spl53_597
<=> ! [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,[spl53_597])]) ).
fof(f4545,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,[],[f2555]) ).
fof(f2555,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,[],[f1609]) ).
fof(f1609,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,[],[f728]) ).
fof(f728,axiom,
! [X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oone__class_Oone(X5) = hAPP(c_Polynomial_Opoly(X5,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X5))),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__1) ).
fof(f10034,plain,
spl53_596,
inference(avatar_split_clause,[],[f4544,f10032]) ).
fof(f10032,plain,
( spl53_596
<=> ! [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,[spl53_596])]) ).
fof(f4544,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,[],[f2554]) ).
fof(f2554,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,[],[f1608]) ).
fof(f1608,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,[],[f426]) ).
fof(f426,axiom,
! [X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oone__class_Oone(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(f10030,plain,
spl53_595,
inference(avatar_split_clause,[],[f4532,f10028]) ).
fof(f10028,plain,
( spl53_595
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Rings_Ocomm__semiring__0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_595])]) ).
fof(f4532,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(cnf_transformation,[],[f2542]) ).
fof(f2542,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(ennf_transformation,[],[f1596]) ).
fof(f1596,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(rectify,[],[f769]) ).
fof(f769,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_Osmult(X5,X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__0__right) ).
fof(f10026,plain,
spl53_594,
inference(avatar_split_clause,[],[f4531,f10024]) ).
fof(f10024,plain,
( spl53_594
<=> ! [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,[spl53_594])]) ).
fof(f4531,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,[],[f2541]) ).
fof(f2541,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,[],[f1595]) ).
fof(f1595,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,[],[f854]) ).
fof(f854,axiom,
! [X33,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_Osynthetic__div(X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__0) ).
fof(f10022,plain,
spl53_593,
inference(avatar_split_clause,[],[f4530,f10020]) ).
fof(f10020,plain,
( spl53_593
<=> ! [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,[spl53_593])]) ).
fof(f4530,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,[],[f2540]) ).
fof(f2540,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,[],[f1594]) ).
fof(f1594,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,[],[f850]) ).
fof(f850,axiom,
! [X6,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_Opcompose(X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pcompose__0) ).
fof(f10018,plain,
( spl53_591
| ~ spl53_592
| ~ spl53_457
| ~ spl53_571 ),
inference(avatar_split_clause,[],[f9832,f9734,f8478,f10015,f10012]) ).
fof(f10012,plain,
( spl53_591
<=> ! [X0] : ~ sP7(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_591])]) ).
fof(f10015,plain,
( spl53_592
<=> hBOOL(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_592])]) ).
fof(f9832,plain,
( ! [X0] :
( ~ hBOOL(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ sP7(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0,c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex)) )
| ~ spl53_457
| ~ spl53_571 ),
inference(superposition,[],[f8479,f9735]) ).
fof(f10010,plain,
spl53_590,
inference(avatar_split_clause,[],[f4529,f10008]) ).
fof(f10008,plain,
( spl53_590
<=> ! [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,[spl53_590])]) ).
fof(f4529,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,[],[f2539]) ).
fof(f2539,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,[],[f1593]) ).
fof(f1593,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,[],[f669]) ).
fof(f669,axiom,
! [X7,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Polynomial_Opoly(X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__0) ).
fof(f10006,plain,
spl53_589,
inference(avatar_split_clause,[],[f4527,f10004]) ).
fof(f10004,plain,
( spl53_589
<=> ! [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,[spl53_589])]) ).
fof(f4527,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,[],[f2537]) ).
fof(f2537,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,[],[f1591]) ).
fof(f1591,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,[],[f314]) ).
fof(f314,axiom,
! [X3,X5] :
( class_Groups_Omonoid__mult(X5)
=> c_Groups_Oone__class_Oone(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Oone__class_Oone(X5)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one) ).
fof(f10002,plain,
spl53_588,
inference(avatar_split_clause,[],[f4523,f10000]) ).
fof(f10000,plain,
( spl53_588
<=> ! [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,[spl53_588])]) ).
fof(f4523,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,[],[f2533]) ).
fof(f2533,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,[],[f1587]) ).
fof(f1587,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,[],[f427]) ).
fof(f427,axiom,
! [X4,X5] :
( class_Power_Opower(X5)
=> c_Groups_Oone__class_Oone(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0) ).
fof(f9998,plain,
spl53_587,
inference(avatar_split_clause,[],[f4514,f9996]) ).
fof(f9996,plain,
( spl53_587
<=> ! [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,[spl53_587])]) ).
fof(f4514,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,[],[f2526]) ).
fof(f2526,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,[],[f1580]) ).
fof(f1580,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,[],[f72]) ).
fof(f72,axiom,
! [X4,X5] :
( class_Rings_Omult__zero(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ozero__class_Ozero(X5)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__left) ).
fof(f9994,plain,
spl53_586,
inference(avatar_split_clause,[],[f4513,f9992]) ).
fof(f9992,plain,
( spl53_586
<=> ! [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,[spl53_586])]) ).
fof(f4513,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,[],[f2525]) ).
fof(f2525,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,[],[f1579]) ).
fof(f1579,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,[],[f75]) ).
fof(f75,axiom,
! [X4,X5] :
( class_Rings_Omult__zero(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__right) ).
fof(f9990,plain,
spl53_585,
inference(avatar_split_clause,[],[f4502,f9988]) ).
fof(f4502,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Ouminus__class_Ouminus(X1,X0)
| ~ class_Groups_Ogroup__add(X1) ),
inference(cnf_transformation,[],[f3573]) ).
fof(f3573,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,X0)
| c_Groups_Ozero__class_Ozero(X1) != X0 )
& ( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Ouminus__class_Ouminus(X1,X0) ) )
| ~ class_Groups_Ogroup__add(X1) ),
inference(nnf_transformation,[],[f2517]) ).
fof(f2517,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_Groups_Ogroup__add(X1) ),
inference(ennf_transformation,[],[f1571]) ).
fof(f1571,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f895]) ).
fof(f895,axiom,
! [X9,X5] :
( class_Groups_Ogroup__add(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) = c_Groups_Ouminus__class_Ouminus(X5,X9)
<=> c_Groups_Ozero__class_Ozero(X5) = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).
fof(f9986,plain,
spl53_584,
inference(avatar_split_clause,[],[f4447,f9984]) ).
fof(f9984,plain,
( spl53_584
<=> ! [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,[spl53_584])]) ).
fof(f4447,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,[],[f2480]) ).
fof(f2480,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,[],[f1535]) ).
fof(f1535,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,[],[f417]) ).
fof(f417,axiom,
! [X4,X5] :
( class_Rings_Olinordered__ring(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__square) ).
fof(f9982,plain,
spl53_583,
inference(avatar_split_clause,[],[f4446,f9980]) ).
fof(f9980,plain,
( spl53_583
<=> ! [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,[spl53_583])]) ).
fof(f4446,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,[],[f2479]) ).
fof(f2479,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,[],[f1534]) ).
fof(f1534,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,[],[f399]) ).
fof(f399,axiom,
! [X4,X5] :
( class_Rings_Olinordered__ring(X5)
=> ~ c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X4),c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
fof(f9978,plain,
spl53_582,
inference(avatar_split_clause,[],[f4440,f9976]) ).
fof(f9976,plain,
( spl53_582
<=> ! [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,[spl53_582])]) ).
fof(f4440,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,[],[f2475]) ).
fof(f2475,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,[],[f1530]) ).
fof(f1530,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,[],[f74]) ).
fof(f74,axiom,
! [X21,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ozero__class_Ozero(X5)),X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).
fof(f9974,plain,
spl53_581,
inference(avatar_split_clause,[],[f4438,f9972]) ).
fof(f4438,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,[],[f2473]) ).
fof(f2473,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,[],[f1528]) ).
fof(f1528,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,[],[f76]) ).
fof(f76,axiom,
! [X4,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).
fof(f9969,plain,
spl53_580,
inference(avatar_split_clause,[],[f4432,f9967]) ).
fof(f9967,plain,
( spl53_580
<=> ! [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,[spl53_580])]) ).
fof(f4432,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,[],[f3547]) ).
fof(f3547,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,[],[f2470]) ).
fof(f2470,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,[],[f1525]) ).
fof(f1525,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,[],[f699]) ).
fof(f699,axiom,
! [X15,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X5,X15)
<=> c_Groups_Ozero__class_Ozero(X5) = X15 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__eq__zero) ).
fof(f9965,plain,
spl53_579,
inference(avatar_split_clause,[],[f4423,f9963]) ).
fof(f9963,plain,
( spl53_579
<=> ! [X0,X1] :
( c_Rings_Oinverse__class_Oinverse(X1,X0) != c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Rings_Odivision__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_579])]) ).
fof(f4423,plain,
! [X0,X1] :
( c_Rings_Oinverse__class_Oinverse(X1,X0) != c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Rings_Odivision__ring(X1) ),
inference(cnf_transformation,[],[f2456]) ).
fof(f2456,plain,
! [X0,X1] :
( c_Rings_Oinverse__class_Oinverse(X1,X0) != c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Rings_Odivision__ring(X1) ),
inference(flattening,[],[f2455]) ).
fof(f2455,plain,
! [X0,X1] :
( c_Rings_Oinverse__class_Oinverse(X1,X0) != c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Rings_Odivision__ring(X1) ),
inference(ennf_transformation,[],[f1516]) ).
fof(f1516,plain,
! [X0,X1] :
( class_Rings_Odivision__ring(X1)
=> ( c_Groups_Ozero__class_Ozero(X1) != X0
=> c_Rings_Oinverse__class_Oinverse(X1,X0) != c_Groups_Ozero__class_Ozero(X1) ) ),
inference(rectify,[],[f781]) ).
fof(f781,axiom,
! [X4,X5] :
( class_Rings_Odivision__ring(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) != X4
=> c_Groups_Ozero__class_Ozero(X5) != c_Rings_Oinverse__class_Oinverse(X5,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__imp__inverse__nonzero) ).
fof(f9961,plain,
spl53_578,
inference(avatar_split_clause,[],[f4420,f9959]) ).
fof(f9959,plain,
( spl53_578
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Rings_Oinverse__class_Oinverse(X1,X0) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_578])]) ).
fof(f4420,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Rings_Oinverse__class_Oinverse(X1,X0) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(cnf_transformation,[],[f3546]) ).
fof(f3546,plain,
! [X0,X1] :
( ( ( c_Rings_Oinverse__class_Oinverse(X1,X0) = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ozero__class_Ozero(X1) != X0 )
& ( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Rings_Oinverse__class_Oinverse(X1,X0) != c_Groups_Ozero__class_Ozero(X1) ) )
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(nnf_transformation,[],[f2452]) ).
fof(f2452,plain,
! [X0,X1] :
( ( c_Rings_Oinverse__class_Oinverse(X1,X0) = c_Groups_Ozero__class_Ozero(X1)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(ennf_transformation,[],[f1514]) ).
fof(f1514,plain,
! [X0,X1] :
( class_Rings_Odivision__ring__inverse__zero(X1)
=> ( c_Rings_Oinverse__class_Oinverse(X1,X0) = c_Groups_Ozero__class_Ozero(X1)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f782]) ).
fof(f782,axiom,
! [X9,X5] :
( class_Rings_Odivision__ring__inverse__zero(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) = c_Rings_Oinverse__class_Oinverse(X5,X9)
<=> c_Groups_Ozero__class_Ozero(X5) = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__nonzero__iff__nonzero) ).
fof(f9957,plain,
spl53_577,
inference(avatar_split_clause,[],[f4413,f9955]) ).
fof(f9955,plain,
( spl53_577
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = X0
| c_Groups_Oone__class_Oone(X1) != c_Rings_Oinverse__class_Oinverse(X1,X0)
| ~ class_Fields_Ofield__inverse__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_577])]) ).
fof(f4413,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = X0
| c_Groups_Oone__class_Oone(X1) != c_Rings_Oinverse__class_Oinverse(X1,X0)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(cnf_transformation,[],[f3545]) ).
fof(f3545,plain,
! [X0,X1] :
( ( ( c_Groups_Oone__class_Oone(X1) = c_Rings_Oinverse__class_Oinverse(X1,X0)
| c_Groups_Oone__class_Oone(X1) != X0 )
& ( c_Groups_Oone__class_Oone(X1) = X0
| c_Groups_Oone__class_Oone(X1) != c_Rings_Oinverse__class_Oinverse(X1,X0) ) )
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(nnf_transformation,[],[f2445]) ).
fof(f2445,plain,
! [X0,X1] :
( ( c_Groups_Oone__class_Oone(X1) = c_Rings_Oinverse__class_Oinverse(X1,X0)
<=> c_Groups_Oone__class_Oone(X1) = X0 )
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(ennf_transformation,[],[f1508]) ).
fof(f1508,plain,
! [X0,X1] :
( class_Fields_Ofield__inverse__zero(X1)
=> ( c_Groups_Oone__class_Oone(X1) = c_Rings_Oinverse__class_Oinverse(X1,X0)
<=> c_Groups_Oone__class_Oone(X1) = X0 ) ),
inference(rectify,[],[f824]) ).
fof(f824,axiom,
! [X15,X5] :
( class_Fields_Ofield__inverse__zero(X5)
=> ( c_Groups_Oone__class_Oone(X5) = c_Rings_Oinverse__class_Oinverse(X5,X15)
<=> c_Groups_Oone__class_Oone(X5) = X15 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__eq__1__iff) ).
fof(f9953,plain,
spl53_576,
inference(avatar_split_clause,[],[f4381,f9951]) ).
fof(f4381,plain,
! [X0,X1] :
( c_Nat__Transfer_Otsub(X0,X1) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f2424]) ).
fof(f2424,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat__Transfer_Otsub(X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
& ( c_Nat__Transfer_Otsub(X0,X1) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
inference(ennf_transformation,[],[f1487]) ).
fof(f1487,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat__Transfer_Otsub(X0,X1) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
=> c_Nat__Transfer_Otsub(X0,X1) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1) ) ),
inference(rectify,[],[f620]) ).
fof(f620,axiom,
! [X7,X21] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,X7)
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat__Transfer_Otsub(X7,X21) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,X7)
=> c_Nat__Transfer_Otsub(X7,X21) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tsub__def) ).
fof(f9949,plain,
spl53_575,
inference(avatar_split_clause,[],[f4283,f9947]) ).
fof(f9947,plain,
( spl53_575
<=> ! [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,[spl53_575])]) ).
fof(f4283,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,[],[f2381]) ).
fof(f2381,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,[],[f1400]) ).
fof(f1400,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,[],[f96]) ).
fof(f96,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oplus__class_Oplus(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Oone__class_Oone(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__two) ).
fof(f9945,plain,
spl53_574,
inference(avatar_split_clause,[],[f4277,f9943]) ).
fof(f9943,plain,
( spl53_574
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Groups_Oab__group__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_574])]) ).
fof(f4277,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f2375]) ).
fof(f2375,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
| ~ class_Groups_Oab__group__add(X0) ),
inference(ennf_transformation,[],[f1394]) ).
fof(f1394,plain,
! [X0] :
( class_Groups_Oab__group__add(X0)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
inference(rectify,[],[f933]) ).
fof(f933,axiom,
! [X5] :
( class_Groups_Oab__group__add(X5)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__poly__code_I1_J) ).
fof(f9941,plain,
spl53_573,
inference(avatar_split_clause,[],[f4162,f9938]) ).
fof(f9938,plain,
( spl53_573
<=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_573])]) ).
fof(f9921,plain,
( spl53_572
| ~ spl53_570
| ~ spl53_571 ),
inference(avatar_split_clause,[],[f9827,f9734,f9519,f9919]) ).
fof(f9919,plain,
( spl53_572
<=> ! [X1] : c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_572])]) ).
fof(f9519,plain,
( spl53_570
<=> ! [X0,X1] : c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_570])]) ).
fof(f9827,plain,
( ! [X1] : c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ spl53_570
| ~ spl53_571 ),
inference(superposition,[],[f9520,f9735]) ).
fof(f9520,plain,
( ! [X0,X1] : c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| ~ spl53_570 ),
inference(avatar_component_clause,[],[f9519]) ).
fof(f9736,plain,
( ~ spl53_196
| spl53_571
| ~ spl53_500
| ~ spl53_570 ),
inference(avatar_split_clause,[],[f9660,f9519,f8882,f9734,f7146]) ).
fof(f8882,plain,
( spl53_500
<=> ! [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,[spl53_500])]) ).
fof(f9660,plain,
( ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) )
| ~ spl53_500
| ~ spl53_570 ),
inference(resolution,[],[f9520,f8883]) ).
fof(f8883,plain,
( ! [X0,X1] :
( ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) )
| ~ spl53_500 ),
inference(avatar_component_clause,[],[f8882]) ).
fof(f9521,plain,
( ~ spl53_196
| spl53_570
| ~ spl53_432
| ~ spl53_519 ),
inference(avatar_split_clause,[],[f9499,f8962,f8372,f9519,f7146]) ).
fof(f8372,plain,
( spl53_432
<=> ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_432])]) ).
fof(f8962,plain,
( spl53_519
<=> ! [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,[spl53_519])]) ).
fof(f9499,plain,
( ! [X0,X1] :
( c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) )
| ~ spl53_432
| ~ spl53_519 ),
inference(superposition,[],[f8963,f8373]) ).
fof(f8373,plain,
( ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ spl53_432 ),
inference(avatar_component_clause,[],[f8372]) ).
fof(f8963,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) )
| ~ spl53_519 ),
inference(avatar_component_clause,[],[f8962]) ).
fof(f9459,plain,
( spl53_569
| ~ spl53_35
| ~ spl53_404 ),
inference(avatar_split_clause,[],[f8274,f8074,f6341,f9457]) ).
fof(f9457,plain,
( spl53_569
<=> ! [X0] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_569])]) ).
fof(f6341,plain,
( spl53_35
<=> class_Divides_Osemiring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_35])]) ).
fof(f8074,plain,
( spl53_404
<=> ! [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,[spl53_404])]) ).
fof(f8274,plain,
( ! [X0] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0
| ~ spl53_35
| ~ spl53_404 ),
inference(resolution,[],[f8075,f6343]) ).
fof(f6343,plain,
( class_Divides_Osemiring__div(tc_Int_Oint)
| ~ spl53_35 ),
inference(avatar_component_clause,[],[f6341]) ).
fof(f8075,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Odiv(X1,X0,c_Groups_Oone__class_Oone(X1)) = X0 )
| ~ spl53_404 ),
inference(avatar_component_clause,[],[f8074]) ).
fof(f9259,plain,
( spl53_568
| ~ spl53_12
| ~ spl53_399 ),
inference(avatar_split_clause,[],[f8266,f8054,f6226,f9257]) ).
fof(f9257,plain,
( spl53_568
<=> ! [X0] : c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_568])]) ).
fof(f6226,plain,
( spl53_12
<=> class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_12])]) ).
fof(f8054,plain,
( spl53_399
<=> ! [X0,X1] :
( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = X0
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_399])]) ).
fof(f8266,plain,
( ! [X0] : c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X0)) = X0
| ~ spl53_12
| ~ spl53_399 ),
inference(resolution,[],[f8055,f6228]) ).
fof(f6228,plain,
( class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal)
| ~ spl53_12 ),
inference(avatar_component_clause,[],[f6226]) ).
fof(f8055,plain,
( ! [X0,X1] :
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = X0 )
| ~ spl53_399 ),
inference(avatar_component_clause,[],[f8054]) ).
fof(f9179,plain,
( spl53_567
| ~ spl53_11
| ~ spl53_399 ),
inference(avatar_split_clause,[],[f8265,f8054,f6221,f9177]) ).
fof(f9177,plain,
( spl53_567
<=> ! [X0] : c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_567])]) ).
fof(f6221,plain,
( spl53_11
<=> class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_11])]) ).
fof(f8265,plain,
( ! [X0] : c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,X0)) = X0
| ~ spl53_11
| ~ spl53_399 ),
inference(resolution,[],[f8055,f6223]) ).
fof(f6223,plain,
( class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex)
| ~ spl53_11 ),
inference(avatar_component_clause,[],[f6221]) ).
fof(f9154,plain,
spl53_566,
inference(avatar_split_clause,[],[f6160,f9152]) ).
fof(f9152,plain,
( spl53_566
<=> ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK21),X1) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK49),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_566])]) ).
fof(f6160,plain,
! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK21),X1) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK49),X1),
inference(forward_demodulation,[],[f5616,f4171]) ).
fof(f5616,plain,
! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK49),X1),
inference(cnf_transformation,[],[f3914]) ).
fof(f3914,plain,
( ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK49),X1)
& c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK49) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK49])],[f2318,f3913]) ).
fof(f3913,plain,
( ? [X0] :
( ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1)
& c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X0) )
=> ( ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK49),X1)
& c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK49) ) ),
introduced(choice_axiom,[]) ).
fof(f2318,plain,
? [X0] :
( ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1)
& c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X0) ),
inference(rectify,[],[f733]) ).
fof(f733,axiom,
? [X82] :
( ! [X2] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X2)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X82),X2)
& c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X82) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096EX_Aq_O_Apsize_Aq_A_061_Apsize_Ap_A_G_A_IALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_J_096) ).
fof(f9150,plain,
spl53_565,
inference(avatar_split_clause,[],[f6076,f9148]) ).
fof(f9148,plain,
( spl53_565
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_565])]) ).
fof(f6076,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ sP2(X0,X1) ),
inference(forward_demodulation,[],[f6075,f4201]) ).
fof(f6075,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ sP2(X0,X1) ),
inference(forward_demodulation,[],[f5726,f4346]) ).
fof(f5726,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
| ~ sP2(X0,X1) ),
inference(definition_unfolding,[],[f4733,f4205]) ).
fof(f4733,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f3651]) ).
fof(f3651,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
& ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ sP2(X0,X1) ) ),
inference(flattening,[],[f3650]) ).
fof(f3650,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
& ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ sP2(X0,X1) ) ),
inference(nnf_transformation,[],[f3482]) ).
fof(f3482,plain,
! [X0,X1] :
( sP2(X0,X1)
<=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f9146,plain,
spl53_564,
inference(avatar_split_clause,[],[f6074,f9144]) ).
fof(f9144,plain,
( spl53_564
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_564])]) ).
fof(f6074,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP2(X0,X1) ),
inference(forward_demodulation,[],[f6073,f4201]) ).
fof(f6073,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP2(X0,X1) ),
inference(forward_demodulation,[],[f6072,f4346]) ).
fof(f6072,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
| ~ sP2(X0,X1) ),
inference(forward_demodulation,[],[f6071,f4201]) ).
fof(f6071,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
| ~ sP2(X0,X1) ),
inference(forward_demodulation,[],[f5725,f4346]) ).
fof(f5725,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
| ~ sP2(X0,X1) ),
inference(definition_unfolding,[],[f4735,f4205,f4205]) ).
fof(f4735,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f3651]) ).
fof(f9142,plain,
spl53_563,
inference(avatar_split_clause,[],[f6070,f9140]) ).
fof(f9140,plain,
( spl53_563
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_563])]) ).
fof(f6070,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP2(X0,X1) ),
inference(forward_demodulation,[],[f6069,f4201]) ).
fof(f6069,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP2(X0,X1) ),
inference(forward_demodulation,[],[f5724,f4346]) ).
fof(f5724,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP2(X0,X1) ),
inference(definition_unfolding,[],[f4736,f4205]) ).
fof(f4736,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f3651]) ).
fof(f9138,plain,
( spl53_562
| ~ spl53_8
| ~ spl53_397 ),
inference(avatar_split_clause,[],[f8263,f8046,f6206,f9136]) ).
fof(f9136,plain,
( spl53_562
<=> ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_562])]) ).
fof(f6206,plain,
( spl53_8
<=> class_Lattices_Oboolean__algebra(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_8])]) ).
fof(f8046,plain,
( spl53_397
<=> ! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0
| ~ class_Lattices_Oboolean__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_397])]) ).
fof(f8263,plain,
( ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool,X0)) = X0
| ~ spl53_8
| ~ spl53_397 ),
inference(resolution,[],[f8047,f6208]) ).
fof(f6208,plain,
( class_Lattices_Oboolean__algebra(tc_HOL_Obool)
| ~ spl53_8 ),
inference(avatar_component_clause,[],[f6206]) ).
fof(f8047,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oboolean__algebra(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0 )
| ~ spl53_397 ),
inference(avatar_component_clause,[],[f8046]) ).
fof(f9134,plain,
spl53_561,
inference(avatar_split_clause,[],[f6060,f9132]) ).
fof(f9132,plain,
( spl53_561
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_561])]) ).
fof(f6060,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ sP1(X0,X1) ),
inference(forward_demodulation,[],[f6059,f4201]) ).
fof(f6059,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ sP1(X0,X1) ),
inference(forward_demodulation,[],[f5719,f4346]) ).
fof(f5719,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
| ~ sP1(X0,X1) ),
inference(definition_unfolding,[],[f4725,f4205]) ).
fof(f4725,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f3648]) ).
fof(f3648,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
& ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ sP1(X0,X1) ) ),
inference(flattening,[],[f3647]) ).
fof(f3647,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
& ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ sP1(X0,X1) ) ),
inference(nnf_transformation,[],[f3480]) ).
fof(f3480,plain,
! [X0,X1] :
( sP1(X0,X1)
<=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f9130,plain,
spl53_560,
inference(avatar_split_clause,[],[f6058,f9128]) ).
fof(f9128,plain,
( spl53_560
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_560])]) ).
fof(f6058,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP1(X0,X1) ),
inference(forward_demodulation,[],[f6057,f4201]) ).
fof(f6057,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP1(X0,X1) ),
inference(forward_demodulation,[],[f6056,f4346]) ).
fof(f6056,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
| ~ sP1(X0,X1) ),
inference(forward_demodulation,[],[f6055,f4201]) ).
fof(f6055,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
| ~ sP1(X0,X1) ),
inference(forward_demodulation,[],[f5718,f4346]) ).
fof(f5718,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
| ~ sP1(X0,X1) ),
inference(definition_unfolding,[],[f4727,f4205,f4205]) ).
fof(f4727,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f3648]) ).
fof(f9126,plain,
spl53_559,
inference(avatar_split_clause,[],[f6054,f9124]) ).
fof(f9124,plain,
( spl53_559
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_559])]) ).
fof(f6054,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP1(X0,X1) ),
inference(forward_demodulation,[],[f6053,f4201]) ).
fof(f6053,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP1(X0,X1) ),
inference(forward_demodulation,[],[f5717,f4346]) ).
fof(f5717,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP1(X0,X1) ),
inference(definition_unfolding,[],[f4728,f4205]) ).
fof(f4728,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f3648]) ).
fof(f9122,plain,
spl53_558,
inference(avatar_split_clause,[],[f6045,f9120]) ).
fof(f9120,plain,
( spl53_558
<=> ! [X2,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_558])]) ).
fof(f6045,plain,
! [X2,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(forward_demodulation,[],[f5816,f5650]) ).
fof(f5650,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(definition_unfolding,[],[f4355,f4205,f4205]) ).
fof(f4355,plain,
! [X0,X1] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X0)),
inference(cnf_transformation,[],[f1464]) ).
fof(f1464,plain,
! [X0,X1] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X0)),
inference(rectify,[],[f313]) ).
fof(f313,axiom,
! [X3,X10] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,c_Nat_OSuc(X3)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(f5816,plain,
! [X2,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(equality_resolution,[],[f5693]) ).
fof(f5693,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X0 ),
inference(definition_unfolding,[],[f4688,f4205]) ).
fof(f4688,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X0 ),
inference(cnf_transformation,[],[f3624]) ).
fof(f3624,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ! [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X0 )
& ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK34(X0,X1))) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK34])],[f3622,f3623]) ).
fof(f3623,plain,
! [X0,X1] :
( ? [X3] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) = X0
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK34(X0,X1))) = X0 ),
introduced(choice_axiom,[]) ).
fof(f3622,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ! [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X0 )
& ( ? [X3] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(rectify,[],[f3621]) ).
fof(f3621,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ! [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X0 )
& ( ? [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f1713]) ).
fof(f1713,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
<=> ? [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = X0 ),
inference(rectify,[],[f203]) ).
fof(f203,axiom,
! [X8,X13] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,X8)
<=> ? [X52] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,X52)) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
fof(f9118,plain,
spl53_557,
inference(avatar_split_clause,[],[f6009,f9116]) ).
fof(f9116,plain,
( spl53_557
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_557])]) ).
fof(f6009,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
inference(forward_demodulation,[],[f5648,f5634]) ).
fof(f5634,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(definition_unfolding,[],[f4206,f4205]) ).
fof(f4206,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f1324]) ).
fof(f1324,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(rectify,[],[f211]) ).
fof(f211,axiom,
! [X3] : c_Nat_OSuc(X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(f5648,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(definition_unfolding,[],[f4343,f4205]) ).
fof(f4343,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
inference(cnf_transformation,[],[f1452]) ).
fof(f1452,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))),
inference(rectify,[],[f202]) ).
fof(f202,axiom,
! [X10,X25] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X25))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
fof(f9114,plain,
spl53_556,
inference(avatar_split_clause,[],[f6008,f9112]) ).
fof(f9112,plain,
( spl53_556
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_556])]) ).
fof(f6008,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))),
inference(forward_demodulation,[],[f5647,f5634]) ).
fof(f5647,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(definition_unfolding,[],[f4342,f4205]) ).
fof(f4342,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))),
inference(cnf_transformation,[],[f1451]) ).
fof(f1451,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))),
inference(rectify,[],[f201]) ).
fof(f201,axiom,
! [X10,X25] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X10))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
fof(f9110,plain,
spl53_555,
inference(avatar_split_clause,[],[f5982,f9108]) ).
fof(f9108,plain,
( spl53_555
<=> ! [X0] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X0) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK21),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_555])]) ).
fof(f5982,plain,
! [X0] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X0) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK21),X0),
inference(forward_demodulation,[],[f4222,f4171]) ).
fof(f4222,plain,
! [X0] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X0) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X0)),
inference(cnf_transformation,[],[f1340]) ).
fof(f1340,plain,
! [X0] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X0) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X0)),
inference(rectify,[],[f626]) ).
fof(f626,axiom,
! [X2] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X2) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_q_I2_J) ).
fof(f9106,plain,
spl53_554,
inference(avatar_split_clause,[],[f5937,f9104]) ).
fof(f5937,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,[],[f5438]) ).
fof(f5438,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,[],[f3259]) ).
fof(f3259,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,[],[f3258]) ).
fof(f3258,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,[],[f2173]) ).
fof(f2173,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,[],[f982]) ).
fof(f982,axiom,
! [X11,X20,X4,X5] :
( class_Rings_Odvd(X5)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X20),X11) = X4
=> c_Rings_Odvd__class_Odvd(X5,X20,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvdI) ).
fof(f9102,plain,
spl53_553,
inference(avatar_split_clause,[],[f5921,f9100]) ).
fof(f9100,plain,
( spl53_553
<=> ! [X4,X0,X2] :
( hBOOL(hAPP(X0,X4))
| ~ sP14(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_553])]) ).
fof(f5921,plain,
! [X2,X0,X4] :
( hBOOL(hAPP(X0,X4))
| ~ sP14(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4),X2) ),
inference(equality_resolution,[],[f5266]) ).
fof(f5266,plain,
! [X2,X0,X1,X4] :
( hBOOL(hAPP(X0,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X1
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f3828]) ).
fof(f9098,plain,
spl53_552,
inference(avatar_split_clause,[],[f5920,f9096]) ).
fof(f9096,plain,
( spl53_552
<=> ! [X4,X0,X2] :
( hBOOL(hAPP(X0,X4))
| ~ sP13(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_552])]) ).
fof(f5920,plain,
! [X2,X0,X4] :
( hBOOL(hAPP(X0,X4))
| ~ sP13(X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4),X2) ),
inference(equality_resolution,[],[f5258]) ).
fof(f5258,plain,
! [X2,X0,X1,X4] :
( hBOOL(hAPP(X0,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X1
| ~ sP13(X0,X1,X2) ),
inference(cnf_transformation,[],[f3822]) ).
fof(f9094,plain,
( spl53_551
| ~ spl53_349
| ~ spl53_394 ),
inference(avatar_split_clause,[],[f8237,f8034,f7807,f9092]) ).
fof(f9092,plain,
( spl53_551
<=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_551])]) ).
fof(f7807,plain,
( spl53_349
<=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_349])]) ).
fof(f8237,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) != X0
| ~ spl53_349
| ~ spl53_394 ),
inference(superposition,[],[f7808,f8035]) ).
fof(f7808,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X0
| ~ spl53_349 ),
inference(avatar_component_clause,[],[f7807]) ).
fof(f9090,plain,
spl53_550,
inference(avatar_split_clause,[],[f5865,f9088]) ).
fof(f9088,plain,
( spl53_550
<=> ! [X2,X0] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ class_Rings_Oidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_550])]) ).
fof(f5865,plain,
! [X2,X0] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ class_Rings_Oidom(X2) ),
inference(equality_resolution,[],[f4973]) ).
fof(f4973,plain,
! [X2,X0,X1] :
( c_Polynomial_Osmult(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Groups_Ozero__class_Ozero(X2) != X1
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f3726]) ).
fof(f9086,plain,
spl53_549,
inference(avatar_split_clause,[],[f5785,f9084]) ).
fof(f9084,plain,
( spl53_549
<=> ! [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,[spl53_549])]) ).
fof(f5785,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,[],[f4459]) ).
fof(f4459,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,[],[f3559]) ).
fof(f9082,plain,
spl53_548,
inference(avatar_split_clause,[],[f5649,f9080]) ).
fof(f9080,plain,
( spl53_548
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_548])]) ).
fof(f5649,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(definition_unfolding,[],[f4344,f4205]) ).
fof(f4344,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Nat_OSuc(X1)),
inference(cnf_transformation,[],[f1453]) ).
fof(f1453,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Nat_OSuc(X1)),
inference(rectify,[],[f446]) ).
fof(f446,axiom,
! [X3,X10] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,X3),c_Nat_OSuc(X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
fof(f9078,plain,
spl53_547,
inference(avatar_split_clause,[],[f5312,f9076]) ).
fof(f9076,plain,
( spl53_547
<=> ! [X2,X0,X1,X3] : hAPP(hAPP(c_Power_Opower_Opower(X3,X2,X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_547])]) ).
fof(f5312,plain,
! [X2,X3,X0,X1] : hAPP(hAPP(c_Power_Opower_Opower(X3,X2,X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
inference(cnf_transformation,[],[f2081]) ).
fof(f2081,plain,
! [X0,X1,X2,X3] : hAPP(hAPP(c_Power_Opower_Opower(X3,X2,X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
inference(rectify,[],[f486]) ).
fof(f486,axiom,
! [X9,X65,X66,X5] : hAPP(hAPP(c_Power_Opower_Opower(X5,X66,X65),X9),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X66,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).
fof(f9074,plain,
spl53_546,
inference(avatar_split_clause,[],[f5272,f9072]) ).
fof(f9072,plain,
( spl53_546
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP14(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_546])]) ).
fof(f5272,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP14(X2,X1,X0) ),
inference(cnf_transformation,[],[f3829]) ).
fof(f3829,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP14(X2,X1,X0) )
& ( sP14(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
inference(nnf_transformation,[],[f3503]) ).
fof(f3503,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
<=> sP14(X2,X1,X0) ),
inference(definition_folding,[],[f3104,f3502]) ).
fof(f3104,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,[],[f2064]) ).
fof(f2064,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,[],[f270]) ).
fof(f270,axiom,
! [X32,X9,X48] :
( hBOOL(hAPP(X48,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X9,X32)))
<=> ~ ( ? [X54] :
( ~ hBOOL(hAPP(X48,X54))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X54) = X9 )
| ( ~ hBOOL(hAPP(X48,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X32) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
fof(f9070,plain,
spl53_545,
inference(avatar_split_clause,[],[f5271,f9068]) ).
fof(f9068,plain,
( spl53_545
<=> ! [X2,X0,X1] :
( sP14(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_545])]) ).
fof(f5271,plain,
! [X2,X0,X1] :
( sP14(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f3829]) ).
fof(f9066,plain,
spl53_544,
inference(avatar_split_clause,[],[f5264,f9064]) ).
fof(f9064,plain,
( spl53_544
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP13(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_544])]) ).
fof(f5264,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP13(X2,X1,X0) ),
inference(cnf_transformation,[],[f3823]) ).
fof(f3823,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP13(X2,X1,X0) )
& ( sP13(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
inference(nnf_transformation,[],[f3501]) ).
fof(f3501,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
<=> sP13(X2,X1,X0) ),
inference(definition_folding,[],[f3103,f3500]) ).
fof(f3103,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,[],[f2063]) ).
fof(f2063,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,[],[f269]) ).
fof(f269,axiom,
! [X32,X9,X48] :
( hBOOL(hAPP(X48,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X9,X32)))
<=> ( ! [X54] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X54) = X9
=> hBOOL(hAPP(X48,X54)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X32)
=> hBOOL(hAPP(X48,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split) ).
fof(f9062,plain,
spl53_543,
inference(avatar_split_clause,[],[f5263,f9060]) ).
fof(f9060,plain,
( spl53_543
<=> ! [X2,X0,X1] :
( sP13(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_543])]) ).
fof(f5263,plain,
! [X2,X0,X1] :
( sP13(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f3823]) ).
fof(f9058,plain,
spl53_542,
inference(avatar_split_clause,[],[f5256,f9056]) ).
fof(f9056,plain,
( spl53_542
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
| ~ sP12(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_542])]) ).
fof(f5256,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
| ~ sP12(X2,X0,X1) ),
inference(cnf_transformation,[],[f3817]) ).
fof(f9054,plain,
spl53_541,
inference(avatar_split_clause,[],[f5251,f9052]) ).
fof(f9052,plain,
( spl53_541
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,sK44(X0,X1,X2)))
| ~ sP12(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_541])]) ).
fof(f5251,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,sK44(X0,X1,X2)))
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f3815]) ).
fof(f3815,plain,
! [X0,X1,X2] :
( ( sP12(X0,X1,X2)
| ! [X3] :
( ~ hBOOL(hAPP(X0,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X3)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X2) ) )
& ( ( hBOOL(hAPP(X0,sK44(X0,X1,X2)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(sK44(X0,X1,X2))))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),sK44(X0,X1,X2)),X2) )
| ~ sP12(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44])],[f3813,f3814]) ).
fof(f3814,plain,
! [X0,X1,X2] :
( ? [X4] :
( hBOOL(hAPP(X0,X4))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X4)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4),X2) )
=> ( hBOOL(hAPP(X0,sK44(X0,X1,X2)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(sK44(X0,X1,X2))))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),sK44(X0,X1,X2)),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f3813,plain,
! [X0,X1,X2] :
( ( sP12(X0,X1,X2)
| ! [X3] :
( ~ hBOOL(hAPP(X0,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X3)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X2) ) )
& ( ? [X4] :
( hBOOL(hAPP(X0,X4))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Nat_OSuc(X4)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4),X2) )
| ~ sP12(X0,X1,X2) ) ),
inference(rectify,[],[f3812]) ).
fof(f3812,plain,
! [X2,X0,X1] :
( ( sP12(X2,X0,X1)
| ! [X3] :
( ~ hBOOL(hAPP(X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Nat_OSuc(X3)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X1) ) )
& ( ? [X3] :
( hBOOL(hAPP(X2,X3))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Nat_OSuc(X3)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3),X1) )
| ~ sP12(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f3498]) ).
fof(f9050,plain,
( spl53_540
| ~ spl53_103
| ~ spl53_390 ),
inference(avatar_split_clause,[],[f8194,f8018,f6681,f9047]) ).
fof(f9047,plain,
( spl53_540
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_540])]) ).
fof(f8018,plain,
( spl53_390
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Ogroup__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_390])]) ).
fof(f8194,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl53_103
| ~ spl53_390 ),
inference(resolution,[],[f8019,f6683]) ).
fof(f8019,plain,
( ! [X0] :
( ~ class_Groups_Ogroup__add(X0)
| c_Groups_Ozero__class_Ozero(X0) = c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ozero__class_Ozero(X0)) )
| ~ spl53_390 ),
inference(avatar_component_clause,[],[f8018]) ).
fof(f9045,plain,
spl53_539,
inference(avatar_split_clause,[],[f5246,f9043]) ).
fof(f9043,plain,
( spl53_539
<=> ! [X2,X0,X1] :
( sP11(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_539])]) ).
fof(f5246,plain,
! [X2,X0,X1] :
( sP11(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f3811]) ).
fof(f9041,plain,
spl53_538,
inference(avatar_split_clause,[],[f5244,f9039]) ).
fof(f9039,plain,
( spl53_538
<=> ! [X2,X0,X1] :
( sP11(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK42(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_538])]) ).
fof(f5244,plain,
! [X2,X0,X1] :
( sP11(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK42(X0,X1,X2))) ),
inference(cnf_transformation,[],[f3809]) ).
fof(f3809,plain,
! [X0,X1,X2] :
( ( sP11(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK42(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK42(X0,X1,X2)),sK43(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK43(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
| ~ sP11(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK42,sK43])],[f3807,f3808]) ).
fof(f3808,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,sK42(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK42(X0,X1,X2)),sK43(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK43(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f3807,plain,
! [X0,X1,X2] :
( ( sP11(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
| ~ sP11(X0,X1,X2) ) ),
inference(rectify,[],[f3806]) ).
fof(f3806,plain,
! [X2,X1,X0] :
( ( sP11(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
| ~ sP11(X2,X1,X0) ) ),
inference(flattening,[],[f3805]) ).
fof(f3805,plain,
! [X2,X1,X0] :
( ( sP11(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
| ~ sP11(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f3496]) ).
fof(f9037,plain,
spl53_537,
inference(avatar_split_clause,[],[f5242,f9035]) ).
fof(f9035,plain,
( spl53_537
<=> ! [X2,X0,X1] :
( sP11(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK43(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_537])]) ).
fof(f5242,plain,
! [X2,X0,X1] :
( sP11(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK43(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f3809]) ).
fof(f9033,plain,
spl53_536,
inference(avatar_split_clause,[],[f5239,f9031]) ).
fof(f9031,plain,
( spl53_536
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)))
| ~ sP10(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_536])]) ).
fof(f5239,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)))
| ~ sP10(X0,X1,X2) ),
inference(cnf_transformation,[],[f3804]) ).
fof(f3804,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)))
| ~ sP10(X0,X1,X2) )
& ( sP10(X0,X1,X2)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0))) ) ),
inference(nnf_transformation,[],[f3495]) ).
fof(f3495,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)))
<=> sP10(X0,X1,X2) ),
inference(definition_folding,[],[f3100,f3494,f3493,f3492]) ).
fof(f3494,plain,
! [X0,X1,X2] :
( sP10(X0,X1,X2)
<=> ( sP9(X2,X1,X0)
& sP8(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,[sP10])]) ).
fof(f3100,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,[],[f2060]) ).
fof(f2060,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,[],[f665]) ).
fof(f665,axiom,
! [X12,X8,X48] :
( hBOOL(hAPP(X48,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X8,X12)))
<=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X12,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ! [X69] :
( ? [X59] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X69),X59) = X8
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X59,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X12,X59) )
=> hBOOL(hAPP(X48,X69)) ) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12)
=> ! [X69] :
( ? [X59] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X69),X59) = X8
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X59,X12)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X59) )
=> hBOOL(hAPP(X48,X69)) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X12
=> hBOOL(hAPP(X48,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__zdiv) ).
fof(f9029,plain,
spl53_535,
inference(avatar_split_clause,[],[f5238,f9027]) ).
fof(f9027,plain,
( spl53_535
<=> ! [X2,X0,X1] :
( sP10(X0,X1,X2)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_535])]) ).
fof(f5238,plain,
! [X2,X0,X1] :
( sP10(X0,X1,X2)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0))) ),
inference(cnf_transformation,[],[f3804]) ).
fof(f9025,plain,
spl53_534,
inference(avatar_split_clause,[],[f5237,f9023]) ).
fof(f9023,plain,
( spl53_534
<=> ! [X2,X0,X1] :
( sP8(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK40(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_534])]) ).
fof(f5237,plain,
! [X2,X0,X1] :
( sP8(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK40(X0,X1,X2))) ),
inference(cnf_transformation,[],[f3803]) ).
fof(f9021,plain,
spl53_533,
inference(avatar_split_clause,[],[f5235,f9019]) ).
fof(f9019,plain,
( spl53_533
<=> ! [X2,X0,X1] :
( sP8(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,sK41(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_533])]) ).
fof(f5235,plain,
! [X2,X0,X1] :
( sP8(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,sK41(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f3803]) ).
fof(f9017,plain,
spl53_532,
inference(avatar_split_clause,[],[f5231,f9015]) ).
fof(f9015,plain,
( spl53_532
<=> ! [X2,X0,X1] :
( sP9(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK38(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_532])]) ).
fof(f5231,plain,
! [X2,X0,X1] :
( sP9(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK38(X0,X1,X2))) ),
inference(cnf_transformation,[],[f3797]) ).
fof(f9013,plain,
spl53_531,
inference(avatar_split_clause,[],[f5228,f9011]) ).
fof(f9011,plain,
( spl53_531
<=> ! [X2,X0,X1] :
( sP9(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,sK39(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_531])]) ).
fof(f5228,plain,
! [X2,X0,X1] :
( sP9(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,sK39(X0,X1,X2)) ),
inference(cnf_transformation,[],[f3797]) ).
fof(f9009,plain,
spl53_530,
inference(avatar_split_clause,[],[f5219,f9007]) ).
fof(f9007,plain,
( spl53_530
<=> ! [X5,X2,X0,X6,X1] :
( hAPP(X0,X5) = hAPP(X0,X6)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_530])]) ).
fof(f5219,plain,
! [X2,X0,X1,X6,X5] :
( hAPP(X0,X5) = hAPP(X0,X6)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0) ),
inference(cnf_transformation,[],[f3789]) ).
fof(f9005,plain,
( spl53_529
| ~ spl53_102
| ~ spl53_390 ),
inference(avatar_split_clause,[],[f8191,f8018,f6676,f9002]) ).
fof(f9002,plain,
( spl53_529
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_529])]) ).
fof(f8191,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ spl53_102
| ~ spl53_390 ),
inference(resolution,[],[f8019,f6678]) ).
fof(f9000,plain,
spl53_528,
inference(avatar_split_clause,[],[f5194,f8998]) ).
fof(f5194,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,[],[f3079]) ).
fof(f3079,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,[],[f2048]) ).
fof(f2048,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,[],[f159]) ).
fof(f159,axiom,
! [X11,X24,X25] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X24),X11)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).
fof(f8996,plain,
spl53_527,
inference(avatar_split_clause,[],[f5191,f8994]) ).
fof(f8994,plain,
( spl53_527
<=> ! [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,[spl53_527])]) ).
fof(f5191,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,[],[f3077]) ).
fof(f3077,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,[],[f2046]) ).
fof(f2046,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,[],[f158]) ).
fof(f158,axiom,
! [X3,X11,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X11),X3)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD2) ).
fof(f8992,plain,
spl53_526,
inference(avatar_split_clause,[],[f5190,f8990]) ).
fof(f8990,plain,
( spl53_526
<=> ! [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,[spl53_526])]) ).
fof(f5190,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,[],[f3076]) ).
fof(f3076,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,[],[f2045]) ).
fof(f2045,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,[],[f157]) ).
fof(f157,axiom,
! [X3,X11,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X11),X3)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD1) ).
fof(f8988,plain,
spl53_525,
inference(avatar_split_clause,[],[f5159,f8986]) ).
fof(f8986,plain,
( spl53_525
<=> ! [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,[spl53_525])]) ).
fof(f5159,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,[],[f3041]) ).
fof(f3041,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,[],[f2022]) ).
fof(f2022,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,[],[f355]) ).
fof(f355,axiom,
! [X3,X11,X24] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,X11)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X24,X3),X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
fof(f8984,plain,
spl53_524,
inference(avatar_split_clause,[],[f5156,f8982]) ).
fof(f8982,plain,
( spl53_524
<=> ! [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,[spl53_524])]) ).
fof(f5156,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,[],[f3038]) ).
fof(f3038,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,[],[f2019]) ).
fof(f2019,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,[],[f525]) ).
fof(f525,axiom,
! [X21,X36,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X36)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X36)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(f8980,plain,
spl53_523,
inference(avatar_split_clause,[],[f5155,f8978]) ).
fof(f8978,plain,
( spl53_523
<=> ! [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,[spl53_523])]) ).
fof(f5155,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,[],[f3037]) ).
fof(f3037,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,[],[f2018]) ).
fof(f2018,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,[],[f526]) ).
fof(f526,axiom,
! [X36,X21,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X21)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X36)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(f8976,plain,
spl53_522,
inference(avatar_split_clause,[],[f5124,f8974]) ).
fof(f8974,plain,
( spl53_522
<=> ! [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,[spl53_522])]) ).
fof(f5124,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,[],[f3005]) ).
fof(f3005,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,[],[f1992]) ).
fof(f1992,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,[],[f169]) ).
fof(f169,axiom,
! [X10,X24,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X24)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).
fof(f8972,plain,
spl53_521,
inference(avatar_split_clause,[],[f5123,f8970]) ).
fof(f8970,plain,
( spl53_521
<=> ! [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,[spl53_521])]) ).
fof(f5123,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,[],[f3004]) ).
fof(f3004,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,[],[f1991]) ).
fof(f1991,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,[],[f168]) ).
fof(f168,axiom,
! [X10,X24,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X24)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).
fof(f8968,plain,
spl53_520,
inference(avatar_split_clause,[],[f5075,f8966]) ).
fof(f8966,plain,
( spl53_520
<=> ! [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,[spl53_520])]) ).
fof(f5075,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,[],[f2945]) ).
fof(f2945,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,[],[f1954]) ).
fof(f1954,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,[],[f986]) ).
fof(f986,axiom,
! [X20,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Rings_Odvd__class_Odvd(X5,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X20),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__triv__right) ).
fof(f8964,plain,
spl53_519,
inference(avatar_split_clause,[],[f5074,f8962]) ).
fof(f5074,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,[],[f2944]) ).
fof(f2944,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,[],[f1953]) ).
fof(f1953,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,[],[f987]) ).
fof(f987,axiom,
! [X20,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Rings_Odvd__class_Odvd(X5,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__triv__left) ).
fof(f8957,plain,
spl53_518,
inference(avatar_split_clause,[],[f5073,f8955]) ).
fof(f8955,plain,
( spl53_518
<=> ! [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,[spl53_518])]) ).
fof(f5073,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,[],[f2943]) ).
fof(f2943,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,[],[f1952]) ).
fof(f1952,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,[],[f189]) ).
fof(f189,axiom,
! [X33,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,X4,X33) = c_Groups_Oplus__class_Oplus(X5,X33,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f8953,plain,
spl53_517,
inference(avatar_split_clause,[],[f5027,f8951]) ).
fof(f8951,plain,
( spl53_517
<=> ! [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,[spl53_517])]) ).
fof(f5027,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,[],[f2893]) ).
fof(f2893,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,[],[f1917]) ).
fof(f1917,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,[],[f296]) ).
fof(f296,axiom,
! [X20,X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Ominus__class_Ominus(X5,X4,X20),X20) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
fof(f8949,plain,
spl53_516,
inference(avatar_split_clause,[],[f5026,f8947]) ).
fof(f8947,plain,
( spl53_516
<=> ! [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,[spl53_516])]) ).
fof(f5026,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,[],[f2892]) ).
fof(f2892,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,[],[f1916]) ).
fof(f1916,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,[],[f295]) ).
fof(f295,axiom,
! [X20,X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ominus__class_Ominus(X5,c_Groups_Oplus__class_Oplus(X5,X4,X20),X20) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
fof(f8945,plain,
spl53_515,
inference(avatar_split_clause,[],[f4734,f8943]) ).
fof(f8943,plain,
( spl53_515
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_515])]) ).
fof(f4734,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f3651]) ).
fof(f8941,plain,
spl53_514,
inference(avatar_split_clause,[],[f4726,f8939]) ).
fof(f8939,plain,
( spl53_514
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_514])]) ).
fof(f4726,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f3648]) ).
fof(f8937,plain,
spl53_513,
inference(avatar_split_clause,[],[f4723,f8935]) ).
fof(f8935,plain,
( spl53_513
<=> ! [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,[spl53_513])]) ).
fof(f4723,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,[],[f3646]) ).
fof(f3646,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,[],[f3645]) ).
fof(f3645,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,[],[f1725]) ).
fof(f1725,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,[],[f308]) ).
fof(f308,axiom,
! [X8,X13] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,X8)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X8
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__0) ).
fof(f8933,plain,
spl53_512,
inference(avatar_split_clause,[],[f4722,f8931]) ).
fof(f8931,plain,
( spl53_512
<=> ! [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,[spl53_512])]) ).
fof(f4722,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,[],[f3646]) ).
fof(f8929,plain,
spl53_511,
inference(avatar_split_clause,[],[f4720,f8927]) ).
fof(f8927,plain,
( spl53_511
<=> ! [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,[spl53_511])]) ).
fof(f4720,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,[],[f3644]) ).
fof(f3644,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,[],[f1724]) ).
fof(f1724,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,[],[f442]) ).
fof(f442,axiom,
! [X8,X13] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X13,X8)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
fof(f8925,plain,
spl53_510,
inference(avatar_split_clause,[],[f4681,f8923]) ).
fof(f8923,plain,
( spl53_510
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_510])]) ).
fof(f4681,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3617]) ).
fof(f3617,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
& ( ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
inference(flattening,[],[f3616]) ).
fof(f3616,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
& ( ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
inference(nnf_transformation,[],[f1710]) ).
fof(f1710,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
<=> ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
inference(rectify,[],[f557]) ).
fof(f557,axiom,
! [X57,X56] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X56,X57)
<=> ( X56 != X57
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X56,X57) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__le) ).
fof(f8921,plain,
spl53_509,
inference(avatar_split_clause,[],[f4664,f8919]) ).
fof(f8919,plain,
( spl53_509
<=> ! [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,[spl53_509])]) ).
fof(f4664,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,[],[f3602]) ).
fof(f3602,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,[],[f3601]) ).
fof(f3601,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,[],[f1704]) ).
fof(f1704,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,[],[f693]) ).
fof(f693,axiom,
! [X40,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X40)
<=> ( X15 = X40
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,X40) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
fof(f8917,plain,
( spl53_508
| ~ spl53_18
| ~ spl53_389 ),
inference(avatar_split_clause,[],[f8185,f8014,f6256,f8914]) ).
fof(f8914,plain,
( spl53_508
<=> 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,[spl53_508])]) ).
fof(f6256,plain,
( spl53_18
<=> class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_18])]) ).
fof(f8014,plain,
( spl53_389
<=> ! [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,[spl53_389])]) ).
fof(f8185,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))
| ~ spl53_18
| ~ spl53_389 ),
inference(resolution,[],[f8015,f6258]) ).
fof(f6258,plain,
( class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)
| ~ spl53_18 ),
inference(avatar_component_clause,[],[f6256]) ).
fof(f8015,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)) )
| ~ spl53_389 ),
inference(avatar_component_clause,[],[f8014]) ).
fof(f8912,plain,
spl53_507,
inference(avatar_split_clause,[],[f4587,f8910]) ).
fof(f8910,plain,
( spl53_507
<=> ! [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,[spl53_507])]) ).
fof(f4587,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,[],[f2603]) ).
fof(f2603,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,[],[f1649]) ).
fof(f1649,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,[],[f706]) ).
fof(f706,axiom,
! [X3,X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X3)
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X10,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__less) ).
fof(f8908,plain,
spl53_506,
inference(avatar_split_clause,[],[f4575,f8906]) ).
fof(f8906,plain,
( spl53_506
<=> ! [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,[spl53_506])]) ).
fof(f4575,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,[],[f2592]) ).
fof(f2592,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,[],[f2591]) ).
fof(f2591,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,[],[f1638]) ).
fof(f1638,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,[],[f163]) ).
fof(f163,axiom,
! [X3,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X10)
=> X3 = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
fof(f8904,plain,
spl53_505,
inference(avatar_split_clause,[],[f4574,f8902]) ).
fof(f8902,plain,
( spl53_505
<=> ! [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,[spl53_505])]) ).
fof(f4574,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,[],[f2590]) ).
fof(f2590,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,[],[f2589]) ).
fof(f2589,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,[],[f1637]) ).
fof(f1637,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,[],[f165]) ).
fof(f165,axiom,
! [X3,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X3)
=> ( X3 != X10
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
fof(f8900,plain,
spl53_504,
inference(avatar_split_clause,[],[f4569,f8898]) ).
fof(f8898,plain,
( spl53_504
<=> ! [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,[spl53_504])]) ).
fof(f4569,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,[],[f2584]) ).
fof(f2584,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,[],[f1632]) ).
fof(f1632,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,[],[f441]) ).
fof(f441,axiom,
! [X3,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X3)
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).
fof(f8896,plain,
spl53_503,
inference(avatar_split_clause,[],[f4566,f8894]) ).
fof(f8894,plain,
( spl53_503
<=> ! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_503])]) ).
fof(f4566,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f2581]) ).
fof(f2581,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(flattening,[],[f2580]) ).
fof(f2580,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(ennf_transformation,[],[f1629]) ).
fof(f1629,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
=> X0 = X1 ) ),
inference(rectify,[],[f607]) ).
fof(f607,axiom,
! [X61,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X36,X61)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X61,X36)
=> X36 = X61 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__antisym) ).
fof(f8892,plain,
spl53_502,
inference(avatar_split_clause,[],[f4564,f8890]) ).
fof(f8890,plain,
( spl53_502
<=> ! [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,[spl53_502])]) ).
fof(f4564,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,[],[f2578]) ).
fof(f2578,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,[],[f2577]) ).
fof(f2577,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,[],[f1627]) ).
fof(f1627,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,[],[f696]) ).
fof(f696,axiom,
! [X61,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X36,X61)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X61,X36)
=> X36 = X61 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__antisym) ).
fof(f8888,plain,
spl53_501,
inference(avatar_split_clause,[],[f4557,f8886]) ).
fof(f8886,plain,
( spl53_501
<=> ! [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,[spl53_501])]) ).
fof(f4557,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,[],[f2569]) ).
fof(f2569,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,[],[f2568]) ).
fof(f2568,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,[],[f1621]) ).
fof(f1621,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,[],[f177]) ).
fof(f177,axiom,
! [X21,X7] :
( X7 != X21
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X21)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
fof(f8884,plain,
spl53_500,
inference(avatar_split_clause,[],[f4549,f8882]) ).
fof(f4549,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,[],[f2560]) ).
fof(f2560,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,[],[f2559]) ).
fof(f2559,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,[],[f1613]) ).
fof(f1613,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,[],[f988]) ).
fof(f988,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> ( c_Rings_Odvd__class_Odvd(X5,c_Groups_Ozero__class_Ozero(X5),X4)
=> c_Groups_Ozero__class_Ozero(X5) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__0__left) ).
fof(f8880,plain,
spl53_499,
inference(avatar_split_clause,[],[f4543,f8878]) ).
fof(f8878,plain,
( spl53_499
<=> ! [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,[spl53_499])]) ).
fof(f4543,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,[],[f2553]) ).
fof(f2553,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,[],[f1607]) ).
fof(f1607,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,[],[f301]) ).
fof(f301,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oone__class_Oone(X5)),X4) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(f8876,plain,
spl53_498,
inference(avatar_split_clause,[],[f4542,f8874]) ).
fof(f8874,plain,
( spl53_498
<=> ! [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,[spl53_498])]) ).
fof(f4542,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,[],[f2552]) ).
fof(f2552,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,[],[f1606]) ).
fof(f1606,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,[],[f300]) ).
fof(f300,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Oone__class_Oone(X5)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(f8872,plain,
( spl53_497
| ~ spl53_17
| ~ spl53_389 ),
inference(avatar_split_clause,[],[f8184,f8014,f6251,f8869]) ).
fof(f8869,plain,
( spl53_497
<=> 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,[spl53_497])]) ).
fof(f6251,plain,
( spl53_17
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_17])]) ).
fof(f8184,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))
| ~ spl53_17
| ~ spl53_389 ),
inference(resolution,[],[f8015,f6253]) ).
fof(f6253,plain,
( class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ spl53_17 ),
inference(avatar_component_clause,[],[f6251]) ).
fof(f8867,plain,
spl53_496,
inference(avatar_split_clause,[],[f4541,f8865]) ).
fof(f8865,plain,
( spl53_496
<=> ! [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,[spl53_496])]) ).
fof(f4541,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,[],[f2551]) ).
fof(f2551,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,[],[f1605]) ).
fof(f1605,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,[],[f347]) ).
fof(f347,axiom,
! [X7,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(f8863,plain,
spl53_495,
inference(avatar_split_clause,[],[f4528,f8861]) ).
fof(f8861,plain,
( spl53_495
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Rings_Ocomm__semiring__0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_495])]) ).
fof(f4528,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(cnf_transformation,[],[f2538]) ).
fof(f2538,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(ennf_transformation,[],[f1592]) ).
fof(f1592,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(rectify,[],[f786]) ).
fof(f786,axiom,
! [X14,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_Osmult(X5,c_Groups_Ozero__class_Ozero(X5),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__0__left) ).
fof(f8859,plain,
spl53_494,
inference(avatar_split_clause,[],[f4526,f8857]) ).
fof(f8857,plain,
( spl53_494
<=> ! [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,[spl53_494])]) ).
fof(f4526,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,[],[f2536]) ).
fof(f2536,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,[],[f1590]) ).
fof(f1590,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,[],[f305]) ).
fof(f305,axiom,
! [X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oone__class_Oone(X5)),X4) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__left) ).
fof(f8855,plain,
spl53_493,
inference(avatar_split_clause,[],[f4525,f8853]) ).
fof(f8853,plain,
( spl53_493
<=> ! [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,[spl53_493])]) ).
fof(f4525,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,[],[f2535]) ).
fof(f2535,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,[],[f1589]) ).
fof(f1589,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,[],[f303]) ).
fof(f303,axiom,
! [X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Oone__class_Oone(X5)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__right) ).
fof(f8851,plain,
spl53_492,
inference(avatar_split_clause,[],[f4524,f8849]) ).
fof(f8849,plain,
( spl53_492
<=> ! [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,[spl53_492])]) ).
fof(f4524,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,[],[f2534]) ).
fof(f2534,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,[],[f1588]) ).
fof(f1588,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,[],[f348]) ).
fof(f348,axiom,
! [X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one__right) ).
fof(f8847,plain,
spl53_491,
inference(avatar_split_clause,[],[f4522,f8845]) ).
fof(f8845,plain,
( spl53_491
<=> ! [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,[spl53_491])]) ).
fof(f4522,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,[],[f2532]) ).
fof(f2532,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,[],[f1586]) ).
fof(f1586,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,[],[f717]) ).
fof(f717,axiom,
! [X6,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X6) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).
fof(f8843,plain,
spl53_490,
inference(avatar_split_clause,[],[f4521,f8841]) ).
fof(f8841,plain,
( spl53_490
<=> ! [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,[spl53_490])]) ).
fof(f4521,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,[],[f2531]) ).
fof(f2531,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,[],[f1585]) ).
fof(f1585,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,[],[f718]) ).
fof(f718,axiom,
! [X14,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),X14,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).
fof(f8839,plain,
spl53_489,
inference(avatar_split_clause,[],[f4512,f8837]) ).
fof(f8837,plain,
( spl53_489
<=> ! [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,[spl53_489])]) ).
fof(f4512,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,[],[f2524]) ).
fof(f2524,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,[],[f1578]) ).
fof(f1578,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,[],[f304]) ).
fof(f304,axiom,
! [X4,X5] :
( class_Groups_Ocomm__monoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oone__class_Oone(X5)),X4) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1) ).
fof(f8835,plain,
spl53_488,
inference(avatar_split_clause,[],[f4511,f8833]) ).
fof(f8833,plain,
( spl53_488
<=> ! [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,[spl53_488])]) ).
fof(f4511,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,[],[f2523]) ).
fof(f2523,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,[],[f1577]) ).
fof(f1577,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,[],[f302]) ).
fof(f302,axiom,
! [X4,X5] :
( class_Groups_Ocomm__monoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X4),c_Groups_Oone__class_Oone(X5)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
fof(f8831,plain,
spl53_487,
inference(avatar_split_clause,[],[f4501,f8829]) ).
fof(f8829,plain,
( spl53_487
<=> ! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,X0) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Ogroup__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_487])]) ).
fof(f4501,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,X0) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Ogroup__add(X1) ),
inference(cnf_transformation,[],[f2516]) ).
fof(f2516,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,X0) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Ogroup__add(X1) ),
inference(ennf_transformation,[],[f1570]) ).
fof(f1570,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ouminus__class_Ouminus(X1,X0) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(rectify,[],[f862]) ).
fof(f862,axiom,
! [X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ouminus__class_Ouminus(X5,X4) = c_Groups_Ominus__class_Ominus(X5,c_Groups_Ozero__class_Ozero(X5),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0) ).
fof(f8825,plain,
spl53_486,
inference(avatar_split_clause,[],[f4500,f8823]) ).
fof(f8823,plain,
( spl53_486
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Groups_Ogroup__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_486])]) ).
fof(f4500,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Groups_Ogroup__add(X1) ),
inference(cnf_transformation,[],[f2515]) ).
fof(f2515,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Groups_Ogroup__add(X1) ),
inference(ennf_transformation,[],[f1569]) ).
fof(f1569,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0) ),
inference(rectify,[],[f916]) ).
fof(f916,axiom,
! [X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Groups_Oplus__class_Oplus(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__minus) ).
fof(f8821,plain,
spl53_485,
inference(avatar_split_clause,[],[f4499,f8819]) ).
fof(f8819,plain,
( spl53_485
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_Groups_Ogroup__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_485])]) ).
fof(f4499,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_Groups_Ogroup__add(X1) ),
inference(cnf_transformation,[],[f2514]) ).
fof(f2514,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_Groups_Ogroup__add(X1) ),
inference(ennf_transformation,[],[f1568]) ).
fof(f1568,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ouminus__class_Ouminus(X1,X0)) ),
inference(rectify,[],[f918]) ).
fof(f918,axiom,
! [X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Ouminus__class_Ouminus(X5,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__minus) ).
fof(f8817,plain,
spl53_484,
inference(avatar_split_clause,[],[f4494,f8815]) ).
fof(f8815,plain,
( spl53_484
<=> ! [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,[spl53_484])]) ).
fof(f4494,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,[],[f2509]) ).
fof(f2509,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,[],[f1563]) ).
fof(f1563,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,[],[f714]) ).
fof(f714,axiom,
! [X14,X5] :
( class_Groups_Oab__group__add(X5)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5),X14,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__poly__code_I2_J) ).
fof(f8813,plain,
spl53_483,
inference(avatar_split_clause,[],[f4493,f8811]) ).
fof(f8811,plain,
( spl53_483
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Groups_Oab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_483])]) ).
fof(f4493,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Groups_Oab__group__add(X1) ),
inference(cnf_transformation,[],[f2508]) ).
fof(f2508,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Groups_Oab__group__add(X1) ),
inference(ennf_transformation,[],[f1562]) ).
fof(f1562,plain,
! [X0,X1] :
( class_Groups_Oab__group__add(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0),X0) ),
inference(rectify,[],[f915]) ).
fof(f915,axiom,
! [X4,X5] :
( class_Groups_Oab__group__add(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Groups_Oplus__class_Oplus(X5,c_Groups_Ouminus__class_Ouminus(X5,X4),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__left__minus) ).
fof(f8809,plain,
spl53_482,
inference(avatar_split_clause,[],[f4448,f8807]) ).
fof(f8807,plain,
( spl53_482
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ouminus__class_Ouminus(X1,X0) != X0
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_482])]) ).
fof(f4448,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ouminus__class_Ouminus(X1,X0) != X0
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3554]) ).
fof(f3554,plain,
! [X0,X1] :
( ( ( c_Groups_Ouminus__class_Ouminus(X1,X0) = X0
| c_Groups_Ozero__class_Ozero(X1) != X0 )
& ( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ouminus__class_Ouminus(X1,X0) != X0 ) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f2481]) ).
fof(f2481,plain,
! [X0,X1] :
( ( c_Groups_Ouminus__class_Ouminus(X1,X0) = X0
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f1536]) ).
fof(f1536,plain,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( c_Groups_Ouminus__class_Ouminus(X1,X0) = X0
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f898]) ).
fof(f898,axiom,
! [X9,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Groups_Ouminus__class_Ouminus(X5,X9) = X9
<=> c_Groups_Ozero__class_Ozero(X5) = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__zero) ).
fof(f8805,plain,
spl53_481,
inference(avatar_split_clause,[],[f4431,f8803]) ).
fof(f8803,plain,
( spl53_481
<=> ! [X0,X1] :
( c_RealVector_Onorm__class_Onorm(X1,X0) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_RealVector_Oreal__normed__vector(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_481])]) ).
fof(f4431,plain,
! [X0,X1] :
( c_RealVector_Onorm__class_Onorm(X1,X0) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(cnf_transformation,[],[f2469]) ).
fof(f2469,plain,
! [X0,X1] :
( c_RealVector_Onorm__class_Onorm(X1,X0) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ouminus__class_Ouminus(X1,X0))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(ennf_transformation,[],[f1524]) ).
fof(f1524,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__vector(X1)
=> c_RealVector_Onorm__class_Onorm(X1,X0) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) ),
inference(rectify,[],[f932]) ).
fof(f932,axiom,
! [X7,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_RealVector_Onorm__class_Onorm(X5,X7) = c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ouminus__class_Ouminus(X5,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__minus__cancel) ).
fof(f8801,plain,
spl53_480,
inference(avatar_split_clause,[],[f4386,f8799]) ).
fof(f8799,plain,
( spl53_480
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| X0 = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_480])]) ).
fof(f4386,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| X0 = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f1491]) ).
fof(f1491,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| X0 = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(rectify,[],[f558]) ).
fof(f558,axiom,
! [X21,X7] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X7)
| X7 = X21
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X7,X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__linear) ).
fof(f8797,plain,
spl53_479,
inference(avatar_split_clause,[],[f4353,f8795]) ).
fof(f8795,plain,
( spl53_479
<=> ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_479])]) ).
fof(f4353,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),
inference(cnf_transformation,[],[f1462]) ).
fof(f1462,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)),
inference(rectify,[],[f868]) ).
fof(f868,axiom,
! [X61,X36] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X36,X61) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X36,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X61)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__int__def) ).
fof(f8793,plain,
spl53_478,
inference(avatar_split_clause,[],[f4351,f8791]) ).
fof(f8791,plain,
( spl53_478
<=> ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_478])]) ).
fof(f4351,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)),
inference(cnf_transformation,[],[f1460]) ).
fof(f1460,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)),
inference(rectify,[],[f860]) ).
fof(f860,axiom,
! [X51,X55] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X55,X51) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X55,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X51)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__diff__def) ).
fof(f8789,plain,
spl53_477,
inference(avatar_split_clause,[],[f4350,f8787]) ).
fof(f8787,plain,
( spl53_477
<=> ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_477])]) ).
fof(f4350,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),
inference(cnf_transformation,[],[f1459]) ).
fof(f1459,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),
inference(rectify,[],[f941]) ).
fof(f941,axiom,
! [X21,X7] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X7,X21) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X7,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X21)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__diff__def) ).
fof(f8785,plain,
( spl53_476
| ~ spl53_448 ),
inference(avatar_split_clause,[],[f8594,f8442,f8783]) ).
fof(f8783,plain,
( spl53_476
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X1)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_476])]) ).
fof(f8442,plain,
( spl53_448
<=> ! [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,[spl53_448])]) ).
fof(f8594,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X1)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl53_448 ),
inference(factoring,[],[f8443]) ).
fof(f8443,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) )
| ~ spl53_448 ),
inference(avatar_component_clause,[],[f8442]) ).
fof(f8781,plain,
spl53_475,
inference(avatar_split_clause,[],[f4310,f8779]) ).
fof(f8779,plain,
( spl53_475
<=> ! [X0] :
( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_475])]) ).
fof(f4310,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ),
inference(cnf_transformation,[],[f2408]) ).
fof(f2408,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ),
inference(ennf_transformation,[],[f1427]) ).
fof(f1427,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X0) ),
inference(rectify,[],[f637]) ).
fof(f637,axiom,
! [X4] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X4
=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__self) ).
fof(f8777,plain,
spl53_474,
inference(avatar_split_clause,[],[f4294,f8775]) ).
fof(f8775,plain,
( spl53_474
<=> ! [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,[spl53_474])]) ).
fof(f4294,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,[],[f2392]) ).
fof(f2392,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,[],[f1411]) ).
fof(f1411,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,[],[f466]) ).
fof(f466,axiom,
! [X5] :
( class_Power_Opower(X5)
=> c_Power_Opower__class_Opower(X5) = c_Power_Opower_Opower(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Otimes__class_Otimes(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__power__power) ).
fof(f8773,plain,
spl53_473,
inference(avatar_split_clause,[],[f4219,f8771]) ).
fof(f8771,plain,
( spl53_473
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_473])]) ).
fof(f4219,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
inference(cnf_transformation,[],[f1337]) ).
fof(f1337,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
inference(rectify,[],[f574]) ).
fof(f574,axiom,
! [X36] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X36),X36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__nonzero) ).
fof(f8769,plain,
spl53_472,
inference(avatar_split_clause,[],[f4161,f8766]) ).
fof(f8766,plain,
( spl53_472
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_472])]) ).
fof(f4161,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(cnf_transformation,[],[f955]) ).
fof(f955,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_i__mult__eq2) ).
fof(f8659,plain,
( spl53_471
| ~ spl53_354
| ~ spl53_446 ),
inference(avatar_split_clause,[],[f8582,f8434,f7843,f8657]) ).
fof(f8657,plain,
( spl53_471
<=> ! [X0] : sP0(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_471])]) ).
fof(f7843,plain,
( spl53_354
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_354])]) ).
fof(f8434,plain,
( spl53_446
<=> ! [X0,X1] :
( sP0(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_446])]) ).
fof(f8582,plain,
( ! [X0] : sP0(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ spl53_354
| ~ spl53_446 ),
inference(trivial_inequality_removal,[],[f8581]) ).
fof(f8581,plain,
( ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| sP0(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) )
| ~ spl53_354
| ~ spl53_446 ),
inference(superposition,[],[f8435,f7844]) ).
fof(f7844,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ spl53_354 ),
inference(avatar_component_clause,[],[f7843]) ).
fof(f8435,plain,
( ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)
| sP0(X1,X0) )
| ~ spl53_446 ),
inference(avatar_component_clause,[],[f8434]) ).
fof(f8560,plain,
( spl53_470
| ~ spl53_16
| ~ spl53_388 ),
inference(avatar_split_clause,[],[f8183,f8010,f6246,f8557]) ).
fof(f8557,plain,
( spl53_470
<=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_470])]) ).
fof(f6246,plain,
( spl53_16
<=> class_Rings_Odivision__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_16])]) ).
fof(f8010,plain,
( spl53_388
<=> ! [X0] :
( c_Groups_Oone__class_Oone(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Odivision__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_388])]) ).
fof(f8183,plain,
( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl53_16
| ~ spl53_388 ),
inference(resolution,[],[f8011,f6248]) ).
fof(f6248,plain,
( class_Rings_Odivision__ring(tc_RealDef_Oreal)
| ~ spl53_16 ),
inference(avatar_component_clause,[],[f6246]) ).
fof(f8011,plain,
( ! [X0] :
( ~ class_Rings_Odivision__ring(X0)
| c_Groups_Oone__class_Oone(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Oone__class_Oone(X0)) )
| ~ spl53_388 ),
inference(avatar_component_clause,[],[f8010]) ).
fof(f8530,plain,
( spl53_469
| ~ spl53_330
| ~ spl53_433 ),
inference(avatar_split_clause,[],[f8384,f8380,f7730,f8527]) ).
fof(f8380,plain,
( spl53_433
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_433])]) ).
fof(f8384,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21))
| ~ spl53_330
| ~ spl53_433 ),
inference(forward_demodulation,[],[f8382,f7732]) ).
fof(f8382,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____))
| ~ spl53_433 ),
inference(avatar_component_clause,[],[f8380]) ).
fof(f8525,plain,
spl53_468,
inference(avatar_split_clause,[],[f6080,f8523]) ).
fof(f8523,plain,
( spl53_468
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_468])]) ).
fof(f6080,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| sP2(X0,X1) ),
inference(forward_demodulation,[],[f6079,f4201]) ).
fof(f6079,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP2(X0,X1) ),
inference(forward_demodulation,[],[f5728,f4346]) ).
fof(f5728,plain,
! [X0,X1] :
( sP2(X0,X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(definition_unfolding,[],[f4739,f4205]) ).
fof(f4739,plain,
! [X0,X1] :
( sP2(X0,X1)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3652]) ).
fof(f3652,plain,
! [X0,X1] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ sP2(X0,X1) )
& ( sP2(X0,X1)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f3483]) ).
fof(f3483,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
<=> sP2(X0,X1) ),
inference(definition_folding,[],[f1727,f3482]) ).
fof(f1727,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
<=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ) ) ),
inference(rectify,[],[f424]) ).
fof(f424,axiom,
! [X8,X13] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,X8)
<=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X8
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X13 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X8
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__1) ).
fof(f8521,plain,
( spl53_467
| ~ spl53_15
| ~ spl53_388 ),
inference(avatar_split_clause,[],[f8182,f8010,f6241,f8518]) ).
fof(f8518,plain,
( spl53_467
<=> c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_467])]) ).
fof(f6241,plain,
( spl53_15
<=> class_Rings_Odivision__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_15])]) ).
fof(f8182,plain,
( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ~ spl53_15
| ~ spl53_388 ),
inference(resolution,[],[f8011,f6243]) ).
fof(f6243,plain,
( class_Rings_Odivision__ring(tc_Complex_Ocomplex)
| ~ spl53_15 ),
inference(avatar_component_clause,[],[f6241]) ).
fof(f8516,plain,
spl53_466,
inference(avatar_split_clause,[],[f6078,f8514]) ).
fof(f8514,plain,
( spl53_466
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_466])]) ).
fof(f6078,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ sP2(X0,X1) ),
inference(forward_demodulation,[],[f6077,f4201]) ).
fof(f6077,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP2(X0,X1) ),
inference(forward_demodulation,[],[f5727,f4346]) ).
fof(f5727,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ sP2(X0,X1) ),
inference(definition_unfolding,[],[f4740,f4205]) ).
fof(f4740,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f3652]) ).
fof(f8512,plain,
spl53_465,
inference(avatar_split_clause,[],[f6064,f8510]) ).
fof(f8510,plain,
( spl53_465
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_465])]) ).
fof(f6064,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| sP1(X0,X1) ),
inference(forward_demodulation,[],[f6063,f4201]) ).
fof(f6063,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP1(X0,X1) ),
inference(forward_demodulation,[],[f5721,f4346]) ).
fof(f5721,plain,
! [X0,X1] :
( sP1(X0,X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(definition_unfolding,[],[f4731,f4205]) ).
fof(f4731,plain,
! [X0,X1] :
( sP1(X0,X1)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3649]) ).
fof(f3649,plain,
! [X0,X1] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ sP1(X0,X1) )
& ( sP1(X0,X1)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f3481]) ).
fof(f3481,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
<=> sP1(X0,X1) ),
inference(definition_folding,[],[f1726,f3480]) ).
fof(f1726,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
<=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ) ) ),
inference(rectify,[],[f425]) ).
fof(f425,axiom,
! [X8,X13] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,X8)
<=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X8
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X13 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X8
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__add) ).
fof(f8508,plain,
spl53_464,
inference(avatar_split_clause,[],[f6062,f8506]) ).
fof(f8506,plain,
( spl53_464
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_464])]) ).
fof(f6062,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ sP1(X0,X1) ),
inference(forward_demodulation,[],[f6061,f4201]) ).
fof(f6061,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP1(X0,X1) ),
inference(forward_demodulation,[],[f5720,f4346]) ).
fof(f5720,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ sP1(X0,X1) ),
inference(definition_unfolding,[],[f4732,f4205]) ).
fof(f4732,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f3649]) ).
fof(f8504,plain,
spl53_463,
inference(avatar_split_clause,[],[f5981,f8502]) ).
fof(f8502,plain,
( spl53_463
<=> ! [X0] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_463])]) ).
fof(f5981,plain,
! [X0] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),
inference(forward_demodulation,[],[f5980,f4201]) ).
fof(f5980,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X0),
inference(forward_demodulation,[],[f5637,f5634]) ).
fof(f5637,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0),
inference(definition_unfolding,[],[f4221,f4205,f4205]) ).
fof(f4221,plain,
! [X0] : c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X0),
inference(cnf_transformation,[],[f1339]) ).
fof(f1339,plain,
! [X0] : c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X0),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X3] : c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__0) ).
fof(f8500,plain,
spl53_462,
inference(avatar_split_clause,[],[f5913,f8498]) ).
fof(f8498,plain,
( spl53_462
<=> ! [X2,X1] :
( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP10(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_462])]) ).
fof(f5913,plain,
! [X2,X1] :
( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP10(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1,X2) ),
inference(equality_resolution,[],[f5221]) ).
fof(f5221,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| ~ sP10(X0,X1,X2) ),
inference(cnf_transformation,[],[f3791]) ).
fof(f3791,plain,
! [X0,X1,X2] :
( ( sP10(X0,X1,X2)
| ~ sP9(X2,X1,X0)
| ~ sP8(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP9(X2,X1,X0)
& sP8(X2,X1,X0)
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP10(X0,X1,X2) ) ),
inference(flattening,[],[f3790]) ).
fof(f3790,plain,
! [X0,X1,X2] :
( ( sP10(X0,X1,X2)
| ~ sP9(X2,X1,X0)
| ~ sP8(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP9(X2,X1,X0)
& sP8(X2,X1,X0)
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP10(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f3494]) ).
fof(f8496,plain,
spl53_461,
inference(avatar_split_clause,[],[f5795,f8494]) ).
fof(f8494,plain,
( spl53_461
<=> ! [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,[spl53_461])]) ).
fof(f5795,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,[],[f4518]) ).
fof(f4518,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,[],[f3577]) ).
fof(f8492,plain,
spl53_460,
inference(avatar_split_clause,[],[f5782,f8490]) ).
fof(f8490,plain,
( spl53_460
<=> ! [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,[spl53_460])]) ).
fof(f5782,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,[],[f4436]) ).
fof(f4436,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,[],[f3549]) ).
fof(f8488,plain,
spl53_459,
inference(avatar_split_clause,[],[f5781,f8486]) ).
fof(f8486,plain,
( spl53_459
<=> ! [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,[spl53_459])]) ).
fof(f5781,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,[],[f4435]) ).
fof(f4435,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,[],[f3548]) ).
fof(f8484,plain,
spl53_458,
inference(avatar_split_clause,[],[f5777,f8482]) ).
fof(f8482,plain,
( spl53_458
<=> ! [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,[spl53_458])]) ).
fof(f5777,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,[],[f4379]) ).
fof(f4379,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,[],[f2423]) ).
fof(f2423,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,[],[f1486]) ).
fof(f1486,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,[],[f78]) ).
fof(f78,axiom,
! [X14,X10] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X10
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X14),X10) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X14),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X10
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X14),X10) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__if) ).
fof(f8480,plain,
spl53_457,
inference(avatar_split_clause,[],[f5214,f8478]) ).
fof(f5214,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f3785]) ).
fof(f3785,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
| ~ sP7(X0,X1,X2) ),
inference(rectify,[],[f3784]) ).
fof(f3784,plain,
! [X2,X1,X0] :
( ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
| ~ sP7(X2,X1,X0) ),
inference(nnf_transformation,[],[f3490]) ).
fof(f3490,plain,
! [X2,X1,X0] :
( ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
| ~ sP7(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f8476,plain,
spl53_456,
inference(avatar_split_clause,[],[f5108,f8474]) ).
fof(f8474,plain,
( spl53_456
<=> ! [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,[spl53_456])]) ).
fof(f5108,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,[],[f3757]) ).
fof(f3757,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,[],[f3756]) ).
fof(f3756,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,[],[f2990]) ).
fof(f2990,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,[],[f1981]) ).
fof(f1981,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,[],[f544]) ).
fof(f544,axiom,
! [X40,X15,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X15,X40)
<=> ( X15 = X40
| c_Orderings_Oord__class_Oless(X5,X15,X40) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less) ).
fof(f8472,plain,
spl53_455,
inference(avatar_split_clause,[],[f5103,f8470]) ).
fof(f8470,plain,
( spl53_455
<=> ! [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,[spl53_455])]) ).
fof(f5103,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,[],[f2988]) ).
fof(f2988,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,[],[f2987]) ).
fof(f2987,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,[],[f1979]) ).
fof(f1979,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,[],[f512]) ).
fof(f512,axiom,
! [X4,X20,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X20,X4)
=> ~ c_Orderings_Oord__class_Oless(X5,X4,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
fof(f8468,plain,
spl53_454,
inference(avatar_split_clause,[],[f5089,f8466]) ).
fof(f8466,plain,
( spl53_454
<=> ! [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,[spl53_454])]) ).
fof(f5089,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,[],[f3752]) ).
fof(f8464,plain,
spl53_453,
inference(avatar_split_clause,[],[f5087,f8462]) ).
fof(f8462,plain,
( spl53_453
<=> ! [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,[spl53_453])]) ).
fof(f5087,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,[],[f2963]) ).
fof(f2963,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,[],[f2962]) ).
fof(f2962,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,[],[f1966]) ).
fof(f1966,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,[],[f537]) ).
fof(f537,axiom,
! [X21,X7,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X7,X21)
=> c_Orderings_Oord__class_Oless__eq(X5,X7,X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
fof(f8460,plain,
spl53_452,
inference(avatar_split_clause,[],[f5083,f8458]) ).
fof(f8458,plain,
( spl53_452
<=> ! [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,[spl53_452])]) ).
fof(f5083,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,[],[f2955]) ).
fof(f2955,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,[],[f2954]) ).
fof(f2954,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,[],[f1962]) ).
fof(f1962,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,[],[f517]) ).
fof(f517,axiom,
! [X21,X7,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X7,X21)
=> ~ c_Orderings_Oord__class_Oless(X5,X21,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
fof(f8456,plain,
spl53_451,
inference(avatar_split_clause,[],[f5024,f8454]) ).
fof(f8454,plain,
( spl53_451
<=> ! [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,[spl53_451])]) ).
fof(f5024,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,[],[f3740]) ).
fof(f3740,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,[],[f3739]) ).
fof(f3739,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,[],[f2891]) ).
fof(f2891,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,[],[f1915]) ).
fof(f1915,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,[],[f522]) ).
fof(f522,axiom,
! [X40,X15,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X15,X40)
<=> ( X15 = X40
| c_Orderings_Oord__class_Oless(X5,X40,X15) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(f8452,plain,
spl53_450,
inference(avatar_split_clause,[],[f5011,f8450]) ).
fof(f8450,plain,
( spl53_450
<=> ! [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,[spl53_450])]) ).
fof(f5011,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,[],[f2884]) ).
fof(f2884,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,[],[f2883]) ).
fof(f2883,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,[],[f1909]) ).
fof(f1909,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,[],[f538]) ).
fof(f538,axiom,
! [X7,X21,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X21,X7)
=> ~ c_Orderings_Oord__class_Oless(X5,X7,X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leD) ).
fof(f8448,plain,
spl53_449,
inference(avatar_split_clause,[],[f5000,f8446]) ).
fof(f8446,plain,
( spl53_449
<=> ! [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,[spl53_449])]) ).
fof(f5000,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,[],[f2866]) ).
fof(f2866,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,[],[f2865]) ).
fof(f2865,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,[],[f1900]) ).
fof(f1900,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,[],[f547]) ).
fof(f547,axiom,
! [X21,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X21,X7)
| c_Orderings_Oord__class_Oless__eq(X5,X7,X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
fof(f8444,plain,
spl53_448,
inference(avatar_split_clause,[],[f4999,f8442]) ).
fof(f4999,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,[],[f2864]) ).
fof(f2864,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,[],[f2863]) ).
fof(f2863,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,[],[f1899]) ).
fof(f1899,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,[],[f502]) ).
fof(f502,axiom,
! [X21,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X21,X7)
| c_Orderings_Oord__class_Oless__eq(X5,X7,X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).
fof(f8440,plain,
spl53_447,
inference(avatar_split_clause,[],[f4719,f8438]) ).
fof(f8438,plain,
( spl53_447
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)
| ~ sP0(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_447])]) ).
fof(f4719,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)
| ~ sP0(X1,X0) ),
inference(cnf_transformation,[],[f3643]) ).
fof(f3643,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)
| ~ sP0(X1,X0) )
& ( sP0(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0) ) ),
inference(nnf_transformation,[],[f3479]) ).
fof(f3479,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)
<=> sP0(X1,X0) ),
inference(definition_folding,[],[f1723,f3478]) ).
fof(f1723,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)
<=> ( ( 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)) )
| ( 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) )
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) ),
inference(rectify,[],[f656]) ).
fof(f656,axiom,
! [X12,X43] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X43,X12)
<=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X12,X43)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X43,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X43,X12)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X43) )
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__eq__0__iff) ).
fof(f8436,plain,
spl53_446,
inference(avatar_split_clause,[],[f4718,f8434]) ).
fof(f4718,plain,
! [X0,X1] :
( sP0(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3643]) ).
fof(f8432,plain,
spl53_445,
inference(avatar_split_clause,[],[f4636,f8430]) ).
fof(f8430,plain,
( spl53_445
<=> ! [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,[spl53_445])]) ).
fof(f4636,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,[],[f2660]) ).
fof(f2660,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,[],[f1686]) ).
fof(f1686,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,[],[f307]) ).
fof(f307,axiom,
! [X3,X10] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X3) = X10
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
fof(f8428,plain,
spl53_444,
inference(avatar_split_clause,[],[f4506,f8426]) ).
fof(f8426,plain,
( spl53_444
<=> ! [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,[spl53_444])]) ).
fof(f4506,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,[],[f2519]) ).
fof(f2519,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,[],[f1573]) ).
fof(f1573,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,[],[f150]) ).
fof(f150,axiom,
! [X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> c_Orderings_Oord__class_Oless(X5,X4,c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Oone__class_Oone(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one) ).
fof(f8424,plain,
spl53_443,
inference(avatar_split_clause,[],[f4480,f8422]) ).
fof(f8422,plain,
( spl53_443
<=> ! [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,[spl53_443])]) ).
fof(f4480,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,[],[f2498]) ).
fof(f2498,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,[],[f1553]) ).
fof(f1553,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,[],[f632]) ).
fof(f632,axiom,
! [X4,X5] :
( class_Divides_Osemiring__div(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Divides_Odiv__class_Odiv(X5,c_Groups_Ozero__class_Ozero(X5),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__0) ).
fof(f8420,plain,
spl53_442,
inference(avatar_split_clause,[],[f4479,f8418]) ).
fof(f8418,plain,
( spl53_442
<=> ! [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,[spl53_442])]) ).
fof(f4479,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,[],[f2497]) ).
fof(f2497,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,[],[f1552]) ).
fof(f1552,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,[],[f631]) ).
fof(f631,axiom,
! [X4,X5] :
( class_Divides_Osemiring__div(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Divides_Odiv__class_Odiv(X5,X4,c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__by__0) ).
fof(f8416,plain,
spl53_441,
inference(avatar_split_clause,[],[f4382,f8414]) ).
fof(f8414,plain,
( spl53_441
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat__Transfer_Otsub(X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_441])]) ).
fof(f4382,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat__Transfer_Otsub(X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f2424]) ).
fof(f8412,plain,
spl53_440,
inference(avatar_split_clause,[],[f4349,f8410]) ).
fof(f8410,plain,
( spl53_440
<=> ! [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,[spl53_440])]) ).
fof(f4349,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,[],[f1458]) ).
fof(f1458,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,[],[f431]) ).
fof(f431,axiom,
! [X10,X3] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__0) ).
fof(f8408,plain,
spl53_439,
inference(avatar_split_clause,[],[f4323,f8406]) ).
fof(f8406,plain,
( spl53_439
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_439])]) ).
fof(f4323,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(cnf_transformation,[],[f3523]) ).
fof(f3523,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ) ),
inference(nnf_transformation,[],[f1438]) ).
fof(f1438,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(rectify,[],[f571]) ).
fof(f571,axiom,
! [X56] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X56)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X56) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).
fof(f8404,plain,
spl53_438,
inference(avatar_split_clause,[],[f4322,f8402]) ).
fof(f8402,plain,
( spl53_438
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_438])]) ).
fof(f4322,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
inference(cnf_transformation,[],[f3523]) ).
fof(f8400,plain,
spl53_437,
inference(avatar_split_clause,[],[f4218,f8398]) ).
fof(f8398,plain,
( spl53_437
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_437])]) ).
fof(f4218,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)),
inference(cnf_transformation,[],[f1336]) ).
fof(f1336,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)),
inference(rectify,[],[f876]) ).
fof(f876,axiom,
! [X7] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X7)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__mod__minus__le__complex__mod) ).
fof(f8396,plain,
( spl53_436
| ~ spl53_232
| ~ spl53_417 ),
inference(avatar_split_clause,[],[f8335,f8126,f7321,f8394]) ).
fof(f8394,plain,
( spl53_436
<=> ! [X0,X1] : sP8(X0,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_436])]) ).
fof(f7321,plain,
( spl53_232
<=> ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_232])]) ).
fof(f8126,plain,
( spl53_417
<=> ! [X2,X0,X1] :
( sP8(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,[spl53_417])]) ).
fof(f8335,plain,
( ! [X0,X1] : sP8(X0,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ spl53_232
| ~ spl53_417 ),
inference(resolution,[],[f8127,f7322]) ).
fof(f7322,plain,
( ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1)
| ~ spl53_232 ),
inference(avatar_component_clause,[],[f7321]) ).
fof(f8127,plain,
( ! [X2,X0,X1] :
( sP8(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) )
| ~ spl53_417 ),
inference(avatar_component_clause,[],[f8126]) ).
fof(f8392,plain,
spl53_435,
inference(avatar_split_clause,[],[f4217,f8390]) ).
fof(f8390,plain,
( spl53_435
<=> ! [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,[spl53_435])]) ).
fof(f4217,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,[],[f1335]) ).
fof(f1335,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,[],[f19]) ).
fof(f19,axiom,
! [X3] : 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)),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0) ).
fof(f8388,plain,
spl53_434,
inference(avatar_split_clause,[],[f4216,f8386]) ).
fof(f8386,plain,
( spl53_434
<=> ! [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,[spl53_434])]) ).
fof(f4216,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,[],[f1334]) ).
fof(f1334,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,[],[f18]) ).
fof(f18,axiom,
! [X10] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0__right) ).
fof(f8383,plain,
spl53_433,
inference(avatar_split_clause,[],[f4160,f8380]) ).
fof(f4160,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)),
inference(cnf_transformation,[],[f552]) ).
fof(f552,axiom,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_k1n) ).
fof(f8374,plain,
( spl53_432
| ~ spl53_336
| ~ spl53_394
| ~ spl53_431 ),
inference(avatar_split_clause,[],[f8370,f8366,f8034,f7755,f8372]) ).
fof(f7755,plain,
( spl53_336
<=> ! [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,[spl53_336])]) ).
fof(f8366,plain,
( spl53_431
<=> ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oplus__class_Oplus(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,[spl53_431])]) ).
fof(f8370,plain,
( ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ spl53_336
| ~ spl53_394
| ~ spl53_431 ),
inference(forward_demodulation,[],[f8369,f7756]) ).
fof(f7756,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| ~ spl53_336 ),
inference(avatar_component_clause,[],[f7755]) ).
fof(f8369,plain,
( ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| ~ spl53_394
| ~ spl53_431 ),
inference(forward_demodulation,[],[f8367,f8035]) ).
fof(f8367,plain,
( ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| ~ spl53_431 ),
inference(avatar_component_clause,[],[f8366]) ).
fof(f8368,plain,
spl53_431,
inference(avatar_split_clause,[],[f5621,f8366]) ).
fof(f5621,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
inference(definition_unfolding,[],[f3918,f4205,f4205]) ).
fof(f3918,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(cnf_transformation,[],[f2323]) ).
fof(f2323,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(ennf_transformation,[],[f1286]) ).
fof(f1286,plain,
~ ? [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(rectify,[],[f1285]) ).
fof(f1285,negated_conjecture,
~ ? [X2,X80] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X80),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X80),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(negated_conjecture,[],[f1284]) ).
fof(f1284,conjecture,
? [X2,X80] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X80),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X80),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f8352,plain,
( spl53_430
| ~ spl53_232
| ~ spl53_416 ),
inference(avatar_split_clause,[],[f8329,f8122,f7321,f8350]) ).
fof(f8350,plain,
( spl53_430
<=> ! [X0,X1] : sP9(X0,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_430])]) ).
fof(f8329,plain,
( ! [X0,X1] : sP9(X0,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ spl53_232
| ~ spl53_416 ),
inference(resolution,[],[f8123,f7322]) ).
fof(f8308,plain,
( spl53_429
| ~ spl53_6
| ~ spl53_386 ),
inference(avatar_split_clause,[],[f8178,f8000,f6196,f8305]) ).
fof(f8305,plain,
( spl53_429
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_429])]) ).
fof(f6196,plain,
( spl53_6
<=> class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_6])]) ).
fof(f8000,plain,
( spl53_386
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Fields_Ofield__inverse__zero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_386])]) ).
fof(f8178,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ spl53_6
| ~ spl53_386 ),
inference(resolution,[],[f8001,f6198]) ).
fof(f6198,plain,
( class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex)
| ~ spl53_6 ),
inference(avatar_component_clause,[],[f6196]) ).
fof(f8001,plain,
( ! [X0] :
( ~ class_Fields_Ofield__inverse__zero(X0)
| c_Groups_Ozero__class_Ozero(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Ozero__class_Ozero(X0)) )
| ~ spl53_386 ),
inference(avatar_component_clause,[],[f8000]) ).
fof(f8271,plain,
( spl53_428
| ~ spl53_4
| ~ spl53_385 ),
inference(avatar_split_clause,[],[f8177,f7996,f6186,f8268]) ).
fof(f8268,plain,
( spl53_428
<=> 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,[spl53_428])]) ).
fof(f6186,plain,
( spl53_4
<=> class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_4])]) ).
fof(f7996,plain,
( spl53_385
<=> ! [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,[spl53_385])]) ).
fof(f8177,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))
| ~ spl53_4
| ~ spl53_385 ),
inference(resolution,[],[f7997,f6188]) ).
fof(f6188,plain,
( class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal)
| ~ spl53_4 ),
inference(avatar_component_clause,[],[f6186]) ).
fof(f7997,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)) )
| ~ spl53_385 ),
inference(avatar_component_clause,[],[f7996]) ).
fof(f8190,plain,
( spl53_427
| ~ spl53_3
| ~ spl53_385 ),
inference(avatar_split_clause,[],[f8176,f7996,f6181,f8187]) ).
fof(f8187,plain,
( spl53_427
<=> 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,[spl53_427])]) ).
fof(f6181,plain,
( spl53_3
<=> class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_3])]) ).
fof(f8176,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))
| ~ spl53_3
| ~ spl53_385 ),
inference(resolution,[],[f7997,f6183]) ).
fof(f6183,plain,
( class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex)
| ~ spl53_3 ),
inference(avatar_component_clause,[],[f6181]) ).
fof(f8166,plain,
( ~ spl53_426
| ~ spl53_330
| spl53_376 ),
inference(avatar_split_clause,[],[f7961,f7957,f7730,f8163]) ).
fof(f8163,plain,
( spl53_426
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_426])]) ).
fof(f7957,plain,
( spl53_376
<=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_376])]) ).
fof(f7961,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21)
| ~ spl53_330
| spl53_376 ),
inference(forward_demodulation,[],[f7959,f7732]) ).
fof(f7959,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| spl53_376 ),
inference(avatar_component_clause,[],[f7957]) ).
fof(f8161,plain,
spl53_425,
inference(avatar_split_clause,[],[f6127,f8158]) ).
fof(f8158,plain,
( spl53_425
<=> 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,[spl53_425])]) ).
fof(f6127,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,[],[f6126,f4217]) ).
fof(f6126,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,[],[f5850,f4217]) ).
fof(f5850,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,[],[f4826]) ).
fof(f4826,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,[],[f2685]) ).
fof(f2685,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,[],[f1776]) ).
fof(f1776,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,[],[f708]) ).
fof(f708,axiom,
! [X3,X10,X11] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X11
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X10,X3) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X3)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X11
=> 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),X11),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__div__cancel__disj) ).
fof(f8156,plain,
spl53_424,
inference(avatar_split_clause,[],[f6001,f8154]) ).
fof(f8154,plain,
( spl53_424
<=> ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_424])]) ).
fof(f6001,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(forward_demodulation,[],[f6000,f4201]) ).
fof(f6000,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(forward_demodulation,[],[f5646,f5634]) ).
fof(f5646,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(definition_unfolding,[],[f4328,f4205]) ).
fof(f4328,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(cnf_transformation,[],[f3529]) ).
fof(f3529,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(nnf_transformation,[],[f1441]) ).
fof(f1441,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(rectify,[],[f429]) ).
fof(f429,axiom,
! [X8] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X8,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc0) ).
fof(f8152,plain,
spl53_423,
inference(avatar_split_clause,[],[f5885,f8150]) ).
fof(f8150,plain,
( spl53_423
<=> ! [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,[spl53_423])]) ).
fof(f5885,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,[],[f5060]) ).
fof(f5060,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,[],[f3747]) ).
fof(f8148,plain,
spl53_422,
inference(avatar_split_clause,[],[f5875,f8146]) ).
fof(f8146,plain,
( spl53_422
<=> ! [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,[spl53_422])]) ).
fof(f5875,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,[],[f5017]) ).
fof(f5017,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,[],[f3736]) ).
fof(f8144,plain,
spl53_421,
inference(avatar_split_clause,[],[f5822,f8142]) ).
fof(f8142,plain,
( spl53_421
<=> ! [X1] : c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_421])]) ).
fof(f5822,plain,
! [X1] : c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)),
inference(equality_resolution,[],[f4710]) ).
fof(f4710,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)
| c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) != X0 ),
inference(cnf_transformation,[],[f3639]) ).
fof(f8140,plain,
spl53_420,
inference(avatar_split_clause,[],[f5783,f8138]) ).
fof(f8138,plain,
( spl53_420
<=> ! [X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_420])]) ).
fof(f5783,plain,
! [X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(equality_resolution,[],[f4449]) ).
fof(f4449,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,X0) = X0
| c_Groups_Ozero__class_Ozero(X1) != X0
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f3554]) ).
fof(f8136,plain,
spl53_419,
inference(avatar_split_clause,[],[f5778,f8134]) ).
fof(f8134,plain,
( spl53_419
<=> ! [X1] :
( c_Groups_Oone__class_Oone(X1) = c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Ofield__inverse__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_419])]) ).
fof(f5778,plain,
! [X1] :
( c_Groups_Oone__class_Oone(X1) = c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(equality_resolution,[],[f4414]) ).
fof(f4414,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = c_Rings_Oinverse__class_Oinverse(X1,X0)
| c_Groups_Oone__class_Oone(X1) != X0
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(cnf_transformation,[],[f3545]) ).
fof(f8132,plain,
spl53_418,
inference(avatar_split_clause,[],[f5633,f8130]) ).
fof(f8130,plain,
( spl53_418
<=> ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_418])]) ).
fof(f5633,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(definition_unfolding,[],[f4195,f4205]) ).
fof(f4195,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X0)),
inference(cnf_transformation,[],[f1313]) ).
fof(f1313,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X0)),
inference(rectify,[],[f91]) ).
fof(f91,axiom,
! [X3] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
fof(f8128,plain,
spl53_417,
inference(avatar_split_clause,[],[f5233,f8126]) ).
fof(f5233,plain,
! [X2,X0,X1] :
( sP8(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(cnf_transformation,[],[f3803]) ).
fof(f8124,plain,
spl53_416,
inference(avatar_split_clause,[],[f5227,f8122]) ).
fof(f5227,plain,
! [X2,X0,X1] :
( sP9(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3797]) ).
fof(f8120,plain,
spl53_415,
inference(avatar_split_clause,[],[f4540,f8118]) ).
fof(f8118,plain,
( spl53_415
<=> ! [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,[spl53_415])]) ).
fof(f4540,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,[],[f2550]) ).
fof(f2550,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,[],[f1604]) ).
fof(f1604,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,[],[f278]) ).
fof(f278,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Ozero__class_Ozero(X5),X4) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(f8116,plain,
spl53_414,
inference(avatar_split_clause,[],[f4539,f8114]) ).
fof(f8114,plain,
( spl53_414
<=> ! [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,[spl53_414])]) ).
fof(f4539,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,[],[f2549]) ).
fof(f2549,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,[],[f1603]) ).
fof(f1603,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,[],[f277]) ).
fof(f277,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(f8112,plain,
spl53_413,
inference(avatar_split_clause,[],[f4538,f8110]) ).
fof(f4538,plain,
! [X0,X1] :
( c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X0) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2548]) ).
fof(f2548,plain,
! [X0,X1] :
( c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X0) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1602]) ).
fof(f1602,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X0) = X0 ),
inference(rectify,[],[f793]) ).
fof(f793,axiom,
! [X14,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Polynomial_Osmult(X5,c_Groups_Oone__class_Oone(X5),X14) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__1__left) ).
fof(f8108,plain,
spl53_412,
inference(avatar_split_clause,[],[f4520,f8106]) ).
fof(f8106,plain,
( spl53_412
<=> ! [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,[spl53_412])]) ).
fof(f4520,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,[],[f2530]) ).
fof(f2530,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,[],[f1584]) ).
fof(f1584,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,[],[f282]) ).
fof(f282,axiom,
! [X4,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Ozero__class_Ozero(X5),X4) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0) ).
fof(f8104,plain,
spl53_411,
inference(avatar_split_clause,[],[f4519,f8102]) ).
fof(f8102,plain,
( spl53_411
<=> ! [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,[spl53_411])]) ).
fof(f4519,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,[],[f2529]) ).
fof(f2529,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,[],[f1583]) ).
fof(f1583,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,[],[f279]) ).
fof(f279,axiom,
! [X4,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(f8100,plain,
spl53_410,
inference(avatar_split_clause,[],[f4510,f8098]) ).
fof(f4510,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,[],[f2522]) ).
fof(f2522,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,[],[f1576]) ).
fof(f1576,plain,
! [X0,X1] :
( class_Groups_Omonoid__add(X1)
=> c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 ),
inference(rectify,[],[f283]) ).
fof(f283,axiom,
! [X4,X5] :
( class_Groups_Omonoid__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Ozero__class_Ozero(X5),X4) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(f8096,plain,
( spl53_409
| ~ spl53_367
| ~ spl53_374 ),
inference(avatar_split_clause,[],[f7949,f7924,f7896,f8094]) ).
fof(f8094,plain,
( spl53_409
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_409])]) ).
fof(f7896,plain,
( spl53_367
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_367])]) ).
fof(f7924,plain,
( spl53_374
<=> ! [X1] : c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_374])]) ).
fof(f7949,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl53_367
| ~ spl53_374 ),
inference(resolution,[],[f7925,f7897]) ).
fof(f7897,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
| ~ spl53_367 ),
inference(avatar_component_clause,[],[f7896]) ).
fof(f7925,plain,
( ! [X1] : c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl53_374 ),
inference(avatar_component_clause,[],[f7924]) ).
fof(f8092,plain,
spl53_408,
inference(avatar_split_clause,[],[f4509,f8090]) ).
fof(f4509,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,[],[f2521]) ).
fof(f2521,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,[],[f1575]) ).
fof(f1575,plain,
! [X0,X1] :
( class_Groups_Omonoid__add(X1)
=> c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f280]) ).
fof(f280,axiom,
! [X4,X5] :
( class_Groups_Omonoid__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(f8088,plain,
spl53_407,
inference(avatar_split_clause,[],[f4498,f8086]) ).
fof(f4498,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,[],[f2513]) ).
fof(f2513,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,[],[f1567]) ).
fof(f1567,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f62]) ).
fof(f62,axiom,
! [X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ominus__class_Ominus(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__right) ).
fof(f8084,plain,
spl53_406,
inference(avatar_split_clause,[],[f4497,f8082]) ).
fof(f4497,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0
| ~ class_Groups_Ogroup__add(X1) ),
inference(cnf_transformation,[],[f2512]) ).
fof(f2512,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0
| ~ class_Groups_Ogroup__add(X1) ),
inference(ennf_transformation,[],[f1566]) ).
fof(f1566,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0 ),
inference(rectify,[],[f889]) ).
fof(f889,axiom,
! [X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Ouminus__class_Ouminus(X5,X4)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__minus) ).
fof(f8080,plain,
spl53_405,
inference(avatar_split_clause,[],[f4496,f8078]) ).
fof(f4496,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,[],[f2511]) ).
fof(f2511,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,[],[f1565]) ).
fof(f1565,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ominus__class_Ominus(X1,X0,X0) ),
inference(rectify,[],[f61]) ).
fof(f61,axiom,
! [X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Groups_Ominus__class_Ominus(X5,X4,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self) ).
fof(f8076,plain,
spl53_404,
inference(avatar_split_clause,[],[f4478,f8074]) ).
fof(f4478,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,[],[f2496]) ).
fof(f2496,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,[],[f1551]) ).
fof(f1551,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Divides_Odiv__class_Odiv(X1,X0,c_Groups_Oone__class_Oone(X1)) = X0 ),
inference(rectify,[],[f630]) ).
fof(f630,axiom,
! [X4,X5] :
( class_Divides_Osemiring__div(X5)
=> c_Divides_Odiv__class_Odiv(X5,X4,c_Groups_Oone__class_Oone(X5)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__by__1) ).
fof(f8072,plain,
spl53_403,
inference(avatar_split_clause,[],[f4444,f8070]) ).
fof(f8070,plain,
( spl53_403
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK28(X0,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_403])]) ).
fof(f4444,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK28(X0,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(cnf_transformation,[],[f3553]) ).
fof(f3553,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)),sK28(X0,X1)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK28(X0,X1)) )
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f2478,f3552]) ).
fof(f3552,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)),sK28(X0,X1)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK28(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2478,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,[],[f1533]) ).
fof(f1533,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,[],[f758]) ).
fof(f758,axiom,
! [X7,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X84] :
( ! [X2] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X7),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X2)),X84))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X84) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Opos__bounded) ).
fof(f8068,plain,
spl53_402,
inference(avatar_split_clause,[],[f4442,f8066]) ).
fof(f8066,plain,
( spl53_402
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK27(X0,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_402])]) ).
fof(f4442,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK27(X0,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(cnf_transformation,[],[f3551]) ).
fof(f3551,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)),sK27(X0,X1)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK27(X0,X1)) )
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f2477,f3550]) ).
fof(f3550,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)),sK27(X0,X1)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK27(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2477,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,[],[f1532]) ).
fof(f1532,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,[],[f759]) ).
fof(f759,axiom,
! [X21,X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X84] :
( ! [X2] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X2)),X84))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X84) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Opos__bounded) ).
fof(f8064,plain,
spl53_401,
inference(avatar_split_clause,[],[f4430,f8062]) ).
fof(f8062,plain,
( spl53_401
<=> ! [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,[spl53_401])]) ).
fof(f4430,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,[],[f2468]) ).
fof(f2468,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,[],[f1523]) ).
fof(f1523,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,[],[f675]) ).
fof(f675,axiom,
! [X7,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__ge__zero) ).
fof(f8060,plain,
spl53_400,
inference(avatar_split_clause,[],[f4429,f8058]) ).
fof(f8058,plain,
( spl53_400
<=> ! [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,[spl53_400])]) ).
fof(f4429,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,[],[f2467]) ).
fof(f2467,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,[],[f1522]) ).
fof(f1522,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,[],[f674]) ).
fof(f674,axiom,
! [X7,X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X7),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__not__less__zero) ).
fof(f8056,plain,
spl53_399,
inference(avatar_split_clause,[],[f4418,f8054]) ).
fof(f4418,plain,
! [X0,X1] :
( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = X0
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(cnf_transformation,[],[f2450]) ).
fof(f2450,plain,
! [X0,X1] :
( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = X0
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(ennf_transformation,[],[f1512]) ).
fof(f1512,plain,
! [X0,X1] :
( class_Rings_Odivision__ring__inverse__zero(X1)
=> c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X0)) = X0 ),
inference(rectify,[],[f790]) ).
fof(f790,axiom,
! [X4,X5] :
( class_Rings_Odivision__ring__inverse__zero(X5)
=> c_Rings_Oinverse__class_Oinverse(X5,c_Rings_Oinverse__class_Oinverse(X5,X4)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__inverse__eq) ).
fof(f8052,plain,
( spl53_398
| ~ spl53_357
| ~ spl53_366 ),
inference(avatar_split_clause,[],[f7940,f7892,f7856,f8050]) ).
fof(f8050,plain,
( spl53_398
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK24(X0))
| ~ class_RealVector_Oreal__normed__algebra(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_398])]) ).
fof(f7856,plain,
( spl53_357
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK24(X0))
| ~ class_RealVector_Oreal__normed__algebra(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_357])]) ).
fof(f7892,plain,
( spl53_366
<=> ! [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,[spl53_366])]) ).
fof(f7940,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK24(X0))
| ~ class_RealVector_Oreal__normed__algebra(X0) )
| ~ spl53_357
| ~ spl53_366 ),
inference(resolution,[],[f7893,f7857]) ).
fof(f7857,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK24(X0))
| ~ class_RealVector_Oreal__normed__algebra(X0) )
| ~ spl53_357 ),
inference(avatar_component_clause,[],[f7856]) ).
fof(f7893,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) )
| ~ spl53_366 ),
inference(avatar_component_clause,[],[f7892]) ).
fof(f8048,plain,
spl53_397,
inference(avatar_split_clause,[],[f4416,f8046]) ).
fof(f4416,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(cnf_transformation,[],[f2447]) ).
fof(f2447,plain,
! [X0,X1] :
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(ennf_transformation,[],[f1510]) ).
fof(f1510,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(X1)
=> c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X0)) = X0 ),
inference(rectify,[],[f886]) ).
fof(f886,axiom,
! [X7,X5] :
( class_Lattices_Oboolean__algebra(X5)
=> c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Ouminus__class_Ouminus(X5,X7)) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__compl) ).
fof(f8044,plain,
spl53_396,
inference(avatar_split_clause,[],[f4348,f8042]) ).
fof(f8042,plain,
( spl53_396
<=> ! [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,[spl53_396])]) ).
fof(f4348,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,[],[f1457]) ).
fof(f1457,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,[],[f345]) ).
fof(f345,axiom,
! [X10,X3] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X10),X3) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
fof(f8040,plain,
spl53_395,
inference(avatar_split_clause,[],[f4347,f8038]) ).
fof(f8038,plain,
( spl53_395
<=> ! [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,[spl53_395])]) ).
fof(f4347,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,[],[f1456]) ).
fof(f1456,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,[],[f346]) ).
fof(f346,axiom,
! [X3,X10] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X3),X3) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
fof(f8036,plain,
spl53_394,
inference(avatar_split_clause,[],[f4346,f8034]) ).
fof(f8032,plain,
spl53_393,
inference(avatar_split_clause,[],[f4345,f8030]) ).
fof(f8030,plain,
( spl53_393
<=> ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_393])]) ).
fof(f4345,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),
inference(cnf_transformation,[],[f1454]) ).
fof(f1454,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),
inference(rectify,[],[f555]) ).
fof(f555,axiom,
! [X61,X36] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X36,X61) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X61,X36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__commute) ).
fof(f8028,plain,
spl53_392,
inference(avatar_split_clause,[],[f4324,f8026]) ).
fof(f8026,plain,
( spl53_392
<=> ! [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,[spl53_392])]) ).
fof(f4324,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,[],[f3524]) ).
fof(f3524,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,[],[f1439]) ).
fof(f1439,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,[],[f320]) ).
fof(f320,axiom,
! [X8] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X8,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__0__eq) ).
fof(f8024,plain,
spl53_391,
inference(avatar_split_clause,[],[f4311,f8022]) ).
fof(f8022,plain,
( spl53_391
<=> ! [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,[spl53_391])]) ).
fof(f4311,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,[],[f2409]) ).
fof(f2409,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,[],[f1428]) ).
fof(f1428,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,[],[f315]) ).
fof(f315,axiom,
! [X3] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X3
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).
fof(f8020,plain,
spl53_390,
inference(avatar_split_clause,[],[f4278,f8018]) ).
fof(f4278,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Ogroup__add(X0) ),
inference(cnf_transformation,[],[f2376]) ).
fof(f2376,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Ogroup__add(X0) ),
inference(ennf_transformation,[],[f1395]) ).
fof(f1395,plain,
! [X0] :
( class_Groups_Ogroup__add(X0)
=> c_Groups_Ozero__class_Ozero(X0) = c_Groups_Ouminus__class_Ouminus(X0,c_Groups_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f894]) ).
fof(f894,axiom,
! [X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__zero) ).
fof(f8016,plain,
spl53_389,
inference(avatar_split_clause,[],[f4235,f8014]) ).
fof(f4235,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,[],[f2334]) ).
fof(f2334,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,[],[f1353]) ).
fof(f1353,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,[],[f698]) ).
fof(f698,axiom,
! [X5] :
( class_RealVector_Oreal__normed__vector(X5)
=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X5,c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__zero) ).
fof(f8012,plain,
spl53_388,
inference(avatar_split_clause,[],[f4234,f8010]) ).
fof(f4234,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Odivision__ring(X0) ),
inference(cnf_transformation,[],[f2333]) ).
fof(f2333,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Odivision__ring(X0) ),
inference(ennf_transformation,[],[f1352]) ).
fof(f1352,plain,
! [X0] :
( class_Rings_Odivision__ring(X0)
=> c_Groups_Oone__class_Oone(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Oone__class_Oone(X0)) ),
inference(rectify,[],[f791]) ).
fof(f791,axiom,
! [X5] :
( class_Rings_Odivision__ring(X5)
=> c_Groups_Oone__class_Oone(X5) = c_Rings_Oinverse__class_Oinverse(X5,c_Groups_Oone__class_Oone(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__1) ).
fof(f8006,plain,
spl53_387,
inference(avatar_split_clause,[],[f4231,f8004]) ).
fof(f8004,plain,
( spl53_387
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Odivision__ring__inverse__zero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_387])]) ).
fof(f4231,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Odivision__ring__inverse__zero(X0) ),
inference(cnf_transformation,[],[f2330]) ).
fof(f2330,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Odivision__ring__inverse__zero(X0) ),
inference(ennf_transformation,[],[f1349]) ).
fof(f1349,plain,
! [X0] :
( class_Rings_Odivision__ring__inverse__zero(X0)
=> c_Groups_Ozero__class_Ozero(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f783]) ).
fof(f783,axiom,
! [X5] :
( class_Rings_Odivision__ring__inverse__zero(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Rings_Oinverse__class_Oinverse(X5,c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__zero) ).
fof(f8002,plain,
spl53_386,
inference(avatar_split_clause,[],[f4230,f8000]) ).
fof(f4230,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Fields_Ofield__inverse__zero(X0) ),
inference(cnf_transformation,[],[f2329]) ).
fof(f2329,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Fields_Ofield__inverse__zero(X0) ),
inference(ennf_transformation,[],[f1348]) ).
fof(f1348,plain,
! [X0] :
( class_Fields_Ofield__inverse__zero(X0)
=> c_Groups_Ozero__class_Ozero(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f822]) ).
fof(f822,axiom,
! [X5] :
( class_Fields_Ofield__inverse__zero(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Rings_Oinverse__class_Oinverse(X5,c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__inverse__zero) ).
fof(f7998,plain,
spl53_385,
inference(avatar_split_clause,[],[f4229,f7996]) ).
fof(f4229,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,[],[f2328]) ).
fof(f2328,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,[],[f1347]) ).
fof(f1347,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,[],[f704]) ).
fof(f704,axiom,
! [X5] :
( class_RealVector_Oreal__normed__algebra__1(X5)
=> c_RealVector_Onorm__class_Onorm(X5,c_Groups_Oone__class_Oone(X5)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__one) ).
fof(f7994,plain,
spl53_384,
inference(avatar_split_clause,[],[f4215,f7992]) ).
fof(f7992,plain,
( spl53_384
<=> ! [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,[spl53_384])]) ).
fof(f4215,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,[],[f1333]) ).
fof(f1333,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,[],[f353]) ).
fof(f353,axiom,
! [X10] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10),X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__square) ).
fof(f7990,plain,
spl53_383,
inference(avatar_split_clause,[],[f4214,f7988]) ).
fof(f7988,plain,
( spl53_383
<=> ! [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,[spl53_383])]) ).
fof(f4214,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,[],[f1332]) ).
fof(f1332,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f366]) ).
fof(f366,axiom,
! [X3] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1) ).
fof(f7986,plain,
spl53_382,
inference(avatar_split_clause,[],[f4213,f7984]) ).
fof(f7984,plain,
( spl53_382
<=> ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_382])]) ).
fof(f4213,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0,
inference(cnf_transformation,[],[f1331]) ).
fof(f1331,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0,
inference(rectify,[],[f471]) ).
fof(f471,axiom,
! [X36] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X36) = X36,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1) ).
fof(f7982,plain,
spl53_381,
inference(avatar_split_clause,[],[f4212,f7980]) ).
fof(f7980,plain,
( spl53_381
<=> ! [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,[spl53_381])]) ).
fof(f4212,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,[],[f1330]) ).
fof(f1330,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0) = X0,
inference(rectify,[],[f739]) ).
fof(f739,axiom,
! [X36] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X36) = X36,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__1) ).
fof(f7978,plain,
spl53_380,
inference(avatar_split_clause,[],[f4211,f7976]) ).
fof(f4211,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,[],[f1329]) ).
fof(f1329,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(rectify,[],[f364]) ).
fof(f364,axiom,
! [X3] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
fof(f7974,plain,
spl53_379,
inference(avatar_split_clause,[],[f4210,f7972]) ).
fof(f4210,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0,
inference(cnf_transformation,[],[f1328]) ).
fof(f1328,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0,
inference(rectify,[],[f472]) ).
fof(f472,axiom,
! [X36] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X36,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1__right) ).
fof(f7970,plain,
spl53_378,
inference(avatar_split_clause,[],[f4209,f7968]) ).
fof(f7968,plain,
( spl53_378
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_378])]) ).
fof(f4209,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0),
inference(cnf_transformation,[],[f1327]) ).
fof(f1327,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0),
inference(rectify,[],[f893]) ).
fof(f893,axiom,
! [X36] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X36),X36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).
fof(f7966,plain,
( ~ spl53_377
| ~ spl53_337
| ~ spl53_372 ),
inference(avatar_split_clause,[],[f7946,f7916,f7759,f7963]) ).
fof(f7963,plain,
( spl53_377
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_377])]) ).
fof(f7759,plain,
( spl53_337
<=> ! [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,[spl53_337])]) ).
fof(f7916,plain,
( spl53_372
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_372])]) ).
fof(f7946,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl53_337
| ~ spl53_372 ),
inference(superposition,[],[f7917,f7760]) ).
fof(f7760,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0
| ~ spl53_337 ),
inference(avatar_component_clause,[],[f7759]) ).
fof(f7917,plain,
( ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ spl53_372 ),
inference(avatar_component_clause,[],[f7916]) ).
fof(f7960,plain,
~ spl53_376,
inference(avatar_split_clause,[],[f4159,f7957]) ).
fof(f4159,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f549]) ).
fof(f549,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_kn) ).
fof(f7955,plain,
~ spl53_375,
inference(avatar_split_clause,[],[f4158,f7952]) ).
fof(f7952,plain,
( spl53_375
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_375])]) ).
fof(f4158,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(cnf_transformation,[],[f622]) ).
fof(f622,axiom,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_a00) ).
fof(f7926,plain,
spl53_374,
inference(avatar_split_clause,[],[f5834,f7924]) ).
fof(f5834,plain,
! [X1] : c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(equality_resolution,[],[f4759]) ).
fof(f4759,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| X0 != X1 ),
inference(cnf_transformation,[],[f3662]) ).
fof(f7922,plain,
spl53_373,
inference(avatar_split_clause,[],[f5632,f7920]) ).
fof(f7920,plain,
( spl53_373
<=> ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_373])]) ).
fof(f5632,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(definition_unfolding,[],[f4194,f4205]) ).
fof(f4194,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X0)),
inference(cnf_transformation,[],[f1312]) ).
fof(f1312,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X0)),
inference(rectify,[],[f89]) ).
fof(f89,axiom,
! [X3] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Nat_OSuc(X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).
fof(f7918,plain,
spl53_372,
inference(avatar_split_clause,[],[f5631,f7916]) ).
fof(f5631,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),
inference(definition_unfolding,[],[f4190,f4205]) ).
fof(f4190,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X0),
inference(cnf_transformation,[],[f1308]) ).
fof(f1308,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X0),
inference(rectify,[],[f339]) ).
fof(f339,axiom,
! [X3] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(f7914,plain,
spl53_371,
inference(avatar_split_clause,[],[f5625,f7912]) ).
fof(f5625,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(definition_unfolding,[],[f4181,f4205]) ).
fof(f4181,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X0),
inference(cnf_transformation,[],[f1299]) ).
fof(f1299,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X0),
inference(rectify,[],[f49]) ).
fof(f49,axiom,
! [X26] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
fof(f7910,plain,
spl53_370,
inference(avatar_split_clause,[],[f5223,f7908]) ).
fof(f7908,plain,
( spl53_370
<=> ! [X2,X0,X1] :
( sP9(X2,X1,X0)
| ~ sP10(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_370])]) ).
fof(f5223,plain,
! [X2,X0,X1] :
( sP9(X2,X1,X0)
| ~ sP10(X0,X1,X2) ),
inference(cnf_transformation,[],[f3791]) ).
fof(f7906,plain,
spl53_369,
inference(avatar_split_clause,[],[f5222,f7904]) ).
fof(f7904,plain,
( spl53_369
<=> ! [X2,X0,X1] :
( sP8(X2,X1,X0)
| ~ sP10(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_369])]) ).
fof(f5222,plain,
! [X2,X0,X1] :
( sP8(X2,X1,X0)
| ~ sP10(X0,X1,X2) ),
inference(cnf_transformation,[],[f3791]) ).
fof(f7902,plain,
spl53_368,
inference(avatar_split_clause,[],[f5213,f7900]) ).
fof(f7900,plain,
( spl53_368
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_368])]) ).
fof(f5213,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f3785]) ).
fof(f7898,plain,
spl53_367,
inference(avatar_split_clause,[],[f4679,f7896]) ).
fof(f4679,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3617]) ).
fof(f7894,plain,
spl53_366,
inference(avatar_split_clause,[],[f4665,f7892]) ).
fof(f4665,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,[],[f3602]) ).
fof(f7890,plain,
spl53_365,
inference(avatar_split_clause,[],[f4582,f7888]) ).
fof(f4582,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,[],[f2598]) ).
fof(f2598,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,[],[f1644]) ).
fof(f1644,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,[],[f172]) ).
fof(f172,axiom,
! [X3,X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X3)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
fof(f7886,plain,
spl53_364,
inference(avatar_split_clause,[],[f4385,f7884]) ).
fof(f7884,plain,
( spl53_364
<=> ! [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,[spl53_364])]) ).
fof(f4385,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,[],[f1490]) ).
fof(f1490,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,[],[f188]) ).
fof(f188,axiom,
! [X3,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X10)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
fof(f7882,plain,
spl53_363,
inference(avatar_split_clause,[],[f4384,f7880]) ).
fof(f7880,plain,
( spl53_363
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_363])]) ).
fof(f4384,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f1489]) ).
fof(f1489,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(rectify,[],[f602]) ).
fof(f602,axiom,
! [X61,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X61,X36)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X36,X61) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__linear) ).
fof(f7878,plain,
spl53_362,
inference(avatar_split_clause,[],[f4383,f7876]) ).
fof(f7876,plain,
( spl53_362
<=> ! [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,[spl53_362])]) ).
fof(f4383,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,[],[f1488]) ).
fof(f1488,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,[],[f691]) ).
fof(f691,axiom,
! [X61,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X61,X36)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X36,X61) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__linear) ).
fof(f7874,plain,
spl53_361,
inference(avatar_split_clause,[],[f4282,f7872]) ).
fof(f7872,plain,
( spl53_361
<=> ! [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,[spl53_361])]) ).
fof(f4282,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,[],[f2380]) ).
fof(f2380,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,[],[f1399]) ).
fof(f1399,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,[],[f94]) ).
fof(f94,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oone__class_Oone(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__one) ).
fof(f7870,plain,
spl53_360,
inference(avatar_split_clause,[],[f4281,f7868]) ).
fof(f7868,plain,
( spl53_360
<=> ! [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,[spl53_360])]) ).
fof(f4281,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,[],[f2379]) ).
fof(f2379,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,[],[f1398]) ).
fof(f1398,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,[],[f95]) ).
fof(f95,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Oone__class_Oone(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__one) ).
fof(f7866,plain,
spl53_359,
inference(avatar_split_clause,[],[f4280,f7864]) ).
fof(f4280,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,[],[f2378]) ).
fof(f2378,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,[],[f1397]) ).
fof(f1397,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,[],[f92]) ).
fof(f92,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
fof(f7862,plain,
spl53_358,
inference(avatar_split_clause,[],[f4279,f7860]) ).
fof(f7860,plain,
( spl53_358
<=> ! [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,[spl53_358])]) ).
fof(f4279,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,[],[f2377]) ).
fof(f2377,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,[],[f1396]) ).
fof(f1396,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,[],[f93]) ).
fof(f93,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> ~ c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
fof(f7858,plain,
spl53_357,
inference(avatar_split_clause,[],[f4236,f7856]) ).
fof(f4236,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK24(X0))
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(cnf_transformation,[],[f3519]) ).
fof(f3519,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))),sK24(X0)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK24(X0)) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f2335,f3518]) ).
fof(f3518,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))),sK24(X0)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK24(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f2335,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,[],[f1354]) ).
fof(f1354,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,[],[f757]) ).
fof(f757,axiom,
! [X5] :
( class_RealVector_Oreal__normed__algebra(X5)
=> ? [X84] :
( ! [X85,X86] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X85),X86)),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(X5,X85)),c_RealVector_Onorm__class_Onorm(X5,X86))),X84))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X84) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Opos__bounded) ).
fof(f7854,plain,
spl53_356,
inference(avatar_split_clause,[],[f4204,f7852]) ).
fof(f4204,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,[],[f1322]) ).
fof(f1322,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,[],[f13]) ).
fof(f13,axiom,
! [X3] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
fof(f7850,plain,
( ~ spl53_355
| ~ spl53_337
| ~ spl53_349 ),
inference(avatar_split_clause,[],[f7835,f7807,f7759,f7847]) ).
fof(f7847,plain,
( spl53_355
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_355])]) ).
fof(f7835,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ spl53_337
| ~ spl53_349 ),
inference(superposition,[],[f7808,f7760]) ).
fof(f7845,plain,
spl53_354,
inference(avatar_split_clause,[],[f4203,f7843]) ).
fof(f4203,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0),
inference(cnf_transformation,[],[f1321]) ).
fof(f1321,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0),
inference(rectify,[],[f629]) ).
fof(f629,axiom,
! [X20] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zero) ).
fof(f7841,plain,
~ spl53_353,
inference(avatar_split_clause,[],[f4157,f7838]) ).
fof(f7838,plain,
( spl53_353
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_353])]) ).
fof(f4157,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____),
inference(cnf_transformation,[],[f625]) ).
fof(f625,axiom,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pc0) ).
fof(f7823,plain,
( spl53_352
| ~ spl53_328 ),
inference(avatar_split_clause,[],[f7723,f7719,f7820]) ).
fof(f7820,plain,
( spl53_352
<=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_352])]) ).
fof(f7719,plain,
( spl53_328
<=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_328])]) ).
fof(f7723,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21)
| ~ spl53_328 ),
inference(forward_demodulation,[],[f7721,f4170]) ).
fof(f7721,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____)
| ~ spl53_328 ),
inference(avatar_component_clause,[],[f7719]) ).
fof(f7818,plain,
spl53_351,
inference(avatar_split_clause,[],[f6161,f7815]) ).
fof(f7815,plain,
( spl53_351
<=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK49) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_351])]) ).
fof(f6161,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK21) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK49),
inference(forward_demodulation,[],[f5615,f4170]) ).
fof(f5615,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK49),
inference(cnf_transformation,[],[f3914]) ).
fof(f7813,plain,
spl53_350,
inference(avatar_split_clause,[],[f5978,f7811]) ).
fof(f7811,plain,
( spl53_350
<=> ! [X0] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_350])]) ).
fof(f5978,plain,
! [X0] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(forward_demodulation,[],[f5977,f4201]) ).
fof(f5977,plain,
! [X0] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X0,
inference(forward_demodulation,[],[f5635,f5634]) ).
fof(f5635,plain,
! [X0] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X0,
inference(definition_unfolding,[],[f4207,f4205]) ).
fof(f4207,plain,
! [X0] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X0,
inference(cnf_transformation,[],[f1325]) ).
fof(f1325,plain,
! [X0] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X0,
inference(rectify,[],[f705]) ).
fof(f705,axiom,
! [X10] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X10,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__1) ).
fof(f7809,plain,
spl53_349,
inference(avatar_split_clause,[],[f5623,f7807]) ).
fof(f5623,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X0,
inference(definition_unfolding,[],[f4173,f4205]) ).
fof(f4173,plain,
! [X0] : c_Nat_OSuc(X0) != X0,
inference(cnf_transformation,[],[f1291]) ).
fof(f1291,plain,
! [X0] : c_Nat_OSuc(X0) != X0,
inference(rectify,[],[f39]) ).
fof(f39,axiom,
! [X3] : c_Nat_OSuc(X3) != X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(f7805,plain,
spl53_348,
inference(avatar_split_clause,[],[f5359,f7803]) ).
fof(f7803,plain,
( spl53_348
<=> ! [X0,X3,X2,X1] :
( sP18(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_348])]) ).
fof(f5359,plain,
! [X2,X3,X0,X1] :
( sP18(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f3509]) ).
fof(f3509,plain,
! [X0,X1,X2,X3] :
( sP18(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(definition_folding,[],[f3144,f3508,f3507]) ).
fof(f3508,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))
<=> sP17(X1,X0,X3,X2) )
| ~ sP18(X2,X3,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).
fof(f3144,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,[],[f2107]) ).
fof(f2107,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,[],[f397]) ).
fof(f397,axiom,
! [X32,X9,X35,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X35),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X35),X32))
<=> ( ( c_Orderings_Oord__class_Oless(X5,X32,X9)
& c_Orderings_Oord__class_Oless(X5,X35,c_Groups_Ozero__class_Ozero(X5)) )
| ( c_Orderings_Oord__class_Oless(X5,X9,X32)
& c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X35) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
fof(f7801,plain,
spl53_347,
inference(avatar_split_clause,[],[f5350,f7799]) ).
fof(f7799,plain,
( spl53_347
<=> ! [X0,X3,X2,X1] :
( sP16(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_347])]) ).
fof(f5350,plain,
! [X2,X3,X0,X1] :
( sP16(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f3506]) ).
fof(f3506,plain,
! [X0,X1,X2,X3] :
( sP16(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(definition_folding,[],[f3143,f3505,f3504]) ).
fof(f3505,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))
<=> sP15(X2,X0,X3,X1) )
| ~ sP16(X1,X3,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f3143,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,[],[f2106]) ).
fof(f2106,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,[],[f398]) ).
fof(f398,axiom,
! [X32,X35,X9,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X32),X35))
<=> ( ( c_Orderings_Oord__class_Oless(X5,X32,X9)
& c_Orderings_Oord__class_Oless(X5,X35,c_Groups_Ozero__class_Ozero(X5)) )
| ( c_Orderings_Oord__class_Oless(X5,X9,X32)
& c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X35) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
fof(f7797,plain,
spl53_346,
inference(avatar_split_clause,[],[f4537,f7795]) ).
fof(f7795,plain,
( spl53_346
<=> ! [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,[spl53_346])]) ).
fof(f4537,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,[],[f2547]) ).
fof(f2547,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,[],[f1601]) ).
fof(f1601,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Rings_Odvd__class_Odvd(X1,c_Groups_Oone__class_Oone(X1),X0) ),
inference(rectify,[],[f991]) ).
fof(f991,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Rings_Odvd__class_Odvd(X5,c_Groups_Oone__class_Oone(X5),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__dvd) ).
fof(f7793,plain,
spl53_345,
inference(avatar_split_clause,[],[f4536,f7791]) ).
fof(f7791,plain,
( spl53_345
<=> ! [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,[spl53_345])]) ).
fof(f4536,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,[],[f2546]) ).
fof(f2546,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,[],[f1600]) ).
fof(f1600,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Rings_Odvd__class_Odvd(X1,X0,c_Groups_Ozero__class_Ozero(X1)) ),
inference(rectify,[],[f960]) ).
fof(f960,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Rings_Odvd__class_Odvd(X5,X4,c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__0__right) ).
fof(f7789,plain,
spl53_344,
inference(avatar_split_clause,[],[f4341,f7787]) ).
fof(f7787,plain,
( spl53_344
<=> ! [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,[spl53_344])]) ).
fof(f4341,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,[],[f1450]) ).
fof(f1450,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,[],[f362]) ).
fof(f362,axiom,
! [X3,X10] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,X3),X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__self) ).
fof(f7785,plain,
spl53_343,
inference(avatar_split_clause,[],[f4340,f7783]) ).
fof(f7783,plain,
( spl53_343
<=> ! [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,[spl53_343])]) ).
fof(f4340,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,[],[f1449]) ).
fof(f1449,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,[],[f672]) ).
fof(f672,axiom,
! [X3,X10] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X10,X3),X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__dividend) ).
fof(f7781,plain,
spl53_342,
inference(avatar_split_clause,[],[f4339,f7779]) ).
fof(f4339,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,[],[f1448]) ).
fof(f1448,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,[],[f192]) ).
fof(f192,axiom,
! [X10,X3] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).
fof(f7777,plain,
spl53_341,
inference(avatar_split_clause,[],[f4338,f7775]) ).
fof(f7775,plain,
( spl53_341
<=> ! [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,[spl53_341])]) ).
fof(f4338,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,[],[f1447]) ).
fof(f1447,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,[],[f193]) ).
fof(f193,axiom,
! [X10,X3] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).
fof(f7773,plain,
spl53_340,
inference(avatar_split_clause,[],[f4337,f7771]) ).
fof(f4337,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,[],[f1446]) ).
fof(f1446,plain,
! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1),
inference(rectify,[],[f196]) ).
fof(f196,axiom,
! [X24,X25] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X24),X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).
fof(f7769,plain,
spl53_339,
inference(avatar_split_clause,[],[f4336,f7767]) ).
fof(f7767,plain,
( spl53_339
<=> ! [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,[spl53_339])]) ).
fof(f4336,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,[],[f1445]) ).
fof(f1445,plain,
! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0),
inference(rectify,[],[f195]) ).
fof(f195,axiom,
! [X25,X24] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X25),X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(f7765,plain,
spl53_338,
inference(avatar_split_clause,[],[f4287,f7763]) ).
fof(f7763,plain,
( spl53_338
<=> ! [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,[spl53_338])]) ).
fof(f4287,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) != c_Groups_Ozero__class_Ozero(X0)
| ~ class_Rings_Ozero__neq__one(X0) ),
inference(cnf_transformation,[],[f2385]) ).
fof(f2385,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) != c_Groups_Ozero__class_Ozero(X0)
| ~ class_Rings_Ozero__neq__one(X0) ),
inference(ennf_transformation,[],[f1404]) ).
fof(f1404,plain,
! [X0] :
( class_Rings_Ozero__neq__one(X0)
=> c_Groups_Oone__class_Oone(X0) != c_Groups_Ozero__class_Ozero(X0) ),
inference(rectify,[],[f298]) ).
fof(f298,axiom,
! [X5] :
( class_Rings_Ozero__neq__one(X5)
=> c_Groups_Ozero__class_Ozero(X5) != c_Groups_Oone__class_Oone(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__neq__zero) ).
fof(f7761,plain,
spl53_337,
inference(avatar_split_clause,[],[f4202,f7759]) ).
fof(f4202,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
inference(cnf_transformation,[],[f1320]) ).
fof(f1320,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
inference(rectify,[],[f310]) ).
fof(f310,axiom,
! [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(f7757,plain,
spl53_336,
inference(avatar_split_clause,[],[f4201,f7755]) ).
fof(f7753,plain,
spl53_335,
inference(avatar_split_clause,[],[f4200,f7751]) ).
fof(f7751,plain,
( spl53_335
<=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_335])]) ).
fof(f4200,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) = X0,
inference(cnf_transformation,[],[f1318]) ).
fof(f1318,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) = X0,
inference(rectify,[],[f572]) ).
fof(f572,axiom,
! [X36] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X36) = X36,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0) ).
fof(f7749,plain,
spl53_334,
inference(avatar_split_clause,[],[f4199,f7747]) ).
fof(f7747,plain,
( spl53_334
<=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_334])]) ).
fof(f4199,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
inference(cnf_transformation,[],[f1317]) ).
fof(f1317,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
inference(rectify,[],[f570]) ).
fof(f570,axiom,
! [X36] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X36,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X36,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0__right) ).
fof(f7745,plain,
spl53_333,
inference(avatar_split_clause,[],[f4198,f7743]) ).
fof(f7743,plain,
( spl53_333
<=> ! [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,[spl53_333])]) ).
fof(f4198,plain,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f1316]) ).
fof(f1316,plain,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X10] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
fof(f7741,plain,
spl53_332,
inference(avatar_split_clause,[],[f4197,f7739]) ).
fof(f7739,plain,
( spl53_332
<=> ! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_332])]) ).
fof(f4197,plain,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = X0,
inference(cnf_transformation,[],[f1315]) ).
fof(f1315,plain,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = X0,
inference(rectify,[],[f963]) ).
fof(f963,axiom,
! [X36] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X36)) = X36,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zminus) ).
fof(f7737,plain,
spl53_331,
inference(avatar_split_clause,[],[f4196,f7735]) ).
fof(f7735,plain,
( spl53_331
<=> ! [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,[spl53_331])]) ).
fof(f4196,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0),
inference(cnf_transformation,[],[f1314]) ).
fof(f1314,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0),
inference(rectify,[],[f54]) ).
fof(f54,axiom,
! [X10] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
fof(f7733,plain,
spl53_330,
inference(avatar_split_clause,[],[f4170,f7730]) ).
fof(f7728,plain,
spl53_329,
inference(avatar_split_clause,[],[f4156,f7725]) ).
fof(f7725,plain,
( spl53_329
<=> c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_329])]) ).
fof(f4156,plain,
c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii),
inference(cnf_transformation,[],[f942]) ).
fof(f942,axiom,
c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__i) ).
fof(f7722,plain,
spl53_328,
inference(avatar_split_clause,[],[f4155,f7719]) ).
fof(f7717,plain,
spl53_327,
inference(avatar_split_clause,[],[f4154,f7714]) ).
fof(f7714,plain,
( spl53_327
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_327])]) ).
fof(f4154,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f902]) ).
fof(f902,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__0) ).
fof(f7712,plain,
spl53_326,
inference(avatar_split_clause,[],[f4153,f7709]) ).
fof(f7709,plain,
( spl53_326
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_326])]) ).
fof(f4153,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f806]) ).
fof(f806,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INVERSE__ZERO) ).
fof(f7707,plain,
spl53_325,
inference(avatar_split_clause,[],[f6106,f7704]) ).
fof(f7704,plain,
( spl53_325
<=> 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,[spl53_325])]) ).
fof(f6106,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,[],[f5846,f5777]) ).
fof(f5846,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,[],[f4785]) ).
fof(f4785,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,[],[f3679]) ).
fof(f7702,plain,
spl53_324,
inference(avatar_split_clause,[],[f5896,f7700]) ).
fof(f7700,plain,
( spl53_324
<=> ! [X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X1)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_324])]) ).
fof(f5896,plain,
! [X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X1)
| ~ class_Orderings_Oorder(X2) ),
inference(equality_resolution,[],[f5105]) ).
fof(f5105,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| X0 != X1
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f3755]) ).
fof(f3755,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,[],[f3754]) ).
fof(f3754,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,[],[f2989]) ).
fof(f2989,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,[],[f1980]) ).
fof(f1980,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,[],[f501]) ).
fof(f501,axiom,
! [X40,X15,X5] :
( class_Orderings_Oorder(X5)
=> ( X15 = X40
<=> ( c_Orderings_Oord__class_Oless__eq(X5,X40,X15)
& c_Orderings_Oord__class_Oless__eq(X5,X15,X40) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(f7698,plain,
spl53_323,
inference(avatar_split_clause,[],[f5893,f7696]) ).
fof(f7696,plain,
( spl53_323
<=> ! [X2,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_323])]) ).
fof(f5893,plain,
! [X2,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
| ~ class_Orderings_Oorder(X2) ),
inference(equality_resolution,[],[f5100]) ).
fof(f5100,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f2982]) ).
fof(f2982,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f2981]) ).
fof(f2981,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f1976]) ).
fof(f1976,plain,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X0)
=> X0 != X1 ) ),
inference(rectify,[],[f514]) ).
fof(f514,axiom,
! [X21,X7,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X7,X21)
=> X7 != X21 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(f7694,plain,
spl53_322,
inference(avatar_split_clause,[],[f5873,f7692]) ).
fof(f7692,plain,
( spl53_322
<=> ! [X2,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_322])]) ).
fof(f5873,plain,
! [X2,X1] :
( ~ c_Orderings_Oord__class_Oless(X2,X1,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(equality_resolution,[],[f5016]) ).
fof(f5016,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f3735]) ).
fof(f3735,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,[],[f3734]) ).
fof(f3734,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,[],[f2887]) ).
fof(f2887,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,[],[f1911]) ).
fof(f1911,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,[],[f523]) ).
fof(f523,axiom,
! [X40,X15,X5] :
( class_Orderings_Olinorder(X5)
=> ( X15 != X40
<=> ( c_Orderings_Oord__class_Oless(X5,X40,X15)
| c_Orderings_Oord__class_Oless(X5,X15,X40) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(f7690,plain,
spl53_321,
inference(avatar_split_clause,[],[f4895,f7688]) ).
fof(f7688,plain,
( spl53_321
<=> ! [X2,X0,X1] :
( sP6(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_321])]) ).
fof(f4895,plain,
! [X2,X0,X1] :
( sP6(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f3489]) ).
fof(f3489,plain,
! [X0,X1,X2] :
( sP6(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(definition_folding,[],[f2757,f3488,f3487]) ).
fof(f3488,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))
<=> sP5(X0,X2,X1) )
| ~ sP6(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f2757,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,[],[f1825]) ).
fof(f1825,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,[],[f415]) ).
fof(f415,axiom,
! [X32,X9,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X32),c_Groups_Ozero__class_Ozero(X5))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X32)
& c_Orderings_Oord__class_Oless__eq(X5,X9,c_Groups_Ozero__class_Ozero(X5)) )
| ( c_Orderings_Oord__class_Oless__eq(X5,X32,c_Groups_Ozero__class_Ozero(X5))
& c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X9) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
fof(f7686,plain,
spl53_320,
inference(avatar_split_clause,[],[f4886,f7684]) ).
fof(f7684,plain,
( spl53_320
<=> ! [X2,X0,X1] :
( sP4(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_320])]) ).
fof(f4886,plain,
! [X2,X0,X1] :
( sP4(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f3486]) ).
fof(f3486,plain,
! [X0,X1,X2] :
( sP4(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(definition_folding,[],[f2756,f3485,f3484]) ).
fof(f3485,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))
<=> sP3(X2,X0,X1) )
| ~ sP4(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f2756,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,[],[f1824]) ).
fof(f1824,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,[],[f416]) ).
fof(f416,axiom,
! [X32,X9,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X9),X32))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X5,X32,c_Groups_Ozero__class_Ozero(X5))
& c_Orderings_Oord__class_Oless__eq(X5,X9,c_Groups_Ozero__class_Ozero(X5)) )
| ( c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X32)
& c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),X9) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
fof(f7682,plain,
spl53_319,
inference(avatar_split_clause,[],[f4556,f7680]) ).
fof(f7680,plain,
( spl53_319
<=> ! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_319])]) ).
fof(f4556,plain,
! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ),
inference(cnf_transformation,[],[f2567]) ).
fof(f2567,plain,
! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ),
inference(ennf_transformation,[],[f1620]) ).
fof(f1620,plain,
! [X0,X1] :
( class_Groups_Ominus(X1)
=> class_Groups_Ominus(tc_fun(X0,X1)) ),
inference(rectify,[],[f1007]) ).
fof(f1007,axiom,
! [X91,X90] :
( class_Groups_Ominus(X90)
=> class_Groups_Ominus(tc_fun(X91,X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
fof(f7678,plain,
spl53_318,
inference(avatar_split_clause,[],[f4555,f7676]) ).
fof(f7676,plain,
( spl53_318
<=> ! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_318])]) ).
fof(f4555,plain,
! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(cnf_transformation,[],[f2566]) ).
fof(f2566,plain,
! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(ennf_transformation,[],[f1619]) ).
fof(f1619,plain,
! [X0,X1] :
( class_Orderings_Oorder(X1)
=> class_Orderings_Oorder(tc_fun(X0,X1)) ),
inference(rectify,[],[f1004]) ).
fof(f1004,axiom,
! [X91,X90] :
( class_Orderings_Oorder(X90)
=> class_Orderings_Oorder(tc_fun(X91,X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(f7674,plain,
spl53_317,
inference(avatar_split_clause,[],[f4554,f7672]) ).
fof(f7672,plain,
( spl53_317
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_317])]) ).
fof(f4554,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f2565]) ).
fof(f2565,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f1618]) ).
fof(f1618,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> c_Orderings_Oord__class_Oless__eq(X1,X0,X0) ),
inference(rectify,[],[f465]) ).
fof(f465,axiom,
! [X7,X5] :
( class_Orderings_Opreorder(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,X7,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).
fof(f7670,plain,
spl53_316,
inference(avatar_split_clause,[],[f4553,f7668]) ).
fof(f7668,plain,
( spl53_316
<=> ! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_316])]) ).
fof(f4553,plain,
! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f2564]) ).
fof(f2564,plain,
! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f1617]) ).
fof(f1617,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> class_Orderings_Opreorder(tc_fun(X0,X1)) ),
inference(rectify,[],[f1003]) ).
fof(f1003,axiom,
! [X91,X90] :
( class_Orderings_Opreorder(X90)
=> class_Orderings_Opreorder(tc_fun(X91,X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(f7666,plain,
spl53_315,
inference(avatar_split_clause,[],[f4552,f7664]) ).
fof(f7664,plain,
( spl53_315
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_315])]) ).
fof(f4552,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f2563]) ).
fof(f2563,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f1616]) ).
fof(f1616,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> ~ c_Orderings_Oord__class_Oless(X1,X0,X0) ),
inference(rectify,[],[f524]) ).
fof(f524,axiom,
! [X7,X5] :
( class_Orderings_Opreorder(X5)
=> ~ c_Orderings_Oord__class_Oless(X5,X7,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(f7662,plain,
spl53_314,
inference(avatar_split_clause,[],[f4551,f7660]) ).
fof(f7660,plain,
( spl53_314
<=> ! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_314])]) ).
fof(f4551,plain,
! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ),
inference(cnf_transformation,[],[f2562]) ).
fof(f2562,plain,
! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ),
inference(ennf_transformation,[],[f1615]) ).
fof(f1615,plain,
! [X0,X1] :
( class_Orderings_Oord(X1)
=> class_Orderings_Oord(tc_fun(X0,X1)) ),
inference(rectify,[],[f1005]) ).
fof(f1005,axiom,
! [X91,X90] :
( class_Orderings_Oord(X90)
=> class_Orderings_Oord(tc_fun(X91,X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(f7658,plain,
spl53_313,
inference(avatar_split_clause,[],[f4550,f7656]) ).
fof(f7656,plain,
( spl53_313
<=> ! [X0,X1] :
( class_Groups_Ouminus(tc_fun(X0,X1))
| ~ class_Groups_Ouminus(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_313])]) ).
fof(f4550,plain,
! [X0,X1] :
( class_Groups_Ouminus(tc_fun(X0,X1))
| ~ class_Groups_Ouminus(X1) ),
inference(cnf_transformation,[],[f2561]) ).
fof(f2561,plain,
! [X0,X1] :
( class_Groups_Ouminus(tc_fun(X0,X1))
| ~ class_Groups_Ouminus(X1) ),
inference(ennf_transformation,[],[f1614]) ).
fof(f1614,plain,
! [X0,X1] :
( class_Groups_Ouminus(X1)
=> class_Groups_Ouminus(tc_fun(X0,X1)) ),
inference(rectify,[],[f1006]) ).
fof(f1006,axiom,
! [X91,X90] :
( class_Groups_Ouminus(X90)
=> class_Groups_Ouminus(tc_fun(X91,X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).
fof(f7654,plain,
spl53_312,
inference(avatar_split_clause,[],[f4535,f7652]) ).
fof(f7652,plain,
( spl53_312
<=> ! [X0,X1] :
( c_Rings_Odvd__class_Odvd(X1,X0,X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_312])]) ).
fof(f4535,plain,
! [X0,X1] :
( c_Rings_Odvd__class_Odvd(X1,X0,X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2545]) ).
fof(f2545,plain,
! [X0,X1] :
( c_Rings_Odvd__class_Odvd(X1,X0,X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1599]) ).
fof(f1599,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Rings_Odvd__class_Odvd(X1,X0,X0) ),
inference(rectify,[],[f990]) ).
fof(f990,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Rings_Odvd__class_Odvd(X5,X4,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__refl) ).
fof(f7650,plain,
spl53_311,
inference(avatar_split_clause,[],[f4415,f7648]) ).
fof(f7648,plain,
( spl53_311
<=> ! [X0,X1] :
( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_311])]) ).
fof(f4415,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(cnf_transformation,[],[f2446]) ).
fof(f2446,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(ennf_transformation,[],[f1509]) ).
fof(f1509,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(X1)
=> class_Lattices_Oboolean__algebra(tc_fun(X0,X1)) ),
inference(rectify,[],[f1002]) ).
fof(f1002,axiom,
! [X91,X90] :
( class_Lattices_Oboolean__algebra(X90)
=> class_Lattices_Oboolean__algebra(tc_fun(X91,X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
fof(f7646,plain,
spl53_310,
inference(avatar_split_clause,[],[f4152,f7643]) ).
fof(f7643,plain,
( spl53_310
<=> 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,[spl53_310])]) ).
fof(f4152,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f573]) ).
fof(f573,axiom,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__less__1) ).
fof(f7641,plain,
spl53_309,
inference(avatar_split_clause,[],[f4150,f7638]) ).
fof(f7638,plain,
( spl53_309
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_309])]) ).
fof(f4150,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f619]) ).
fof(f619,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(f7636,plain,
~ spl53_308,
inference(avatar_split_clause,[],[f4147,f7633]) ).
fof(f7633,plain,
( spl53_308
<=> c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_308])]) ).
fof(f4147,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
inference(cnf_transformation,[],[f628]) ).
fof(f628,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096constant_A_Ipoly_Aq_J_A_061_061_062_AFalse_096) ).
fof(f7631,plain,
~ spl53_307,
inference(avatar_split_clause,[],[f4146,f7628]) ).
fof(f7628,plain,
( spl53_307
<=> c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_307])]) ).
fof(f4146,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____)),
inference(cnf_transformation,[],[f624]) ).
fof(f624,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less_Oprems) ).
fof(f7626,plain,
~ spl53_306,
inference(avatar_split_clause,[],[f4145,f7623]) ).
fof(f7623,plain,
( spl53_306
<=> c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_306])]) ).
fof(f4145,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p)),
inference(cnf_transformation,[],[f623]) ).
fof(f623,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms) ).
fof(f7621,plain,
spl53_305,
inference(avatar_split_clause,[],[f6068,f7618]) ).
fof(f7618,plain,
( spl53_305
<=> sP2(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_305])]) ).
fof(f6068,plain,
sP2(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f6067,f4201]) ).
fof(f6067,plain,
sP2(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(forward_demodulation,[],[f5833,f4346]) ).
fof(f5833,plain,
sP2(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(equality_resolution,[],[f5832]) ).
fof(f5832,plain,
! [X1] :
( sP2(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1 ),
inference(equality_resolution,[],[f5723]) ).
fof(f5723,plain,
! [X0,X1] :
( sP2(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1 ),
inference(definition_unfolding,[],[f4737,f4205]) ).
fof(f4737,plain,
! [X0,X1] :
( sP2(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(cnf_transformation,[],[f3651]) ).
fof(f7616,plain,
spl53_304,
inference(avatar_split_clause,[],[f6066,f7613]) ).
fof(f7613,plain,
( spl53_304
<=> sP2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_304])]) ).
fof(f6066,plain,
sP2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_demodulation,[],[f6065,f4201]) ).
fof(f6065,plain,
sP2(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_demodulation,[],[f5831,f4346]) ).
fof(f5831,plain,
sP2(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f5830]) ).
fof(f5830,plain,
! [X1] :
( sP2(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(equality_resolution,[],[f5722]) ).
fof(f5722,plain,
! [X0,X1] :
( sP2(X0,X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(definition_unfolding,[],[f4738,f4205]) ).
fof(f4738,plain,
! [X0,X1] :
( sP2(X0,X1)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f3651]) ).
fof(f7611,plain,
spl53_303,
inference(avatar_split_clause,[],[f6052,f7608]) ).
fof(f7608,plain,
( spl53_303
<=> sP1(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_303])]) ).
fof(f6052,plain,
sP1(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f6051,f4201]) ).
fof(f6051,plain,
sP1(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(forward_demodulation,[],[f5829,f4346]) ).
fof(f5829,plain,
sP1(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(equality_resolution,[],[f5828]) ).
fof(f5828,plain,
! [X1] :
( sP1(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1 ),
inference(equality_resolution,[],[f5716]) ).
fof(f5716,plain,
! [X0,X1] :
( sP1(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1 ),
inference(definition_unfolding,[],[f4729,f4205]) ).
fof(f4729,plain,
! [X0,X1] :
( sP1(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(cnf_transformation,[],[f3648]) ).
fof(f7606,plain,
spl53_302,
inference(avatar_split_clause,[],[f6050,f7603]) ).
fof(f7603,plain,
( spl53_302
<=> sP1(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_302])]) ).
fof(f6050,plain,
sP1(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_demodulation,[],[f6049,f4201]) ).
fof(f6049,plain,
sP1(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_demodulation,[],[f5827,f4346]) ).
fof(f5827,plain,
sP1(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f5826]) ).
fof(f5826,plain,
! [X1] :
( sP1(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(equality_resolution,[],[f5715]) ).
fof(f5715,plain,
! [X0,X1] :
( sP1(X0,X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(definition_unfolding,[],[f4730,f4205]) ).
fof(f4730,plain,
! [X0,X1] :
( sP1(X0,X1)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f3648]) ).
fof(f7601,plain,
spl53_301,
inference(avatar_split_clause,[],[f5916,f7599]) ).
fof(f7599,plain,
( spl53_301
<=> ! [X0,X1] : sP11(X0,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_301])]) ).
fof(f5916,plain,
! [X0,X1] : sP11(X0,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f5241]) ).
fof(f5241,plain,
! [X2,X0,X1] :
( sP11(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ),
inference(cnf_transformation,[],[f3809]) ).
fof(f7597,plain,
spl53_300,
inference(avatar_split_clause,[],[f4307,f7595]) ).
fof(f7595,plain,
( spl53_300
<=> ! [X0] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_300])]) ).
fof(f4307,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2405]) ).
fof(f2405,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1424]) ).
fof(f1424,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1252]) ).
fof(f1252,axiom,
! [X90] :
( class_Rings_Ocomm__semiring__1(X90)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(f7593,plain,
spl53_299,
inference(avatar_split_clause,[],[f4306,f7591]) ).
fof(f7591,plain,
( spl53_299
<=> ! [X0] :
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_299])]) ).
fof(f4306,plain,
! [X0] :
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2404]) ).
fof(f2404,plain,
! [X0] :
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1423]) ).
fof(f1423,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1261]) ).
fof(f1261,axiom,
! [X90] :
( class_Rings_Ocomm__semiring__1(X90)
=> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).
fof(f7589,plain,
spl53_298,
inference(avatar_split_clause,[],[f4305,f7587]) ).
fof(f7587,plain,
( spl53_298
<=> ! [X0] :
( class_Power_Opower(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_298])]) ).
fof(f4305,plain,
! [X0] :
( class_Power_Opower(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2403]) ).
fof(f2403,plain,
! [X0] :
( class_Power_Opower(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1422]) ).
fof(f1422,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Power_Opower(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1277]) ).
fof(f1277,axiom,
! [X90] :
( class_Rings_Ocomm__semiring__1(X90)
=> class_Power_Opower(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).
fof(f7585,plain,
spl53_297,
inference(avatar_split_clause,[],[f4304,f7583]) ).
fof(f7583,plain,
( spl53_297
<=> ! [X0] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_297])]) ).
fof(f4304,plain,
! [X0] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2402]) ).
fof(f2402,plain,
! [X0] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1421]) ).
fof(f1421,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1257]) ).
fof(f1257,axiom,
! [X90] :
( class_Rings_Ocomm__semiring__1(X90)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
fof(f7581,plain,
spl53_296,
inference(avatar_split_clause,[],[f4303,f7579]) ).
fof(f7579,plain,
( spl53_296
<=> ! [X0] :
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_296])]) ).
fof(f4303,plain,
! [X0] :
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2401]) ).
fof(f2401,plain,
! [X0] :
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1420]) ).
fof(f1420,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1245]) ).
fof(f1245,axiom,
! [X90] :
( class_Rings_Ocomm__semiring__1(X90)
=> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).
fof(f7577,plain,
spl53_295,
inference(avatar_split_clause,[],[f4302,f7575]) ).
fof(f7575,plain,
( spl53_295
<=> ! [X0] :
( class_Groups_Oone(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_295])]) ).
fof(f4302,plain,
! [X0] :
( class_Groups_Oone(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2400]) ).
fof(f2400,plain,
! [X0] :
( class_Groups_Oone(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1419]) ).
fof(f1419,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Groups_Oone(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1282]) ).
fof(f1282,axiom,
! [X90] :
( class_Rings_Ocomm__semiring__1(X90)
=> class_Groups_Oone(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).
fof(f7573,plain,
spl53_294,
inference(avatar_split_clause,[],[f4301,f7571]) ).
fof(f7571,plain,
( spl53_294
<=> ! [X0] :
( class_Rings_Odvd(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_294])]) ).
fof(f4301,plain,
! [X0] :
( class_Rings_Odvd(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2399]) ).
fof(f2399,plain,
! [X0] :
( class_Rings_Odvd(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1418]) ).
fof(f1418,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Rings_Odvd(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1283]) ).
fof(f1283,axiom,
! [X90] :
( class_Rings_Ocomm__semiring__1(X90)
=> class_Rings_Odvd(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Odvd) ).
fof(f7569,plain,
spl53_293,
inference(avatar_split_clause,[],[f4300,f7567]) ).
fof(f7567,plain,
( spl53_293
<=> ! [X0] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_293])]) ).
fof(f4300,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2398]) ).
fof(f2398,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1417]) ).
fof(f1417,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1253]) ).
fof(f1253,axiom,
! [X90] :
( class_Rings_Ocomm__semiring__0(X90)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
fof(f7565,plain,
spl53_292,
inference(avatar_split_clause,[],[f4299,f7563]) ).
fof(f7563,plain,
( spl53_292
<=> ! [X0] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_292])]) ).
fof(f4299,plain,
! [X0] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2397]) ).
fof(f2397,plain,
! [X0] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1416]) ).
fof(f1416,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1267]) ).
fof(f1267,axiom,
! [X90] :
( class_Rings_Ocomm__semiring__0(X90)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).
fof(f7561,plain,
spl53_291,
inference(avatar_split_clause,[],[f4298,f7559]) ).
fof(f7559,plain,
( spl53_291
<=> ! [X0] :
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_291])]) ).
fof(f4298,plain,
! [X0] :
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2396]) ).
fof(f2396,plain,
! [X0] :
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1415]) ).
fof(f1415,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1264]) ).
fof(f1264,axiom,
! [X90] :
( class_Rings_Ocomm__semiring__0(X90)
=> class_Rings_Osemiring__0(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).
fof(f7557,plain,
spl53_290,
inference(avatar_split_clause,[],[f4297,f7555]) ).
fof(f7555,plain,
( spl53_290
<=> ! [X0] :
( class_Rings_Osemiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_290])]) ).
fof(f4297,plain,
! [X0] :
( class_Rings_Osemiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2395]) ).
fof(f2395,plain,
! [X0] :
( class_Rings_Osemiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1414]) ).
fof(f1414,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Rings_Osemiring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1272]) ).
fof(f1272,axiom,
! [X90] :
( class_Rings_Ocomm__semiring__0(X90)
=> class_Rings_Osemiring(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).
fof(f7553,plain,
spl53_289,
inference(avatar_split_clause,[],[f4296,f7551]) ).
fof(f7551,plain,
( spl53_289
<=> ! [X0] :
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_289])]) ).
fof(f4296,plain,
! [X0] :
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2394]) ).
fof(f2394,plain,
! [X0] :
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1413]) ).
fof(f1413,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1244]) ).
fof(f1244,axiom,
! [X90] :
( class_Rings_Ocomm__semiring__0(X90)
=> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).
fof(f7549,plain,
spl53_288,
inference(avatar_split_clause,[],[f4295,f7547]) ).
fof(f7547,plain,
( spl53_288
<=> ! [X0] :
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_288])]) ).
fof(f4295,plain,
! [X0] :
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2393]) ).
fof(f2393,plain,
! [X0] :
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1412]) ).
fof(f1412,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1255]) ).
fof(f1255,axiom,
! [X90] :
( class_Rings_Ocomm__semiring__0(X90)
=> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).
fof(f7545,plain,
spl53_287,
inference(avatar_split_clause,[],[f4293,f7543]) ).
fof(f7543,plain,
( spl53_287
<=> ! [X0] :
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_287])]) ).
fof(f4293,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2391]) ).
fof(f2391,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(ennf_transformation,[],[f1410]) ).
fof(f1410,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(X0)
=> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1249]) ).
fof(f1249,axiom,
! [X90] :
( class_Groups_Ocomm__monoid__add(X90)
=> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).
fof(f7541,plain,
spl53_286,
inference(avatar_split_clause,[],[f4292,f7539]) ).
fof(f7539,plain,
( spl53_286
<=> ! [X0] :
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_286])]) ).
fof(f4292,plain,
! [X0] :
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2390]) ).
fof(f2390,plain,
! [X0] :
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(ennf_transformation,[],[f1409]) ).
fof(f1409,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(X0)
=> class_Groups_Omonoid__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1263]) ).
fof(f1263,axiom,
! [X90] :
( class_Groups_Ocomm__monoid__add(X90)
=> class_Groups_Omonoid__add(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).
fof(f7537,plain,
spl53_285,
inference(avatar_split_clause,[],[f4291,f7535]) ).
fof(f7535,plain,
( spl53_285
<=> ! [X0] :
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_285])]) ).
fof(f4291,plain,
! [X0] :
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2389]) ).
fof(f2389,plain,
! [X0] :
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(ennf_transformation,[],[f1408]) ).
fof(f1408,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(X0)
=> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1246]) ).
fof(f1246,axiom,
! [X90] :
( class_Groups_Ocomm__monoid__add(X90)
=> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).
fof(f7533,plain,
spl53_284,
inference(avatar_split_clause,[],[f4289,f7531]) ).
fof(f7531,plain,
( spl53_284
<=> ! [X0] :
( class_Groups_Ozero(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_284])]) ).
fof(f4289,plain,
! [X0] :
( class_Groups_Ozero(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f2387]) ).
fof(f2387,plain,
! [X0] :
( class_Groups_Ozero(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ozero(X0) ),
inference(ennf_transformation,[],[f1406]) ).
fof(f1406,plain,
! [X0] :
( class_Groups_Ozero(X0)
=> class_Groups_Ozero(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1278]) ).
fof(f1278,axiom,
! [X90] :
( class_Groups_Ozero(X90)
=> class_Groups_Ozero(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).
fof(f7529,plain,
spl53_283,
inference(avatar_split_clause,[],[f4286,f7527]) ).
fof(f7527,plain,
( spl53_283
<=> ! [X0] :
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_283])]) ).
fof(f4286,plain,
! [X0] :
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2384]) ).
fof(f2384,plain,
! [X0] :
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(ennf_transformation,[],[f1403]) ).
fof(f1403,plain,
! [X0] :
( class_Groups_Ocancel__comm__monoid__add(X0)
=> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1241]) ).
fof(f1241,axiom,
! [X90] :
( class_Groups_Ocancel__comm__monoid__add(X90)
=> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).
fof(f7525,plain,
spl53_282,
inference(avatar_split_clause,[],[f4285,f7523]) ).
fof(f7523,plain,
( spl53_282
<=> ! [X0] :
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_282])]) ).
fof(f4285,plain,
! [X0] :
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2383]) ).
fof(f2383,plain,
! [X0] :
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(ennf_transformation,[],[f1402]) ).
fof(f1402,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,
! [X90] :
( class_Groups_Ocancel__comm__monoid__add(X90)
=> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).
fof(f7521,plain,
spl53_281,
inference(avatar_split_clause,[],[f4284,f7519]) ).
fof(f7519,plain,
( spl53_281
<=> ! [X0] :
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_281])]) ).
fof(f4284,plain,
! [X0] :
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2382]) ).
fof(f2382,plain,
! [X0] :
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(ennf_transformation,[],[f1401]) ).
fof(f1401,plain,
! [X0] :
( class_Groups_Ocancel__comm__monoid__add(X0)
=> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1233]) ).
fof(f1233,axiom,
! [X90] :
( class_Groups_Ocancel__comm__monoid__add(X90)
=> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).
fof(f7517,plain,
spl53_280,
inference(avatar_split_clause,[],[f4276,f7515]) ).
fof(f7515,plain,
( spl53_280
<=> ! [X0] :
( class_Groups_Ominus(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_280])]) ).
fof(f4276,plain,
! [X0] :
( class_Groups_Ominus(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f2374]) ).
fof(f2374,plain,
! [X0] :
( class_Groups_Ominus(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(ennf_transformation,[],[f1393]) ).
fof(f1393,plain,
! [X0] :
( class_Groups_Oab__group__add(X0)
=> class_Groups_Ominus(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1276]) ).
fof(f1276,axiom,
! [X90] :
( class_Groups_Oab__group__add(X90)
=> class_Groups_Ominus(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ominus) ).
fof(f7513,plain,
spl53_279,
inference(avatar_split_clause,[],[f4275,f7511]) ).
fof(f7511,plain,
( spl53_279
<=> ! [X0] :
( class_Groups_Ouminus(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_279])]) ).
fof(f4275,plain,
! [X0] :
( class_Groups_Ouminus(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f2373]) ).
fof(f2373,plain,
! [X0] :
( class_Groups_Ouminus(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(ennf_transformation,[],[f1392]) ).
fof(f1392,plain,
! [X0] :
( class_Groups_Oab__group__add(X0)
=> class_Groups_Ouminus(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1274]) ).
fof(f1274,axiom,
! [X90] :
( class_Groups_Oab__group__add(X90)
=> class_Groups_Ouminus(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ouminus) ).
fof(f7509,plain,
spl53_278,
inference(avatar_split_clause,[],[f4274,f7507]) ).
fof(f7507,plain,
( spl53_278
<=> ! [X0] :
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_278])]) ).
fof(f4274,plain,
! [X0] :
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f2372]) ).
fof(f2372,plain,
! [X0] :
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(ennf_transformation,[],[f1391]) ).
fof(f1391,plain,
! [X0] :
( class_Groups_Oab__group__add(X0)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1265]) ).
fof(f1265,axiom,
! [X90] :
( class_Groups_Oab__group__add(X90)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
fof(f7505,plain,
spl53_277,
inference(avatar_split_clause,[],[f4273,f7503]) ).
fof(f7503,plain,
( spl53_277
<=> ! [X0] :
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_277])]) ).
fof(f4273,plain,
! [X0] :
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f2371]) ).
fof(f2371,plain,
! [X0] :
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(ennf_transformation,[],[f1390]) ).
fof(f1390,plain,
! [X0] :
( class_Groups_Oab__group__add(X0)
=> class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1256]) ).
fof(f1256,axiom,
! [X90] :
( class_Groups_Oab__group__add(X90)
=> class_Groups_Oab__group__add(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).
fof(f7501,plain,
spl53_276,
inference(avatar_split_clause,[],[f4272,f7499]) ).
fof(f7499,plain,
( spl53_276
<=> ! [X0] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_276])]) ).
fof(f4272,plain,
! [X0] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f2370]) ).
fof(f2370,plain,
! [X0] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(ennf_transformation,[],[f1389]) ).
fof(f1389,plain,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1224]) ).
fof(f1224,axiom,
! [X90] :
( class_Rings_Oidom(X90)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f7497,plain,
spl53_275,
inference(avatar_split_clause,[],[f4271,f7495]) ).
fof(f7495,plain,
( spl53_275
<=> ! [X0] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_275])]) ).
fof(f4271,plain,
! [X0] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f2369]) ).
fof(f2369,plain,
! [X0] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(ennf_transformation,[],[f1388]) ).
fof(f1388,plain,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1248]) ).
fof(f1248,axiom,
! [X90] :
( class_Rings_Oidom(X90)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
fof(f7493,plain,
spl53_274,
inference(avatar_split_clause,[],[f4270,f7491]) ).
fof(f7491,plain,
( spl53_274
<=> ! [X0] :
( class_Rings_Oidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_274])]) ).
fof(f4270,plain,
! [X0] :
( class_Rings_Oidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f2368]) ).
fof(f2368,plain,
! [X0] :
( class_Rings_Oidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(ennf_transformation,[],[f1387]) ).
fof(f1387,plain,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Rings_Oidom(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1280]) ).
fof(f1280,axiom,
! [X90] :
( class_Rings_Oidom(X90)
=> class_Rings_Oidom(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).
fof(f7489,plain,
spl53_273,
inference(avatar_split_clause,[],[f4269,f7487]) ).
fof(f7487,plain,
( spl53_273
<=> ! [X0] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_273])]) ).
fof(f4269,plain,
! [X0] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f2367]) ).
fof(f2367,plain,
! [X0] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(ennf_transformation,[],[f1386]) ).
fof(f1386,plain,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1234]) ).
fof(f1234,axiom,
! [X90] :
( class_Rings_Oidom(X90)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).
fof(f7485,plain,
spl53_272,
inference(avatar_split_clause,[],[f4268,f7483]) ).
fof(f7483,plain,
( spl53_272
<=> ! [X0] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_272])]) ).
fof(f4268,plain,
! [X0] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f2366]) ).
fof(f2366,plain,
! [X0] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(ennf_transformation,[],[f1385]) ).
fof(f1385,plain,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1237]) ).
fof(f1237,axiom,
! [X90] :
( class_Rings_Oidom(X90)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).
fof(f7481,plain,
spl53_271,
inference(avatar_split_clause,[],[f4267,f7479]) ).
fof(f7479,plain,
( spl53_271
<=> ! [X0] :
( class_Int_Onumber(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_271])]) ).
fof(f4267,plain,
! [X0] :
( class_Int_Onumber(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(cnf_transformation,[],[f2365]) ).
fof(f2365,plain,
! [X0] :
( class_Int_Onumber(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(ennf_transformation,[],[f1384]) ).
fof(f1384,plain,
! [X0] :
( class_Rings_Ocomm__ring__1(X0)
=> class_Int_Onumber(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1281]) ).
fof(f1281,axiom,
! [X90] :
( class_Rings_Ocomm__ring__1(X90)
=> class_Int_Onumber(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Onumber) ).
fof(f7477,plain,
spl53_270,
inference(avatar_split_clause,[],[f4266,f7475]) ).
fof(f7475,plain,
( spl53_270
<=> ! [X0] :
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_270])]) ).
fof(f4266,plain,
! [X0] :
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(cnf_transformation,[],[f2364]) ).
fof(f2364,plain,
! [X0] :
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(ennf_transformation,[],[f1383]) ).
fof(f1383,plain,
! [X0] :
( class_Rings_Ocomm__ring__1(X0)
=> class_Int_Onumber__ring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1271]) ).
fof(f1271,axiom,
! [X90] :
( class_Rings_Ocomm__ring__1(X90)
=> class_Int_Onumber__ring(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Onumber__ring) ).
fof(f7473,plain,
spl53_269,
inference(avatar_split_clause,[],[f4265,f7471]) ).
fof(f7471,plain,
( spl53_269
<=> ! [X0] :
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_269])]) ).
fof(f4265,plain,
! [X0] :
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(cnf_transformation,[],[f2363]) ).
fof(f2363,plain,
! [X0] :
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(ennf_transformation,[],[f1382]) ).
fof(f1382,plain,
! [X0] :
( class_Rings_Ocomm__ring__1(X0)
=> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1262]) ).
fof(f1262,axiom,
! [X90] :
( class_Rings_Ocomm__ring__1(X90)
=> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).
fof(f7469,plain,
spl53_268,
inference(avatar_split_clause,[],[f4264,f7467]) ).
fof(f7467,plain,
( spl53_268
<=> ! [X0] :
( class_Rings_Oring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_268])]) ).
fof(f4264,plain,
! [X0] :
( class_Rings_Oring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(cnf_transformation,[],[f2362]) ).
fof(f2362,plain,
! [X0] :
( class_Rings_Oring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(ennf_transformation,[],[f1381]) ).
fof(f1381,plain,
! [X0] :
( class_Rings_Ocomm__ring__1(X0)
=> class_Rings_Oring__1(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1275]) ).
fof(f1275,axiom,
! [X90] :
( class_Rings_Ocomm__ring__1(X90)
=> class_Rings_Oring__1(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).
fof(f7465,plain,
spl53_267,
inference(avatar_split_clause,[],[f4263,f7463]) ).
fof(f7463,plain,
( spl53_267
<=> ! [X0] :
( class_Rings_Oring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_267])]) ).
fof(f4263,plain,
! [X0] :
( class_Rings_Oring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ),
inference(cnf_transformation,[],[f2361]) ).
fof(f2361,plain,
! [X0] :
( class_Rings_Oring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ),
inference(ennf_transformation,[],[f1380]) ).
fof(f1380,plain,
! [X0] :
( class_Rings_Ocomm__ring(X0)
=> class_Rings_Oring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1279]) ).
fof(f1279,axiom,
! [X90] :
( class_Rings_Ocomm__ring(X90)
=> class_Rings_Oring(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).
fof(f7461,plain,
spl53_266,
inference(avatar_split_clause,[],[f4262,f7459]) ).
fof(f7459,plain,
( spl53_266
<=> ! [X0] :
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_266])]) ).
fof(f4262,plain,
! [X0] :
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ),
inference(cnf_transformation,[],[f2360]) ).
fof(f2360,plain,
! [X0] :
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ),
inference(ennf_transformation,[],[f1379]) ).
fof(f1379,plain,
! [X0] :
( class_Rings_Ocomm__ring(X0)
=> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1268]) ).
fof(f1268,axiom,
! [X90] :
( class_Rings_Ocomm__ring(X90)
=> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).
fof(f7457,plain,
spl53_265,
inference(avatar_split_clause,[],[f4261,f7455]) ).
fof(f7455,plain,
( spl53_265
<=> ! [X0] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_265])]) ).
fof(f4261,plain,
! [X0] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2359]) ).
fof(f2359,plain,
! [X0] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1378]) ).
fof(f1378,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Orderings_Oorder(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1269]) ).
fof(f1269,axiom,
! [X90] :
( class_Rings_Olinordered__idom(X90)
=> class_Orderings_Oorder(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oorder) ).
fof(f7453,plain,
spl53_264,
inference(avatar_split_clause,[],[f4260,f7451]) ).
fof(f7451,plain,
( spl53_264
<=> ! [X0] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_264])]) ).
fof(f4260,plain,
! [X0] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2358]) ).
fof(f2358,plain,
! [X0] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1377]) ).
fof(f1377,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Orderings_Opreorder(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1259]) ).
fof(f1259,axiom,
! [X90] :
( class_Rings_Olinordered__idom(X90)
=> class_Orderings_Opreorder(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(f7449,plain,
spl53_263,
inference(avatar_split_clause,[],[f4259,f7447]) ).
fof(f7447,plain,
( spl53_263
<=> ! [X0] :
( class_Orderings_Oord(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_263])]) ).
fof(f4259,plain,
! [X0] :
( class_Orderings_Oord(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2357]) ).
fof(f2357,plain,
! [X0] :
( class_Orderings_Oord(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1376]) ).
fof(f1376,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Orderings_Oord(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1273]) ).
fof(f1273,axiom,
! [X90] :
( class_Rings_Olinordered__idom(X90)
=> class_Orderings_Oord(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).
fof(f7445,plain,
spl53_262,
inference(avatar_split_clause,[],[f4258,f7443]) ).
fof(f7443,plain,
( spl53_262
<=> ! [X0] :
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_262])]) ).
fof(f4258,plain,
! [X0] :
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2356]) ).
fof(f2356,plain,
! [X0] :
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1375]) ).
fof(f1375,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1243]) ).
fof(f1243,axiom,
! [X90] :
( class_Rings_Olinordered__idom(X90)
=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).
fof(f7441,plain,
spl53_261,
inference(avatar_split_clause,[],[f4257,f7439]) ).
fof(f7439,plain,
( spl53_261
<=> ! [X0] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_261])]) ).
fof(f4257,plain,
! [X0] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2355]) ).
fof(f2355,plain,
! [X0] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1374]) ).
fof(f1374,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Orderings_Olinorder(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1260]) ).
fof(f1260,axiom,
! [X90] :
( class_Rings_Olinordered__idom(X90)
=> class_Orderings_Olinorder(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(f7437,plain,
spl53_260,
inference(avatar_split_clause,[],[f4256,f7435]) ).
fof(f7435,plain,
( spl53_260
<=> ! [X0] :
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_260])]) ).
fof(f4256,plain,
! [X0] :
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2354]) ).
fof(f2354,plain,
! [X0] :
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1373]) ).
fof(f1373,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1229]) ).
fof(f1229,axiom,
! [X90] :
( class_Rings_Olinordered__idom(X90)
=> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).
fof(f7433,plain,
spl53_259,
inference(avatar_split_clause,[],[f4255,f7431]) ).
fof(f7431,plain,
( spl53_259
<=> ! [X0] :
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_259])]) ).
fof(f4255,plain,
! [X0] :
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2353]) ).
fof(f2353,plain,
! [X0] :
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1372]) ).
fof(f1372,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1231]) ).
fof(f1231,axiom,
! [X90] :
( class_Rings_Olinordered__idom(X90)
=> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).
fof(f7429,plain,
spl53_258,
inference(avatar_split_clause,[],[f4254,f7427]) ).
fof(f7427,plain,
( spl53_258
<=> ! [X0] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_258])]) ).
fof(f4254,plain,
! [X0] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2352]) ).
fof(f2352,plain,
! [X0] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1371]) ).
fof(f1371,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1226]) ).
fof(f1226,axiom,
! [X90] :
( class_Rings_Olinordered__idom(X90)
=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f7425,plain,
spl53_257,
inference(avatar_split_clause,[],[f4253,f7423]) ).
fof(f7423,plain,
( spl53_257
<=> ! [X0] :
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_257])]) ).
fof(f4253,plain,
! [X0] :
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2351]) ).
fof(f2351,plain,
! [X0] :
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1370]) ).
fof(f1370,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1225]) ).
fof(f1225,axiom,
! [X90] :
( class_Rings_Olinordered__idom(X90)
=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f7421,plain,
spl53_256,
inference(avatar_split_clause,[],[f4252,f7419]) ).
fof(f7419,plain,
( spl53_256
<=> ! [X0] :
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_256])]) ).
fof(f4252,plain,
! [X0] :
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2350]) ).
fof(f2350,plain,
! [X0] :
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1369]) ).
fof(f1369,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1235]) ).
fof(f1235,axiom,
! [X90] :
( class_Rings_Olinordered__idom(X90)
=> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).
fof(f7417,plain,
spl53_255,
inference(avatar_split_clause,[],[f4251,f7415]) ).
fof(f7415,plain,
( spl53_255
<=> ! [X0] :
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_255])]) ).
fof(f4251,plain,
! [X0] :
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2349]) ).
fof(f2349,plain,
! [X0] :
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1368]) ).
fof(f1368,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1247]) ).
fof(f1247,axiom,
! [X90] :
( class_Rings_Olinordered__idom(X90)
=> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).
fof(f7413,plain,
spl53_254,
inference(avatar_split_clause,[],[f4250,f7411]) ).
fof(f7411,plain,
( spl53_254
<=> ! [X0] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_254])]) ).
fof(f4250,plain,
! [X0] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2348]) ).
fof(f2348,plain,
! [X0] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1367]) ).
fof(f1367,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Int_Oring__char__0(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1270]) ).
fof(f1270,axiom,
! [X90] :
( class_Rings_Olinordered__idom(X90)
=> class_Int_Oring__char__0(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).
fof(f7409,plain,
spl53_253,
inference(avatar_split_clause,[],[f4249,f7407]) ).
fof(f7407,plain,
( spl53_253
<=> ! [X0] :
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_253])]) ).
fof(f4249,plain,
! [X0] :
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2347]) ).
fof(f2347,plain,
! [X0] :
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1366]) ).
fof(f1366,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1230]) ).
fof(f1230,axiom,
! [X90] :
( class_Rings_Olinordered__idom(X90)
=> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).
fof(f7405,plain,
spl53_252,
inference(avatar_split_clause,[],[f4248,f7403]) ).
fof(f7403,plain,
( spl53_252
<=> ! [X0] :
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_252])]) ).
fof(f4248,plain,
! [X0] :
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2346]) ).
fof(f2346,plain,
! [X0] :
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1365]) ).
fof(f1365,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1242]) ).
fof(f1242,axiom,
! [X90] :
( class_Rings_Olinordered__idom(X90)
=> class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).
fof(f7401,plain,
spl53_251,
inference(avatar_split_clause,[],[f4247,f7399]) ).
fof(f7399,plain,
( spl53_251
<=> ! [X0] :
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_251])]) ).
fof(f4247,plain,
! [X0] :
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2345]) ).
fof(f2345,plain,
! [X0] :
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1364]) ).
fof(f1364,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1238]) ).
fof(f1238,axiom,
! [X90] :
( class_Rings_Olinordered__idom(X90)
=> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).
fof(f7397,plain,
spl53_250,
inference(avatar_split_clause,[],[f4246,f7395]) ).
fof(f7395,plain,
( spl53_250
<=> ! [X0] :
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_250])]) ).
fof(f4246,plain,
! [X0] :
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2344]) ).
fof(f2344,plain,
! [X0] :
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1363]) ).
fof(f1363,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1227]) ).
fof(f1227,axiom,
! [X90] :
( class_Rings_Olinordered__idom(X90)
=> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).
fof(f7393,plain,
spl53_249,
inference(avatar_split_clause,[],[f4245,f7391]) ).
fof(f7391,plain,
( spl53_249
<=> ! [X0] :
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_249])]) ).
fof(f4245,plain,
! [X0] :
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2343]) ).
fof(f2343,plain,
! [X0] :
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1362]) ).
fof(f1362,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1251]) ).
fof(f1251,axiom,
! [X90] :
( class_Rings_Olinordered__idom(X90)
=> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).
fof(f7389,plain,
spl53_248,
inference(avatar_split_clause,[],[f4244,f7387]) ).
fof(f7387,plain,
( spl53_248
<=> ! [X0] :
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_248])]) ).
fof(f4244,plain,
! [X0] :
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2342]) ).
fof(f2342,plain,
! [X0] :
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1361]) ).
fof(f1361,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1240]) ).
fof(f1240,axiom,
! [X90] :
( class_Rings_Olinordered__idom(X90)
=> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).
fof(f7385,plain,
spl53_247,
inference(avatar_split_clause,[],[f4243,f7383]) ).
fof(f7383,plain,
( spl53_247
<=> ! [X0] :
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_247])]) ).
fof(f4243,plain,
! [X0] :
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2341]) ).
fof(f2341,plain,
! [X0] :
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1360]) ).
fof(f1360,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1236]) ).
fof(f1236,axiom,
! [X90] :
( class_Rings_Olinordered__idom(X90)
=> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).
fof(f7381,plain,
spl53_246,
inference(avatar_split_clause,[],[f4242,f7379]) ).
fof(f7379,plain,
( spl53_246
<=> ! [X0] :
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_246])]) ).
fof(f4242,plain,
! [X0] :
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2340]) ).
fof(f2340,plain,
! [X0] :
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1359]) ).
fof(f1359,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1232]) ).
fof(f1232,axiom,
! [X90] :
( class_Rings_Olinordered__idom(X90)
=> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).
fof(f7377,plain,
spl53_245,
inference(avatar_split_clause,[],[f4241,f7375]) ).
fof(f7375,plain,
( spl53_245
<=> ! [X0] :
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_245])]) ).
fof(f4241,plain,
! [X0] :
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2339]) ).
fof(f2339,plain,
! [X0] :
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1358]) ).
fof(f1358,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1258]) ).
fof(f1258,axiom,
! [X90] :
( class_Rings_Olinordered__idom(X90)
=> class_Rings_Oordered__ring(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).
fof(f7373,plain,
spl53_244,
inference(avatar_split_clause,[],[f4240,f7371]) ).
fof(f7371,plain,
( spl53_244
<=> ! [X0] :
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_244])]) ).
fof(f4240,plain,
! [X0] :
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2338]) ).
fof(f2338,plain,
! [X0] :
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1357]) ).
fof(f1357,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1250]) ).
fof(f1250,axiom,
! [X90] :
( class_Rings_Olinordered__idom(X90)
=> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).
fof(f7369,plain,
spl53_243,
inference(avatar_split_clause,[],[f4239,f7367]) ).
fof(f7367,plain,
( spl53_243
<=> ! [X0] :
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_243])]) ).
fof(f4239,plain,
! [X0] :
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2337]) ).
fof(f2337,plain,
! [X0] :
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1356]) ).
fof(f1356,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1239]) ).
fof(f1239,axiom,
! [X90] :
( class_Rings_Olinordered__idom(X90)
=> class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).
fof(f7365,plain,
spl53_242,
inference(avatar_split_clause,[],[f4238,f7363]) ).
fof(f7363,plain,
( spl53_242
<=> ! [X0] :
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_242])]) ).
fof(f4238,plain,
! [X0] :
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2336]) ).
fof(f2336,plain,
! [X0] :
( class_Rings_Olinordered__semiring__1__strict(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__semiring__1__strict(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1228]) ).
fof(f1228,axiom,
! [X90] :
( class_Rings_Olinordered__idom(X90)
=> class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).
fof(f7361,plain,
spl53_241,
inference(avatar_split_clause,[],[f4233,f7359]) ).
fof(f7359,plain,
( spl53_241
<=> ! [X0] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0))
| ~ class_Fields_Ofield(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_241])]) ).
fof(f4233,plain,
! [X0] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0))
| ~ class_Fields_Ofield(X0) ),
inference(cnf_transformation,[],[f2332]) ).
fof(f2332,plain,
! [X0] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0))
| ~ class_Fields_Ofield(X0) ),
inference(ennf_transformation,[],[f1351]) ).
fof(f1351,plain,
! [X0] :
( class_Fields_Ofield(X0)
=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1254]) ).
fof(f1254,axiom,
! [X90] :
( class_Fields_Ofield(X90)
=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Osemiring__div) ).
fof(f7357,plain,
spl53_240,
inference(avatar_split_clause,[],[f4232,f7355]) ).
fof(f7355,plain,
( spl53_240
<=> ! [X0] :
( class_Divides_Oring__div(tc_Polynomial_Opoly(X0))
| ~ class_Fields_Ofield(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_240])]) ).
fof(f4232,plain,
! [X0] :
( class_Divides_Oring__div(tc_Polynomial_Opoly(X0))
| ~ class_Fields_Ofield(X0) ),
inference(cnf_transformation,[],[f2331]) ).
fof(f2331,plain,
! [X0] :
( class_Divides_Oring__div(tc_Polynomial_Opoly(X0))
| ~ class_Fields_Ofield(X0) ),
inference(ennf_transformation,[],[f1350]) ).
fof(f1350,plain,
! [X0] :
( class_Fields_Ofield(X0)
=> class_Divides_Oring__div(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1266]) ).
fof(f1266,axiom,
! [X90] :
( class_Fields_Ofield(X90)
=> class_Divides_Oring__div(tc_Polynomial_Opoly(X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Oring__div) ).
fof(f7353,plain,
spl53_239,
inference(avatar_split_clause,[],[f4192,f7351]) ).
fof(f7351,plain,
( spl53_239
<=> ! [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,[spl53_239])]) ).
fof(f4192,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f1310]) ).
fof(f1310,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
inference(rectify,[],[f321]) ).
fof(f321,axiom,
! [X3] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(f7349,plain,
spl53_238,
inference(avatar_split_clause,[],[f4191,f7347]) ).
fof(f7347,plain,
( spl53_238
<=> ! [X0] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_238])]) ).
fof(f4191,plain,
! [X0] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0) = X0,
inference(cnf_transformation,[],[f1309]) ).
fof(f1309,plain,
! [X0] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0) = X0,
inference(rectify,[],[f617]) ).
fof(f617,axiom,
! [X11] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X11) = X11,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__is__id) ).
fof(f7345,plain,
spl53_237,
inference(avatar_split_clause,[],[f4187,f7343]) ).
fof(f4187,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f1305]) ).
fof(f1305,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rectify,[],[f317]) ).
fof(f317,axiom,
! [X3] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
fof(f7341,plain,
spl53_236,
inference(avatar_split_clause,[],[f4180,f7339]) ).
fof(f7339,plain,
( spl53_236
<=> ! [X0] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_236])]) ).
fof(f4180,plain,
! [X0] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,X0),
inference(cnf_transformation,[],[f1298]) ).
fof(f1298,plain,
! [X0] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,X0),
inference(rectify,[],[f754]) ).
fof(f754,axiom,
! [X61] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,X61),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__i__not__number__of) ).
fof(f7337,plain,
~ spl53_235,
inference(avatar_split_clause,[],[f4144,f7334]) ).
fof(f7334,plain,
( spl53_235
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_235])]) ).
fof(f4144,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f742]) ).
fof(f742,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).
fof(f7332,plain,
~ spl53_234,
inference(avatar_split_clause,[],[f4143,f7329]) ).
fof(f7329,plain,
( spl53_234
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_234])]) ).
fof(f4143,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(cnf_transformation,[],[f575]) ).
fof(f575,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
fof(f7327,plain,
spl53_233,
inference(avatar_split_clause,[],[f5823,f7325]) ).
fof(f7325,plain,
( spl53_233
<=> ! [X0] : sP0(X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_233])]) ).
fof(f5823,plain,
! [X0] : sP0(X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(equality_resolution,[],[f4715]) ).
fof(f4715,plain,
! [X0,X1] :
( sP0(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1 ),
inference(cnf_transformation,[],[f3642]) ).
fof(f7323,plain,
spl53_232,
inference(avatar_split_clause,[],[f5814,f7321]) ).
fof(f5814,plain,
! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(equality_resolution,[],[f4680]) ).
fof(f4680,plain,
! [X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3617]) ).
fof(f7319,plain,
spl53_231,
inference(avatar_split_clause,[],[f5813,f7317]) ).
fof(f7317,plain,
( spl53_231
<=> ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_231])]) ).
fof(f5813,plain,
! [X1] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(equality_resolution,[],[f4675]) ).
fof(f4675,plain,
! [X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f3614]) ).
fof(f3614,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,[],[f3613]) ).
fof(f3613,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,[],[f1708]) ).
fof(f1708,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,[],[f692]) ).
fof(f692,axiom,
! [X40,X15] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,X40)
<=> ( X15 != X40
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X40) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__less__def) ).
fof(f7315,plain,
~ spl53_230,
inference(avatar_split_clause,[],[f5618,f7312]) ).
fof(f7312,plain,
( spl53_230
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK50 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_230])]) ).
fof(f5618,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != sK50,
inference(cnf_transformation,[],[f3917]) ).
fof(f7310,plain,
~ spl53_229,
inference(avatar_split_clause,[],[f5617,f7307]) ).
fof(f7307,plain,
( spl53_229
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = sK51 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_229])]) ).
fof(f5617,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != sK51,
inference(cnf_transformation,[],[f3917]) ).
fof(f7305,plain,
spl53_228,
inference(avatar_split_clause,[],[f4179,f7303]) ).
fof(f7303,plain,
( spl53_228
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_228])]) ).
fof(f4179,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0),
inference(cnf_transformation,[],[f1297]) ).
fof(f1297,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0),
inference(rectify,[],[f194]) ).
fof(f194,axiom,
! [X3] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
fof(f7301,plain,
spl53_227,
inference(avatar_split_clause,[],[f4178,f7299]) ).
fof(f4178,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f1296]) ).
fof(f1296,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0),
inference(rectify,[],[f601]) ).
fof(f601,axiom,
! [X61] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X61,X61),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__refl) ).
fof(f7297,plain,
spl53_226,
inference(avatar_split_clause,[],[f4177,f7295]) ).
fof(f7295,plain,
( spl53_226
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_226])]) ).
fof(f4177,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0),
inference(cnf_transformation,[],[f1295]) ).
fof(f1295,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0),
inference(rectify,[],[f689]) ).
fof(f689,axiom,
! [X61] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X61,X61),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__refl) ).
fof(f7293,plain,
spl53_225,
inference(avatar_split_clause,[],[f4175,f7291]) ).
fof(f7291,plain,
( spl53_225
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_225])]) ).
fof(f4175,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0),
inference(cnf_transformation,[],[f1293]) ).
fof(f1293,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0),
inference(rectify,[],[f176]) ).
fof(f176,axiom,
! [X3] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(f7289,plain,
~ spl53_224,
inference(avatar_split_clause,[],[f4142,f7286]) ).
fof(f4142,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Oii,
inference(cnf_transformation,[],[f755]) ).
fof(f755,axiom,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Oii,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__i__not__zero) ).
fof(f7284,plain,
~ spl53_223,
inference(avatar_split_clause,[],[f4141,f7281]) ).
fof(f7281,plain,
( spl53_223
<=> c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Oii ),
introduced(avatar_definition,[new_symbols(naming,[spl53_223])]) ).
fof(f4141,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Complex_Oii,
inference(cnf_transformation,[],[f756]) ).
fof(f756,axiom,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Complex_Oii,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__i__not__one) ).
fof(f7279,plain,
~ spl53_222,
inference(avatar_split_clause,[],[f4140,f7276]) ).
fof(f7276,plain,
( spl53_222
<=> v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_222])]) ).
fof(f4140,plain,
v_k____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
v_k____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_kas_I2_J) ).
fof(f7274,plain,
~ spl53_221,
inference(avatar_split_clause,[],[f4139,f7271]) ).
fof(f7271,plain,
( spl53_221
<=> v_a____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_221])]) ).
fof(f4139,plain,
v_a____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
v_a____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_kas_I1_J) ).
fof(f7269,plain,
spl53_220,
inference(avatar_split_clause,[],[f4138,f7266]) ).
fof(f7266,plain,
( spl53_220
<=> class_Groups_Ominus(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_220])]) ).
fof(f4138,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(cnf_transformation,[],[f1101]) ).
fof(f1101,axiom,
class_Groups_Ominus(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
fof(f7264,plain,
spl53_219,
inference(avatar_split_clause,[],[f4137,f7261]) ).
fof(f7261,plain,
( spl53_219
<=> class_Groups_Ominus(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_219])]) ).
fof(f4137,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(cnf_transformation,[],[f1060]) ).
fof(f1060,axiom,
class_Groups_Ominus(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).
fof(f7259,plain,
spl53_218,
inference(avatar_split_clause,[],[f4136,f7256]) ).
fof(f7256,plain,
( spl53_218
<=> class_Groups_Ominus(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_218])]) ).
fof(f4136,plain,
class_Groups_Ominus(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1172]) ).
fof(f1172,axiom,
class_Groups_Ominus(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ominus) ).
fof(f7254,plain,
spl53_217,
inference(avatar_split_clause,[],[f4135,f7251]) ).
fof(f7251,plain,
( spl53_217
<=> class_Groups_Ominus(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_217])]) ).
fof(f4135,plain,
class_Groups_Ominus(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1215]) ).
fof(f1215,axiom,
class_Groups_Ominus(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ominus) ).
fof(f7249,plain,
spl53_216,
inference(avatar_split_clause,[],[f4134,f7246]) ).
fof(f7246,plain,
( spl53_216
<=> class_Groups_Ominus(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_216])]) ).
fof(f4134,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(cnf_transformation,[],[f1112]) ).
fof(f1112,axiom,
class_Groups_Ominus(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
fof(f7244,plain,
spl53_215,
inference(avatar_split_clause,[],[f4133,f7241]) ).
fof(f7241,plain,
( spl53_215
<=> class_Orderings_Oorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_215])]) ).
fof(f4133,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f1098]) ).
fof(f1098,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(f7239,plain,
spl53_214,
inference(avatar_split_clause,[],[f4132,f7236]) ).
fof(f7236,plain,
( spl53_214
<=> class_Orderings_Oorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_214])]) ).
fof(f4132,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',arity_Int__Oint__Orderings_Oorder) ).
fof(f7234,plain,
spl53_213,
inference(avatar_split_clause,[],[f4131,f7231]) ).
fof(f7231,plain,
( spl53_213
<=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_213])]) ).
fof(f4131,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1165]) ).
fof(f1165,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
fof(f7229,plain,
spl53_212,
inference(avatar_split_clause,[],[f4130,f7226]) ).
fof(f7226,plain,
( spl53_212
<=> class_Orderings_Oorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_212])]) ).
fof(f4130,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f1109]) ).
fof(f1109,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(f7224,plain,
spl53_211,
inference(avatar_split_clause,[],[f4129,f7221]) ).
fof(f7221,plain,
( spl53_211
<=> class_Orderings_Opreorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_211])]) ).
fof(f4129,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f1092]) ).
fof(f1092,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(f7219,plain,
spl53_210,
inference(avatar_split_clause,[],[f4128,f7216]) ).
fof(f7216,plain,
( spl53_210
<=> class_Orderings_Opreorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_210])]) ).
fof(f4128,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',arity_Int__Oint__Orderings_Opreorder) ).
fof(f7214,plain,
spl53_209,
inference(avatar_split_clause,[],[f4127,f7211]) ).
fof(f7211,plain,
( spl53_209
<=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_209])]) ).
fof(f4127,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1156]) ).
fof(f1156,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
fof(f7209,plain,
spl53_208,
inference(avatar_split_clause,[],[f4126,f7206]) ).
fof(f7206,plain,
( spl53_208
<=> class_Orderings_Opreorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_208])]) ).
fof(f4126,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f1108]) ).
fof(f1108,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(f7204,plain,
spl53_207,
inference(avatar_split_clause,[],[f4125,f7201]) ).
fof(f7201,plain,
( spl53_207
<=> class_Orderings_Oord(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_207])]) ).
fof(f4125,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(cnf_transformation,[],[f1100]) ).
fof(f1100,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(f7199,plain,
spl53_206,
inference(avatar_split_clause,[],[f4124,f7196]) ).
fof(f7196,plain,
( spl53_206
<=> class_Orderings_Oord(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_206])]) ).
fof(f4124,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(cnf_transformation,[],[f1057]) ).
fof(f1057,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
fof(f7194,plain,
spl53_205,
inference(avatar_split_clause,[],[f4123,f7191]) ).
fof(f7191,plain,
( spl53_205
<=> class_Orderings_Oord(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_205])]) ).
fof(f4123,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1169]) ).
fof(f1169,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oord) ).
fof(f7189,plain,
spl53_204,
inference(avatar_split_clause,[],[f4122,f7186]) ).
fof(f7186,plain,
( spl53_204
<=> class_Orderings_Oord(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_204])]) ).
fof(f4122,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(cnf_transformation,[],[f1110]) ).
fof(f1110,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(f7184,plain,
spl53_203,
inference(avatar_split_clause,[],[f4121,f7181]) ).
fof(f7181,plain,
( spl53_203
<=> class_Groups_Ouminus(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_203])]) ).
fof(f4121,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(cnf_transformation,[],[f1058]) ).
fof(f1058,axiom,
class_Groups_Ouminus(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).
fof(f7179,plain,
spl53_202,
inference(avatar_split_clause,[],[f4120,f7176]) ).
fof(f7176,plain,
( spl53_202
<=> class_Groups_Ouminus(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_202])]) ).
fof(f4120,plain,
class_Groups_Ouminus(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1170]) ).
fof(f1170,axiom,
class_Groups_Ouminus(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ouminus) ).
fof(f7174,plain,
spl53_201,
inference(avatar_split_clause,[],[f4119,f7171]) ).
fof(f7171,plain,
( spl53_201
<=> class_Groups_Ouminus(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_201])]) ).
fof(f4119,plain,
class_Groups_Ouminus(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1213]) ).
fof(f1213,axiom,
class_Groups_Ouminus(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ouminus) ).
fof(f7169,plain,
spl53_200,
inference(avatar_split_clause,[],[f4118,f7166]) ).
fof(f7166,plain,
( spl53_200
<=> class_Groups_Ouminus(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_200])]) ).
fof(f4118,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(cnf_transformation,[],[f1111]) ).
fof(f1111,axiom,
class_Groups_Ouminus(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).
fof(f7164,plain,
spl53_199,
inference(avatar_split_clause,[],[f4117,f7161]) ).
fof(f4117,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(cnf_transformation,[],[f1087]) ).
fof(f1087,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(f7159,plain,
spl53_198,
inference(avatar_split_clause,[],[f4116,f7156]) ).
fof(f4116,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',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(f7154,plain,
spl53_197,
inference(avatar_split_clause,[],[f4115,f7151]) ).
fof(f4115,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1149]) ).
fof(f1149,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(f7149,plain,
spl53_196,
inference(avatar_split_clause,[],[f4114,f7146]) ).
fof(f4114,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1197]) ).
fof(f1197,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(f7144,plain,
spl53_195,
inference(avatar_split_clause,[],[f4113,f7141]) ).
fof(f7141,plain,
( spl53_195
<=> class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_195])]) ).
fof(f4113,plain,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f1088]) ).
fof(f1088,axiom,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).
fof(f7139,plain,
spl53_194,
inference(avatar_split_clause,[],[f4112,f7136]) ).
fof(f7136,plain,
( spl53_194
<=> class_Rings_Ocomm__semiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_194])]) ).
fof(f4112,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',arity_Int__Oint__Rings_Ocomm__semiring__0) ).
fof(f7134,plain,
spl53_193,
inference(avatar_split_clause,[],[f4111,f7131]) ).
fof(f7131,plain,
( spl53_193
<=> class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_193])]) ).
fof(f4111,plain,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1150]) ).
fof(f1150,axiom,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__0) ).
fof(f7129,plain,
spl53_192,
inference(avatar_split_clause,[],[f4110,f7126]) ).
fof(f7126,plain,
( spl53_192
<=> class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_192])]) ).
fof(f4110,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1198]) ).
fof(f1198,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(f7124,plain,
spl53_191,
inference(avatar_split_clause,[],[f4109,f7121]) ).
fof(f7121,plain,
( spl53_191
<=> class_Groups_Omonoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_191])]) ).
fof(f4109,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f1094]) ).
fof(f1094,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
fof(f7119,plain,
spl53_190,
inference(avatar_split_clause,[],[f4108,f7116]) ).
fof(f7116,plain,
( spl53_190
<=> class_Groups_Omonoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_190])]) ).
fof(f4108,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',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(f7114,plain,
spl53_189,
inference(avatar_split_clause,[],[f4107,f7111]) ).
fof(f7111,plain,
( spl53_189
<=> class_Groups_Omonoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_189])]) ).
fof(f4107,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1158]) ).
fof(f1158,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
fof(f7109,plain,
spl53_188,
inference(avatar_split_clause,[],[f4106,f7106]) ).
fof(f7106,plain,
( spl53_188
<=> class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_188])]) ).
fof(f4106,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1203]) ).
fof(f1203,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
fof(f7104,plain,
spl53_187,
inference(avatar_split_clause,[],[f4105,f7101]) ).
fof(f7101,plain,
( spl53_187
<=> class_Power_Opower(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_187])]) ).
fof(f4105,plain,
class_Power_Opower(tc_Nat_Onat),
inference(cnf_transformation,[],[f1102]) ).
fof(f1102,axiom,
class_Power_Opower(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
fof(f7099,plain,
spl53_186,
inference(avatar_split_clause,[],[f4104,f7096]) ).
fof(f7096,plain,
( spl53_186
<=> class_Power_Opower(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_186])]) ).
fof(f4104,plain,
class_Power_Opower(tc_Int_Oint),
inference(cnf_transformation,[],[f1061]) ).
fof(f1061,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
fof(f7094,plain,
spl53_185,
inference(avatar_split_clause,[],[f4103,f7091]) ).
fof(f7091,plain,
( spl53_185
<=> class_Power_Opower(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_185])]) ).
fof(f4103,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1174]) ).
fof(f1174,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Power_Opower) ).
fof(f7089,plain,
spl53_184,
inference(avatar_split_clause,[],[f4102,f7086]) ).
fof(f7086,plain,
( spl53_184
<=> class_Power_Opower(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_184])]) ).
fof(f4102,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1217]) ).
fof(f1217,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).
fof(f7084,plain,
spl53_183,
inference(avatar_split_clause,[],[f4101,f7081]) ).
fof(f7081,plain,
( spl53_183
<=> class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_183])]) ).
fof(f4101,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1086]) ).
fof(f1086,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(f7079,plain,
spl53_182,
inference(avatar_split_clause,[],[f4100,f7076]) ).
fof(f7076,plain,
( spl53_182
<=> class_Groups_Ocomm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_182])]) ).
fof(f4100,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',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(f7074,plain,
spl53_181,
inference(avatar_split_clause,[],[f4099,f7071]) ).
fof(f7071,plain,
( spl53_181
<=> class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_181])]) ).
fof(f4099,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1146]) ).
fof(f1146,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
fof(f7069,plain,
spl53_180,
inference(avatar_split_clause,[],[f4098,f7066]) ).
fof(f7066,plain,
( spl53_180
<=> class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_180])]) ).
fof(f4098,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1196]) ).
fof(f1196,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
fof(f7064,plain,
spl53_179,
inference(avatar_split_clause,[],[f4097,f7061]) ).
fof(f7061,plain,
( spl53_179
<=> class_Groups_Ozero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_179])]) ).
fof(f4097,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f1103]) ).
fof(f1103,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
fof(f7059,plain,
spl53_178,
inference(avatar_split_clause,[],[f4096,f7056]) ).
fof(f7056,plain,
( spl53_178
<=> class_Int_Onumber(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_178])]) ).
fof(f4096,plain,
class_Int_Onumber(tc_Nat_Onat),
inference(cnf_transformation,[],[f1104]) ).
fof(f1104,axiom,
class_Int_Onumber(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).
fof(f7054,plain,
spl53_177,
inference(avatar_split_clause,[],[f4095,f7051]) ).
fof(f7051,plain,
( spl53_177
<=> class_Int_Onumber(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_177])]) ).
fof(f4095,plain,
class_Int_Onumber(tc_Int_Oint),
inference(cnf_transformation,[],[f1065]) ).
fof(f1065,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber) ).
fof(f7049,plain,
spl53_176,
inference(avatar_split_clause,[],[f4094,f7046]) ).
fof(f7046,plain,
( spl53_176
<=> class_Groups_Ozero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_176])]) ).
fof(f4094,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(cnf_transformation,[],[f1062]) ).
fof(f1062,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
fof(f7044,plain,
spl53_175,
inference(avatar_split_clause,[],[f4093,f7041]) ).
fof(f7041,plain,
( spl53_175
<=> class_Groups_Ozero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_175])]) ).
fof(f4093,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1175]) ).
fof(f1175,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).
fof(f7039,plain,
spl53_174,
inference(avatar_split_clause,[],[f4092,f7036]) ).
fof(f7036,plain,
( spl53_174
<=> class_Int_Onumber(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_174])]) ).
fof(f4092,plain,
class_Int_Onumber(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1178]) ).
fof(f1178,axiom,
class_Int_Onumber(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber) ).
fof(f7034,plain,
spl53_173,
inference(avatar_split_clause,[],[f4091,f7031]) ).
fof(f7031,plain,
( spl53_173
<=> class_Int_Onumber(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_173])]) ).
fof(f4091,plain,
class_Int_Onumber(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1221]) ).
fof(f1221,axiom,
class_Int_Onumber(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber) ).
fof(f7029,plain,
spl53_172,
inference(avatar_split_clause,[],[f4090,f7026]) ).
fof(f7026,plain,
( spl53_172
<=> class_Groups_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_172])]) ).
fof(f4090,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1218]) ).
fof(f1218,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(f7024,plain,
spl53_171,
inference(avatar_split_clause,[],[f4089,f7021]) ).
fof(f7021,plain,
( spl53_171
<=> class_Rings_Ozero__neq__one(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_171])]) ).
fof(f4089,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(cnf_transformation,[],[f1091]) ).
fof(f1091,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(f7019,plain,
spl53_170,
inference(avatar_split_clause,[],[f4088,f7016]) ).
fof(f7016,plain,
( spl53_170
<=> class_Rings_Ono__zero__divisors(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_170])]) ).
fof(f4088,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(cnf_transformation,[],[f1085]) ).
fof(f1085,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
fof(f7014,plain,
spl53_169,
inference(avatar_split_clause,[],[f4087,f7011]) ).
fof(f7011,plain,
( spl53_169
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_169])]) ).
fof(f4087,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(cnf_transformation,[],[f1068]) ).
fof(f1068,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f7009,plain,
spl53_168,
inference(avatar_split_clause,[],[f4086,f7006]) ).
fof(f7006,plain,
( spl53_168
<=> class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_168])]) ).
fof(f4086,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1078]) ).
fof(f1078,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(f7004,plain,
spl53_167,
inference(avatar_split_clause,[],[f4085,f7001]) ).
fof(f7001,plain,
( spl53_167
<=> class_Rings_Omult__zero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_167])]) ).
fof(f4085,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(cnf_transformation,[],[f1097]) ).
fof(f1097,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
fof(f6999,plain,
spl53_166,
inference(avatar_split_clause,[],[f4084,f6996]) ).
fof(f6996,plain,
( spl53_166
<=> class_Rings_Ozero__neq__one(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_166])]) ).
fof(f4084,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',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(f6994,plain,
spl53_165,
inference(avatar_split_clause,[],[f4083,f6991]) ).
fof(f6991,plain,
( spl53_165
<=> class_Rings_Omult__zero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_165])]) ).
fof(f4083,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',arity_Int__Oint__Rings_Omult__zero) ).
fof(f6989,plain,
spl53_164,
inference(avatar_split_clause,[],[f4082,f6986]) ).
fof(f6986,plain,
( spl53_164
<=> class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_164])]) ).
fof(f4082,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1025]) ).
fof(f1025,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
fof(f6984,plain,
spl53_163,
inference(avatar_split_clause,[],[f4081,f6981]) ).
fof(f6981,plain,
( spl53_163
<=> class_Rings_Ono__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_163])]) ).
fof(f4081,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',arity_Int__Oint__Rings_Ono__zero__divisors) ).
fof(f6979,plain,
spl53_162,
inference(avatar_split_clause,[],[f4080,f6976]) ).
fof(f6976,plain,
( spl53_162
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_162])]) ).
fof(f4080,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(cnf_transformation,[],[f1008]) ).
fof(f1008,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f6974,plain,
spl53_161,
inference(avatar_split_clause,[],[f4079,f6971]) ).
fof(f6971,plain,
( spl53_161
<=> class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_161])]) ).
fof(f4079,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1154]) ).
fof(f1154,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).
fof(f6969,plain,
spl53_160,
inference(avatar_split_clause,[],[f4078,f6966]) ).
fof(f6966,plain,
( spl53_160
<=> class_Rings_Omult__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_160])]) ).
fof(f4078,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1163]) ).
fof(f1163,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).
fof(f6964,plain,
spl53_159,
inference(avatar_split_clause,[],[f4077,f6961]) ).
fof(f6961,plain,
( spl53_159
<=> class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_159])]) ).
fof(f4077,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1136]) ).
fof(f1136,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
fof(f6959,plain,
spl53_158,
inference(avatar_split_clause,[],[f4076,f6956]) ).
fof(f6956,plain,
( spl53_158
<=> class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_158])]) ).
fof(f4076,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1145]) ).
fof(f1145,axiom,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).
fof(f6954,plain,
spl53_157,
inference(avatar_split_clause,[],[f4075,f6951]) ).
fof(f6951,plain,
( spl53_157
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_157])]) ).
fof(f4075,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1113]) ).
fof(f1113,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f6949,plain,
spl53_156,
inference(avatar_split_clause,[],[f4074,f6946]) ).
fof(f6946,plain,
( spl53_156
<=> class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_156])]) ).
fof(f4074,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1190]) ).
fof(f1190,axiom,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).
fof(f6944,plain,
spl53_155,
inference(avatar_split_clause,[],[f4073,f6941]) ).
fof(f6941,plain,
( spl53_155
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_155])]) ).
fof(f4073,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1181]) ).
fof(f1181,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f6939,plain,
spl53_154,
inference(avatar_split_clause,[],[f4072,f6936]) ).
fof(f6936,plain,
( spl53_154
<=> class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_154])]) ).
fof(f4072,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1202]) ).
fof(f1202,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
fof(f6934,plain,
spl53_153,
inference(avatar_split_clause,[],[f4071,f6931]) ).
fof(f6931,plain,
( spl53_153
<=> class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_153])]) ).
fof(f4071,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1195]) ).
fof(f1195,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
fof(f6929,plain,
spl53_152,
inference(avatar_split_clause,[],[f4070,f6926]) ).
fof(f6926,plain,
( spl53_152
<=> class_Rings_Omult__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_152])]) ).
fof(f4070,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1208]) ).
fof(f1208,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).
fof(f6924,plain,
spl53_151,
inference(avatar_split_clause,[],[f4069,f6921]) ).
fof(f6921,plain,
( spl53_151
<=> class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_151])]) ).
fof(f4069,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',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).
fof(f6919,plain,
spl53_150,
inference(avatar_split_clause,[],[f4068,f6916]) ).
fof(f6916,plain,
( spl53_150
<=> class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_150])]) ).
fof(f4068,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f1082]) ).
fof(f1082,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
fof(f6914,plain,
spl53_149,
inference(avatar_split_clause,[],[f4067,f6911]) ).
fof(f6911,plain,
( spl53_149
<=> class_Rings_Osemiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_149])]) ).
fof(f4067,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1099]) ).
fof(f1099,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
fof(f6909,plain,
spl53_148,
inference(avatar_split_clause,[],[f4066,f6906]) ).
fof(f6906,plain,
( spl53_148
<=> class_Rings_Osemiring__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_148])]) ).
fof(f4066,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f1096]) ).
fof(f1096,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(f6904,plain,
spl53_147,
inference(avatar_split_clause,[],[f4065,f6901]) ).
fof(f6901,plain,
( spl53_147
<=> class_Rings_Osemiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_147])]) ).
fof(f4065,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',arity_Int__Oint__Rings_Osemiring__0) ).
fof(f6899,plain,
spl53_146,
inference(avatar_split_clause,[],[f4064,f6896]) ).
fof(f6896,plain,
( spl53_146
<=> class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_146])]) ).
fof(f4064,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f1029]) ).
fof(f1029,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
fof(f6894,plain,
spl53_145,
inference(avatar_split_clause,[],[f4063,f6891]) ).
fof(f6891,plain,
( spl53_145
<=> class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_145])]) ).
fof(f4063,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',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).
fof(f6889,plain,
spl53_144,
inference(avatar_split_clause,[],[f4062,f6886]) ).
fof(f6886,plain,
( spl53_144
<=> class_Rings_Osemiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_144])]) ).
fof(f4062,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1056]) ).
fof(f1056,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
fof(f6884,plain,
spl53_143,
inference(avatar_split_clause,[],[f4061,f6881]) ).
fof(f6881,plain,
( spl53_143
<=> class_Rings_Osemiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_143])]) ).
fof(f4061,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1168]) ).
fof(f1168,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).
fof(f6879,plain,
spl53_142,
inference(avatar_split_clause,[],[f4060,f6876]) ).
fof(f6876,plain,
( spl53_142
<=> class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_142])]) ).
fof(f4060,plain,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1141]) ).
fof(f1141,axiom,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).
fof(f6874,plain,
spl53_141,
inference(avatar_split_clause,[],[f4059,f6871]) ).
fof(f6871,plain,
( spl53_141
<=> class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_141])]) ).
fof(f4059,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',arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add) ).
fof(f6869,plain,
spl53_140,
inference(avatar_split_clause,[],[f4058,f6866]) ).
fof(f6866,plain,
( spl53_140
<=> class_Rings_Osemiring__0(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_140])]) ).
fof(f4058,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1161]) ).
fof(f1161,axiom,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__0) ).
fof(f6864,plain,
spl53_139,
inference(avatar_split_clause,[],[f4057,f6861]) ).
fof(f6861,plain,
( spl53_139
<=> class_Rings_Osemiring__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_139])]) ).
fof(f4057,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1206]) ).
fof(f1206,axiom,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).
fof(f6859,plain,
spl53_138,
inference(avatar_split_clause,[],[f4056,f6856]) ).
fof(f6856,plain,
( spl53_138
<=> class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_138])]) ).
fof(f4056,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1193]) ).
fof(f1193,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
fof(f6854,plain,
spl53_137,
inference(avatar_split_clause,[],[f4055,f6851]) ).
fof(f6851,plain,
( spl53_137
<=> class_Rings_Osemiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_137])]) ).
fof(f4055,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1212]) ).
fof(f1212,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).
fof(f6849,plain,
spl53_136,
inference(avatar_split_clause,[],[f4054,f6846]) ).
fof(f6846,plain,
( spl53_136
<=> class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_136])]) ).
fof(f4054,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',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).
fof(f6844,plain,
spl53_135,
inference(avatar_split_clause,[],[f4053,f6841]) ).
fof(f6841,plain,
( spl53_135
<=> class_Groups_Omonoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_135])]) ).
fof(f4053,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1095]) ).
fof(f1095,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(f6839,plain,
spl53_134,
inference(avatar_split_clause,[],[f4052,f6836]) ).
fof(f6836,plain,
( spl53_134
<=> class_Groups_Omonoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_134])]) ).
fof(f4052,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',arity_Int__Oint__Groups_Omonoid__add) ).
fof(f6834,plain,
spl53_133,
inference(avatar_split_clause,[],[f4051,f6831]) ).
fof(f4051,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1160]) ).
fof(f1160,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).
fof(f6829,plain,
spl53_132,
inference(avatar_split_clause,[],[f4050,f6826]) ).
fof(f4050,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1205]) ).
fof(f1205,axiom,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).
fof(f6824,plain,
spl53_131,
inference(avatar_split_clause,[],[f4049,f6821]) ).
fof(f6821,plain,
( spl53_131
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_131])]) ).
fof(f4049,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1075]) ).
fof(f1075,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(f6819,plain,
spl53_130,
inference(avatar_split_clause,[],[f4048,f6816]) ).
fof(f6816,plain,
( spl53_130
<=> class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_130])]) ).
fof(f4048,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f1081]) ).
fof(f1081,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
fof(f6814,plain,
spl53_129,
inference(avatar_split_clause,[],[f4047,f6811]) ).
fof(f6811,plain,
( spl53_129
<=> class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_129])]) ).
fof(f4047,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1083]) ).
fof(f1083,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(f6809,plain,
spl53_128,
inference(avatar_split_clause,[],[f4046,f6806]) ).
fof(f6806,plain,
( spl53_128
<=> class_Rings_Ocomm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_128])]) ).
fof(f4046,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1090]) ).
fof(f1090,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
fof(f6804,plain,
spl53_127,
inference(avatar_split_clause,[],[f4045,f6801]) ).
fof(f6801,plain,
( spl53_127
<=> class_Groups_Oone(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_127])]) ).
fof(f4045,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(cnf_transformation,[],[f1105]) ).
fof(f1105,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
fof(f6799,plain,
spl53_126,
inference(avatar_split_clause,[],[f4044,f6796]) ).
fof(f4044,plain,
class_Rings_Odvd(tc_Nat_Onat),
inference(cnf_transformation,[],[f1106]) ).
fof(f1106,axiom,
class_Rings_Odvd(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).
fof(f6794,plain,
spl53_125,
inference(avatar_split_clause,[],[f4043,f6791]) ).
fof(f6791,plain,
( spl53_125
<=> class_Groups_Oab__semigroup__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_125])]) ).
fof(f4043,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f1028]) ).
fof(f1028,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
fof(f6789,plain,
spl53_124,
inference(avatar_split_clause,[],[f4042,f6786]) ).
fof(f6786,plain,
( spl53_124
<=> class_Groups_Oone(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_124])]) ).
fof(f4042,plain,
class_Groups_Oone(tc_Int_Oint),
inference(cnf_transformation,[],[f1066]) ).
fof(f1066,axiom,
class_Groups_Oone(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
fof(f6784,plain,
spl53_123,
inference(avatar_split_clause,[],[f4041,f6781]) ).
fof(f6781,plain,
( spl53_123
<=> class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_123])]) ).
fof(f4041,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1030]) ).
fof(f1030,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
fof(f6779,plain,
spl53_122,
inference(avatar_split_clause,[],[f4040,f6776]) ).
fof(f6776,plain,
( spl53_122
<=> class_Rings_Ocomm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_122])]) ).
fof(f4040,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',arity_Int__Oint__Rings_Ocomm__semiring) ).
fof(f6774,plain,
spl53_121,
inference(avatar_split_clause,[],[f4039,f6771]) ).
fof(f6771,plain,
( spl53_121
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_121])]) ).
fof(f4039,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1017]) ).
fof(f1017,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
fof(f6769,plain,
spl53_120,
inference(avatar_split_clause,[],[f4038,f6766]) ).
fof(f4038,plain,
class_Rings_Odvd(tc_Int_Oint),
inference(cnf_transformation,[],[f1067]) ).
fof(f1067,axiom,
class_Rings_Odvd(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).
fof(f6764,plain,
spl53_119,
inference(avatar_split_clause,[],[f4037,f6761]) ).
fof(f6761,plain,
( spl53_119
<=> class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_119])]) ).
fof(f4037,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1127]) ).
fof(f1127,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).
fof(f6759,plain,
spl53_118,
inference(avatar_split_clause,[],[f4036,f6756]) ).
fof(f6756,plain,
( spl53_118
<=> class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_118])]) ).
fof(f4036,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1142]) ).
fof(f1142,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).
fof(f6754,plain,
spl53_117,
inference(avatar_split_clause,[],[f4035,f6751]) ).
fof(f6751,plain,
( spl53_117
<=> class_Groups_Oone(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_117])]) ).
fof(f4035,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1179]) ).
fof(f1179,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).
fof(f6749,plain,
spl53_116,
inference(avatar_split_clause,[],[f4034,f6746]) ).
fof(f6746,plain,
( spl53_116
<=> class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_116])]) ).
fof(f4034,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1140]) ).
fof(f1140,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).
fof(f6744,plain,
spl53_115,
inference(avatar_split_clause,[],[f4033,f6741]) ).
fof(f6741,plain,
( spl53_115
<=> class_Rings_Ocomm__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_115])]) ).
fof(f4033,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1152]) ).
fof(f1152,axiom,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).
fof(f6739,plain,
spl53_114,
inference(avatar_split_clause,[],[f4032,f6736]) ).
fof(f6736,plain,
( spl53_114
<=> class_Rings_Odvd(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_114])]) ).
fof(f4032,plain,
class_Rings_Odvd(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1180]) ).
fof(f1180,axiom,
class_Rings_Odvd(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odvd) ).
fof(f6734,plain,
spl53_113,
inference(avatar_split_clause,[],[f4031,f6731]) ).
fof(f6731,plain,
( spl53_113
<=> class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_113])]) ).
fof(f4031,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1200]) ).
fof(f1200,axiom,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).
fof(f6729,plain,
spl53_112,
inference(avatar_split_clause,[],[f4030,f6726]) ).
fof(f6726,plain,
( spl53_112
<=> class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_112])]) ).
fof(f4030,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1194]) ).
fof(f1194,axiom,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).
fof(f6724,plain,
spl53_111,
inference(avatar_split_clause,[],[f4029,f6721]) ).
fof(f6721,plain,
( spl53_111
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_111])]) ).
fof(f4029,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1186]) ).
fof(f1186,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).
fof(f6719,plain,
spl53_110,
inference(avatar_split_clause,[],[f4028,f6716]) ).
fof(f6716,plain,
( spl53_110
<=> class_Rings_Odvd(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_110])]) ).
fof(f4028,plain,
class_Rings_Odvd(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1223]) ).
fof(f1223,axiom,
class_Rings_Odvd(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odvd) ).
fof(f6714,plain,
spl53_109,
inference(avatar_split_clause,[],[f4027,f6711]) ).
fof(f6711,plain,
( spl53_109
<=> class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_109])]) ).
fof(f4027,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1192]) ).
fof(f1192,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
fof(f6709,plain,
spl53_108,
inference(avatar_split_clause,[],[f4026,f6706]) ).
fof(f6706,plain,
( spl53_108
<=> class_Groups_Oone(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_108])]) ).
fof(f4026,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1222]) ).
fof(f1222,axiom,
class_Groups_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).
fof(f6704,plain,
spl53_107,
inference(avatar_split_clause,[],[f4025,f6701]) ).
fof(f6701,plain,
( spl53_107
<=> class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_107])]) ).
fof(f4025,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(cnf_transformation,[],[f1080]) ).
fof(f1080,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(f6699,plain,
spl53_106,
inference(avatar_split_clause,[],[f4024,f6696]) ).
fof(f4024,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(cnf_transformation,[],[f1027]) ).
fof(f1027,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
fof(f6694,plain,
spl53_105,
inference(avatar_split_clause,[],[f4023,f6691]) ).
fof(f6691,plain,
( spl53_105
<=> class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_105])]) ).
fof(f4023,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1139]) ).
fof(f1139,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(f6689,plain,
spl53_104,
inference(avatar_split_clause,[],[f4022,f6686]) ).
fof(f4022,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',arity_Int__Oint__Groups_Ogroup__add) ).
fof(f6684,plain,
spl53_103,
inference(avatar_split_clause,[],[f4021,f6681]) ).
fof(f4021,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1162]) ).
fof(f1162,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(f6679,plain,
spl53_102,
inference(avatar_split_clause,[],[f4020,f6676]) ).
fof(f4020,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1207]) ).
fof(f1207,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(f6674,plain,
spl53_101,
inference(avatar_split_clause,[],[f4019,f6671]) ).
fof(f6671,plain,
( spl53_101
<=> class_Orderings_Olinorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_101])]) ).
fof(f4019,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f1093]) ).
fof(f1093,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(f6669,plain,
spl53_100,
inference(avatar_split_clause,[],[f4018,f6666]) ).
fof(f6666,plain,
( spl53_100
<=> class_Orderings_Olinorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_100])]) ).
fof(f4018,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',arity_Int__Oint__Orderings_Olinorder) ).
fof(f6664,plain,
spl53_99,
inference(avatar_split_clause,[],[f4017,f6661]) ).
fof(f6661,plain,
( spl53_99
<=> class_Groups_Oab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_99])]) ).
fof(f4017,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',arity_Int__Oint__Groups_Oab__group__add) ).
fof(f6659,plain,
spl53_98,
inference(avatar_split_clause,[],[f4016,f6656]) ).
fof(f6656,plain,
( spl53_98
<=> class_Groups_Oab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_98])]) ).
fof(f4016,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1153]) ).
fof(f1153,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).
fof(f6654,plain,
spl53_97,
inference(avatar_split_clause,[],[f4015,f6651]) ).
fof(f6651,plain,
( spl53_97
<=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_97])]) ).
fof(f4015,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1157]) ).
fof(f1157,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(f6649,plain,
spl53_96,
inference(avatar_split_clause,[],[f4014,f6646]) ).
fof(f6646,plain,
( spl53_96
<=> class_Groups_Oab__group__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_96])]) ).
fof(f4014,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1201]) ).
fof(f1201,axiom,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).
fof(f6644,plain,
spl53_95,
inference(avatar_split_clause,[],[f4013,f6641]) ).
fof(f6641,plain,
( spl53_95
<=> class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_95])]) ).
fof(f4013,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f1072]) ).
fof(f1072,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
fof(f6639,plain,
spl53_94,
inference(avatar_split_clause,[],[f4012,f6636]) ).
fof(f6636,plain,
( spl53_94
<=> class_Int_Onumber__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_94])]) ).
fof(f4012,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f1055]) ).
fof(f1055,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).
fof(f6634,plain,
spl53_93,
inference(avatar_split_clause,[],[f4011,f6631]) ).
fof(f6631,plain,
( spl53_93
<=> class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_93])]) ).
fof(f4011,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f1013]) ).
fof(f1013,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
fof(f6629,plain,
spl53_92,
inference(avatar_split_clause,[],[f4010,f6626]) ).
fof(f6626,plain,
( spl53_92
<=> class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_92])]) ).
fof(f4010,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1120]) ).
fof(f1120,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).
fof(f6624,plain,
spl53_91,
inference(avatar_split_clause,[],[f4009,f6621]) ).
fof(f6621,plain,
( spl53_91
<=> class_Int_Onumber__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_91])]) ).
fof(f4009,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1167]) ).
fof(f1167,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
fof(f6619,plain,
spl53_90,
inference(avatar_split_clause,[],[f4008,f6616]) ).
fof(f6616,plain,
( spl53_90
<=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_90])]) ).
fof(f4008,plain,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1211]) ).
fof(f1211,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber__ring) ).
fof(f6614,plain,
spl53_89,
inference(avatar_split_clause,[],[f4007,f6611]) ).
fof(f6611,plain,
( spl53_89
<=> class_Rings_Oidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_89])]) ).
fof(f4007,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(cnf_transformation,[],[f1064]) ).
fof(f1064,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
fof(f6609,plain,
spl53_88,
inference(avatar_split_clause,[],[f4006,f6606]) ).
fof(f6606,plain,
( spl53_88
<=> class_Rings_Oidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_88])]) ).
fof(f4006,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1177]) ).
fof(f1177,axiom,
class_Rings_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).
fof(f6604,plain,
spl53_87,
inference(avatar_split_clause,[],[f4005,f6601]) ).
fof(f6601,plain,
( spl53_87
<=> class_Rings_Oidom(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_87])]) ).
fof(f4005,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1220]) ).
fof(f1220,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
fof(f6599,plain,
spl53_86,
inference(avatar_split_clause,[],[f4004,f6596]) ).
fof(f6596,plain,
( spl53_86
<=> class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_86])]) ).
fof(f4004,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1074]) ).
fof(f1074,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(f6594,plain,
spl53_85,
inference(avatar_split_clause,[],[f4003,f6591]) ).
fof(f6591,plain,
( spl53_85
<=> class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_85])]) ).
fof(f4003,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1015]) ).
fof(f1015,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
fof(f6589,plain,
spl53_84,
inference(avatar_split_clause,[],[f4002,f6586]) ).
fof(f6586,plain,
( spl53_84
<=> class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_84])]) ).
fof(f4002,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1125]) ).
fof(f1125,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).
fof(f6584,plain,
spl53_83,
inference(avatar_split_clause,[],[f4001,f6581]) ).
fof(f6581,plain,
( spl53_83
<=> class_Rings_Ocomm__ring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_83])]) ).
fof(f4001,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',arity_Int__Oint__Rings_Ocomm__ring__1) ).
fof(f6579,plain,
spl53_82,
inference(avatar_split_clause,[],[f4000,f6576]) ).
fof(f6576,plain,
( spl53_82
<=> class_Rings_Ocomm__ring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_82])]) ).
fof(f4000,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1159]) ).
fof(f1159,axiom,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).
fof(f6574,plain,
spl53_81,
inference(avatar_split_clause,[],[f3999,f6571]) ).
fof(f6571,plain,
( spl53_81
<=> class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_81])]) ).
fof(f3999,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1204]) ).
fof(f1204,axiom,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).
fof(f6569,plain,
spl53_80,
inference(avatar_split_clause,[],[f3998,f6566]) ).
fof(f6566,plain,
( spl53_80
<=> class_Rings_Oring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_80])]) ).
fof(f3998,plain,
class_Rings_Oring(tc_Int_Oint),
inference(cnf_transformation,[],[f1063]) ).
fof(f1063,axiom,
class_Rings_Oring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
fof(f6564,plain,
spl53_79,
inference(avatar_split_clause,[],[f3997,f6561]) ).
fof(f6561,plain,
( spl53_79
<=> class_Rings_Oring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_79])]) ).
fof(f3997,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1176]) ).
fof(f1176,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).
fof(f6559,plain,
spl53_78,
inference(avatar_split_clause,[],[f3996,f6556]) ).
fof(f6556,plain,
( spl53_78
<=> class_Rings_Oring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_78])]) ).
fof(f3996,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1219]) ).
fof(f1219,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).
fof(f6554,plain,
spl53_77,
inference(avatar_split_clause,[],[f3995,f6551]) ).
fof(f6551,plain,
( spl53_77
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_77])]) ).
fof(f3995,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(cnf_transformation,[],[f1070]) ).
fof(f1070,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f6549,plain,
spl53_76,
inference(avatar_split_clause,[],[f3994,f6546]) ).
fof(f6546,plain,
( spl53_76
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_76])]) ).
fof(f3994,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(cnf_transformation,[],[f1010]) ).
fof(f1010,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f6544,plain,
spl53_75,
inference(avatar_split_clause,[],[f3993,f6541]) ).
fof(f6541,plain,
( spl53_75
<=> class_Rings_Ocomm__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_75])]) ).
fof(f3993,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',arity_Int__Oint__Rings_Ocomm__ring) ).
fof(f6539,plain,
spl53_74,
inference(avatar_split_clause,[],[f3992,f6536]) ).
fof(f6536,plain,
( spl53_74
<=> class_Rings_Ocomm__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_74])]) ).
fof(f3992,plain,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1164]) ).
fof(f1164,axiom,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring) ).
fof(f6534,plain,
spl53_73,
inference(avatar_split_clause,[],[f3991,f6531]) ).
fof(f6531,plain,
( spl53_73
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_73])]) ).
fof(f3991,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1115]) ).
fof(f1115,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f6529,plain,
spl53_72,
inference(avatar_split_clause,[],[f3990,f6526]) ).
fof(f6526,plain,
( spl53_72
<=> class_Rings_Ocomm__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_72])]) ).
fof(f3990,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1209]) ).
fof(f1209,axiom,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).
fof(f6524,plain,
spl53_71,
inference(avatar_split_clause,[],[f3989,f6521]) ).
fof(f6521,plain,
( spl53_71
<=> class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_71])]) ).
fof(f3989,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1076]) ).
fof(f1076,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
fof(f6519,plain,
spl53_70,
inference(avatar_split_clause,[],[f3988,f6516]) ).
fof(f6516,plain,
( spl53_70
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_70])]) ).
fof(f3988,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1069]) ).
fof(f1069,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f6514,plain,
spl53_69,
inference(avatar_split_clause,[],[f3987,f6511]) ).
fof(f6511,plain,
( spl53_69
<=> class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_69])]) ).
fof(f3987,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1019]) ).
fof(f1019,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
fof(f6509,plain,
spl53_68,
inference(avatar_split_clause,[],[f3986,f6506]) ).
fof(f6506,plain,
( spl53_68
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_68])]) ).
fof(f3986,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1009]) ).
fof(f1009,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f6504,plain,
spl53_67,
inference(avatar_split_clause,[],[f3985,f6501]) ).
fof(f6501,plain,
( spl53_67
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_67])]) ).
fof(f3985,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1114]) ).
fof(f1114,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f6499,plain,
spl53_66,
inference(avatar_split_clause,[],[f3984,f6496]) ).
fof(f6496,plain,
( spl53_66
<=> class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_66])]) ).
fof(f3984,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1129]) ).
fof(f1129,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).
fof(f6494,plain,
spl53_65,
inference(avatar_split_clause,[],[f3983,f6491]) ).
fof(f6491,plain,
( spl53_65
<=> class_Rings_Oordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_65])]) ).
fof(f3983,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1084]) ).
fof(f1084,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
fof(f6489,plain,
spl53_64,
inference(avatar_split_clause,[],[f3982,f6486]) ).
fof(f6486,plain,
( spl53_64
<=> class_Rings_Oordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_64])]) ).
fof(f3982,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1031]) ).
fof(f1031,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
fof(f6484,plain,
spl53_63,
inference(avatar_split_clause,[],[f3981,f6481]) ).
fof(f6481,plain,
( spl53_63
<=> class_Rings_Oordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_63])]) ).
fof(f3981,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1144]) ).
fof(f1144,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).
fof(f6479,plain,
spl53_62,
inference(avatar_split_clause,[],[f3980,f6476]) ).
fof(f6476,plain,
( spl53_62
<=> class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_62])]) ).
fof(f3980,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1073]) ).
fof(f1073,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(f6474,plain,
spl53_61,
inference(avatar_split_clause,[],[f3979,f6471]) ).
fof(f6471,plain,
( spl53_61
<=> class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_61])]) ).
fof(f3979,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1014]) ).
fof(f1014,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
fof(f6469,plain,
spl53_60,
inference(avatar_split_clause,[],[f3978,f6466]) ).
fof(f6466,plain,
( spl53_60
<=> class_Int_Oring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_60])]) ).
fof(f3978,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',arity_Int__Oint__Int_Oring__char__0) ).
fof(f6464,plain,
spl53_59,
inference(avatar_split_clause,[],[f3977,f6461]) ).
fof(f6461,plain,
( spl53_59
<=> class_Int_Oring__char__0(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_59])]) ).
fof(f3977,plain,
class_Int_Oring__char__0(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1166]) ).
fof(f1166,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).
fof(f6459,plain,
spl53_58,
inference(avatar_split_clause,[],[f3976,f6456]) ).
fof(f6456,plain,
( spl53_58
<=> class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_58])]) ).
fof(f3976,plain,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1123]) ).
fof(f1123,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).
fof(f6454,plain,
spl53_57,
inference(avatar_split_clause,[],[f3975,f6451]) ).
fof(f6451,plain,
( spl53_57
<=> class_Int_Oring__char__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_57])]) ).
fof(f3975,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1210]) ).
fof(f1210,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(f6449,plain,
spl53_56,
inference(avatar_split_clause,[],[f3974,f6446]) ).
fof(f6446,plain,
( spl53_56
<=> class_Rings_Olinordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_56])]) ).
fof(f3974,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1079]) ).
fof(f1079,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
fof(f6444,plain,
spl53_55,
inference(avatar_split_clause,[],[f3973,f6441]) ).
fof(f6441,plain,
( spl53_55
<=> class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_55])]) ).
fof(f3973,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f1018]) ).
fof(f1018,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
fof(f6439,plain,
spl53_54,
inference(avatar_split_clause,[],[f3972,f6436]) ).
fof(f6436,plain,
( spl53_54
<=> class_Rings_Olinordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_54])]) ).
fof(f3972,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1026]) ).
fof(f1026,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
fof(f6434,plain,
spl53_53,
inference(avatar_split_clause,[],[f3971,f6431]) ).
fof(f6431,plain,
( spl53_53
<=> class_Rings_Oring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_53])]) ).
fof(f3971,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f1059]) ).
fof(f1059,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
fof(f6429,plain,
spl53_52,
inference(avatar_split_clause,[],[f3970,f6426]) ).
fof(f6426,plain,
( spl53_52
<=> class_Rings_Oring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_52])]) ).
fof(f3970,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1171]) ).
fof(f1171,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).
fof(f6424,plain,
spl53_51,
inference(avatar_split_clause,[],[f3969,f6421]) ).
fof(f6421,plain,
( spl53_51
<=> class_Rings_Olinordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_51])]) ).
fof(f3969,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1137]) ).
fof(f1137,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).
fof(f6419,plain,
spl53_50,
inference(avatar_split_clause,[],[f3968,f6416]) ).
fof(f6416,plain,
( spl53_50
<=> class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_50])]) ).
fof(f3968,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1128]) ).
fof(f1128,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).
fof(f6414,plain,
spl53_49,
inference(avatar_split_clause,[],[f3967,f6411]) ).
fof(f3967,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1187]) ).
fof(f1187,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).
fof(f6409,plain,
spl53_48,
inference(avatar_split_clause,[],[f3966,f6406]) ).
fof(f6406,plain,
( spl53_48
<=> class_Rings_Oring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_48])]) ).
fof(f3966,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1214]) ).
fof(f1214,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).
fof(f6404,plain,
spl53_47,
inference(avatar_split_clause,[],[f3965,f6401]) ).
fof(f6401,plain,
( spl53_47
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_47])]) ).
fof(f3965,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f1071]) ).
fof(f1071,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
fof(f6399,plain,
spl53_46,
inference(avatar_split_clause,[],[f3964,f6396]) ).
fof(f6396,plain,
( spl53_46
<=> class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_46])]) ).
fof(f3964,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1077]) ).
fof(f1077,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
fof(f6394,plain,
spl53_45,
inference(avatar_split_clause,[],[f3963,f6391]) ).
fof(f6391,plain,
( spl53_45
<=> class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_45])]) ).
fof(f3963,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f1021]) ).
fof(f1021,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
fof(f6389,plain,
spl53_44,
inference(avatar_split_clause,[],[f3962,f6386]) ).
fof(f6386,plain,
( spl53_44
<=> class_Rings_Oordered__comm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_44])]) ).
fof(f3962,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1022]) ).
fof(f1022,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
fof(f6384,plain,
spl53_43,
inference(avatar_split_clause,[],[f3961,f6381]) ).
fof(f6381,plain,
( spl53_43
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_43])]) ).
fof(f3961,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f1011]) ).
fof(f1011,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
fof(f6379,plain,
spl53_42,
inference(avatar_split_clause,[],[f3960,f6376]) ).
fof(f6376,plain,
( spl53_42
<=> class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_42])]) ).
fof(f3960,plain,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1133]) ).
fof(f1133,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).
fof(f6374,plain,
spl53_41,
inference(avatar_split_clause,[],[f3959,f6371]) ).
fof(f6371,plain,
( spl53_41
<=> class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_41])]) ).
fof(f3959,plain,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1132]) ).
fof(f1132,axiom,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).
fof(f6369,plain,
spl53_40,
inference(avatar_split_clause,[],[f3958,f6366]) ).
fof(f6366,plain,
( spl53_40
<=> class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_40])]) ).
fof(f3958,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1116]) ).
fof(f1116,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).
fof(f6364,plain,
spl53_39,
inference(avatar_split_clause,[],[f3957,f6361]) ).
fof(f6361,plain,
( spl53_39
<=> class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_39])]) ).
fof(f3957,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1189]) ).
fof(f1189,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).
fof(f6359,plain,
spl53_38,
inference(avatar_split_clause,[],[f3956,f6356]) ).
fof(f6356,plain,
( spl53_38
<=> class_Rings_Olinordered__idom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_38])]) ).
fof(f3956,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',arity_Int__Oint__Rings_Olinordered__idom) ).
fof(f6354,plain,
spl53_37,
inference(avatar_split_clause,[],[f3955,f6351]) ).
fof(f6351,plain,
( spl53_37
<=> class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_37])]) ).
fof(f3955,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1148]) ).
fof(f1148,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(f6349,plain,
spl53_36,
inference(avatar_split_clause,[],[f3954,f6346]) ).
fof(f6346,plain,
( spl53_36
<=> class_Divides_Osemiring__div(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_36])]) ).
fof(f3954,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(cnf_transformation,[],[f1089]) ).
fof(f1089,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).
fof(f6344,plain,
spl53_35,
inference(avatar_split_clause,[],[f3953,f6341]) ).
fof(f3953,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',arity_Int__Oint__Divides_Osemiring__div) ).
fof(f6339,plain,
spl53_34,
inference(avatar_split_clause,[],[f3952,f6336]) ).
fof(f6336,plain,
( spl53_34
<=> class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_34])]) ).
fof(f3952,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1024]) ).
fof(f1024,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
fof(f6334,plain,
spl53_33,
inference(avatar_split_clause,[],[f3951,f6331]) ).
fof(f6331,plain,
( spl53_33
<=> class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_33])]) ).
fof(f3951,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1135]) ).
fof(f1135,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).
fof(f6329,plain,
spl53_32,
inference(avatar_split_clause,[],[f3950,f6326]) ).
fof(f6326,plain,
( spl53_32
<=> class_Rings_Olinordered__ring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_32])]) ).
fof(f3950,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f1020]) ).
fof(f1020,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
fof(f6324,plain,
spl53_31,
inference(avatar_split_clause,[],[f3949,f6321]) ).
fof(f6321,plain,
( spl53_31
<=> class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_31])]) ).
fof(f3949,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1131]) ).
fof(f1131,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).
fof(f6319,plain,
spl53_30,
inference(avatar_split_clause,[],[f3948,f6316]) ).
fof(f6316,plain,
( spl53_30
<=> class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_30])]) ).
fof(f3948,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1016]) ).
fof(f1016,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
fof(f6314,plain,
spl53_29,
inference(avatar_split_clause,[],[f3947,f6311]) ).
fof(f6311,plain,
( spl53_29
<=> class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_29])]) ).
fof(f3947,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1126]) ).
fof(f1126,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
fof(f6309,plain,
spl53_28,
inference(avatar_split_clause,[],[f3946,f6306]) ).
fof(f6306,plain,
( spl53_28
<=> class_Rings_Oordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_28])]) ).
fof(f3946,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',arity_Int__Oint__Rings_Oordered__ring) ).
fof(f6304,plain,
spl53_27,
inference(avatar_split_clause,[],[f3945,f6301]) ).
fof(f6301,plain,
( spl53_27
<=> class_Rings_Oordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_27])]) ).
fof(f3945,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1155]) ).
fof(f1155,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).
fof(f6299,plain,
spl53_26,
inference(avatar_split_clause,[],[f3944,f6296]) ).
fof(f6296,plain,
( spl53_26
<=> class_Rings_Olinordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_26])]) ).
fof(f3944,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',arity_Int__Oint__Rings_Olinordered__ring) ).
fof(f6294,plain,
spl53_25,
inference(avatar_split_clause,[],[f3943,f6291]) ).
fof(f6291,plain,
( spl53_25
<=> class_Rings_Olinordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_25])]) ).
fof(f3943,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1147]) ).
fof(f1147,axiom,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).
fof(f6289,plain,
spl53_24,
inference(avatar_split_clause,[],[f3942,f6286]) ).
fof(f6286,plain,
( spl53_24
<=> class_Rings_Olinordered__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_24])]) ).
fof(f3942,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f1023]) ).
fof(f1023,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
fof(f6284,plain,
spl53_23,
inference(avatar_split_clause,[],[f3941,f6281]) ).
fof(f6281,plain,
( spl53_23
<=> class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_23])]) ).
fof(f3941,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f1012]) ).
fof(f1012,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
fof(f6279,plain,
spl53_22,
inference(avatar_split_clause,[],[f3940,f6276]) ).
fof(f6276,plain,
( spl53_22
<=> class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_22])]) ).
fof(f3940,plain,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1118]) ).
fof(f1118,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).
fof(f6274,plain,
spl53_21,
inference(avatar_split_clause,[],[f3939,f6271]) ).
fof(f6271,plain,
( spl53_21
<=> class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_21])]) ).
fof(f3939,plain,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1134]) ).
fof(f1134,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).
fof(f6269,plain,
spl53_20,
inference(avatar_split_clause,[],[f3938,f6266]) ).
fof(f6266,plain,
( spl53_20
<=> class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_20])]) ).
fof(f3938,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1124]) ).
fof(f1124,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(f6264,plain,
spl53_19,
inference(avatar_split_clause,[],[f3937,f6261]) ).
fof(f3937,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1185]) ).
fof(f1185,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(f6259,plain,
spl53_18,
inference(avatar_split_clause,[],[f3936,f6256]) ).
fof(f3936,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1130]) ).
fof(f1130,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(f6254,plain,
spl53_17,
inference(avatar_split_clause,[],[f3935,f6251]) ).
fof(f3935,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1188]) ).
fof(f1188,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f6249,plain,
spl53_16,
inference(avatar_split_clause,[],[f3934,f6246]) ).
fof(f3934,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1151]) ).
fof(f1151,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).
fof(f6244,plain,
spl53_15,
inference(avatar_split_clause,[],[f3933,f6241]) ).
fof(f3933,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1199]) ).
fof(f1199,axiom,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).
fof(f6239,plain,
spl53_14,
inference(avatar_split_clause,[],[f3932,f6236]) ).
fof(f6236,plain,
( spl53_14
<=> class_Fields_Ofield(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_14])]) ).
fof(f3932,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1173]) ).
fof(f1173,axiom,
class_Fields_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield) ).
fof(f6234,plain,
spl53_13,
inference(avatar_split_clause,[],[f3931,f6231]) ).
fof(f6231,plain,
( spl53_13
<=> class_Fields_Ofield(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_13])]) ).
fof(f3931,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1216]) ).
fof(f1216,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
fof(f6229,plain,
spl53_12,
inference(avatar_split_clause,[],[f3930,f6226]) ).
fof(f3930,plain,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1121]) ).
fof(f1121,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) ).
fof(f6224,plain,
spl53_11,
inference(avatar_split_clause,[],[f3929,f6221]) ).
fof(f3929,plain,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1183]) ).
fof(f1183,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).
fof(f6219,plain,
spl53_10,
inference(avatar_split_clause,[],[f3928,f6216]) ).
fof(f6216,plain,
( spl53_10
<=> class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_10])]) ).
fof(f3928,plain,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1119]) ).
fof(f1119,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
fof(f6214,plain,
spl53_9,
inference(avatar_split_clause,[],[f3927,f6211]) ).
fof(f6211,plain,
( spl53_9
<=> class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_9])]) ).
fof(f3927,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1182]) ).
fof(f1182,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
fof(f6209,plain,
spl53_8,
inference(avatar_split_clause,[],[f3926,f6206]) ).
fof(f3926,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(cnf_transformation,[],[f1107]) ).
fof(f1107,axiom,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).
fof(f6204,plain,
spl53_7,
inference(avatar_split_clause,[],[f3925,f6201]) ).
fof(f6201,plain,
( spl53_7
<=> class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_7])]) ).
fof(f3925,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1138]) ).
fof(f1138,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).
fof(f6199,plain,
spl53_6,
inference(avatar_split_clause,[],[f3924,f6196]) ).
fof(f3924,plain,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1191]) ).
fof(f1191,axiom,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).
fof(f6194,plain,
spl53_5,
inference(avatar_split_clause,[],[f3923,f6191]) ).
fof(f6191,plain,
( spl53_5
<=> class_Divides_Oring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_5])]) ).
fof(f3923,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',arity_Int__Oint__Divides_Oring__div) ).
fof(f6189,plain,
spl53_4,
inference(avatar_split_clause,[],[f3922,f6186]) ).
fof(f3922,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1122]) ).
fof(f1122,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
fof(f6184,plain,
spl53_3,
inference(avatar_split_clause,[],[f3921,f6181]) ).
fof(f3921,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1184]) ).
fof(f1184,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(f6179,plain,
spl53_2,
inference(avatar_split_clause,[],[f3920,f6176]) ).
fof(f6176,plain,
( spl53_2
<=> class_Fields_Olinordered__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_2])]) ).
fof(f3920,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1143]) ).
fof(f1143,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).
fof(f6174,plain,
spl53_1,
inference(avatar_split_clause,[],[f3919,f6171]) ).
fof(f6171,plain,
( spl53_1
<=> class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_1])]) ).
fof(f3919,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1117]) ).
fof(f1117,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11 % Problem : SWW256+1 : TPTP v8.1.2. Released v5.2.0.
% 0.08/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Apr 30 03:35:25 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % (22327)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.43 % (22330)WARNING: value z3 for option sas not known
% 0.17/0.43 % (22329)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.17/0.43 % (22332)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.17/0.43 % (22333)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.17/0.43 % (22334)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.17/0.43 % (22331)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.17/0.43 % (22328)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.17/0.43 % (22330)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 2.61/0.77 TRYING [1]
% 2.61/0.82 TRYING [2]
% 2.61/0.84 % (22332)First to succeed.
% 3.53/0.91 % (22332)Refutation found. Thanks to Tanya!
% 3.53/0.91 % SZS status Theorem for theBenchmark
% 3.53/0.91 % SZS output start Proof for theBenchmark
% See solution above
% 3.68/0.97 % (22332)------------------------------
% 3.68/0.97 % (22332)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 3.68/0.97 % (22332)Termination reason: Refutation
% 3.68/0.97
% 3.68/0.97 % (22332)Memory used [KB]: 8632
% 3.68/0.97 % (22332)Time elapsed: 0.481 s
% 3.68/0.97 % (22332)Instructions burned: 885 (million)
% 3.68/0.97 % (22332)------------------------------
% 3.68/0.97 % (22332)------------------------------
% 3.68/0.97 % (22327)Success in time 0.596 s
%------------------------------------------------------------------------------